These manuals are transcribed in Grade II Braille and in the Computer Braille Code (CBC), as adopted May 1987 by BANA. As described in full on braille page p7 volume I, all Nemeth data entry is shown cell-for-cell within full cells.
Since CBC is still new, here's a quick overview: Dots 4-5-6 is CBC'S "special" character; it never appears alone. A complete paragraph transcribed in CBC is prec $$ and followed by one blank line. CBC embedded within a Grade II paragraph begins with dots 4-5-6, 3-4-6 and ends with dots 4-5-6, 1-5-6. Dots 4-5-6 precedes a single capital letter. Dots 4-5-6, 3-4-5 signals caps lock; caps release is shown either by a space or by dots 4-5-6, 1-2-6. Dots 4-5-6, 1-6 begins emphasis and dots 4-5-6, 3-4 ends emphasis. If embedded CBC starts in caps lock or emphasis, then the begin emphasis or caps lock indicator is substituted for the generic begin CBC indicator, dots 4-5-6, 3-4-6. CBC is used whenever print shows a dialogue between you and the computer; the computer's prompts are emphasized while your responses are plain CBC.
The continuation indicator, dots 4-5-6, 1-2-3-4-6, appears at the end of braille lines when one inkprint line requires more than one braille line. Dots 4-5-6 precedes any isolated lower-cell sign. A single inkprint underbar is shown with two dot 4-5-6's in a row. When five or more spaces are significant, CBC uses a countable space indicator, whose total length shows total spaces in inkprint. This countable spaces indicator begins with space, dots 4-5-6 and ends with one space; with full cells in between.
The BEX Thick Reference Card contains a chart showing
the correspondence between each printable ASCII character and its CBC
version. _ $$ represents five cells: dots 4-5-6, space, dots
1-2-4-6, dots 1-2-4-6, space. =]= represents three cells:
dots 4-5-6, dots 4-5-6, dots 1-2-4-5-6.
MathematiX software and documentation copyright 1989 by Raised Dot Computing, Inc. ALL RIGHTS RESERVED. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means--electronic, audio recording, thermoforming, or photocopying--without the prior written permission of the copyright holder.
BEX, MathematiX, and the MathematiX logo are trademarks of Raised Dot Computing, Inc. Apple Computer, Apple IIc, Apple IIcing, Apple IIe, Apple IIgs, Apple Super Serial Card, Apple Parallel Card are registered trademarks of Apple Computer, Inc. Braille 'n Speak is a trademark of Blazie Engineering. Echo, Cricket, and TEXTALKER are trademarks of Street Electronics, Corp. VersaBraille and VersaBraille II are trademarks of Telesensory Systems, Inc. This Manual mentions scores of trademarked names. We have made every effort to include the name of the trademark holder at the time we mention the product.
We wish to express our deep appreciation to the following individuals, who answered questions and tested the software:
with especial thanks to
and of course, Dr. Abraham Nemeth and his Code, who made it all possible.
While these folks kindly assisted us in developing MathematiX, they are in no way responsible for the accuracy of the software or its documentation.
Written and edited with RDC'S BEX on an Apple IIgs. Braille manual transcribed with RDC'S ClasX and TranscriBEX software. Inkprint manual, in Palatino, Bookman, and Courier, created with Microsoft Word 4.0. on an Apple Macintosh SE and Apple LaserWriter Plus. (Word files created from BEX chapters using Contextual Replace and Microsoft's RTF/Interchange Format. File transfer with BEX and Hayes's Smartcom II software.)
THREE Q# page
1THREE Q#
ChapterWRONG#$$
Commands$$ Commands$$ Commands$$ Commands That Don't Work in
MathematiXcontrol-B P
#$$ Commands
and Tix Vertical ToolsControl-DMathematiX adds a Math Menu to your existing BEX program. The Math Menu lets you get verbal and regular print mathematical output from BEX chapters containing Nemeth Code braille. With MathematiX you can now use BEX to prepare documents that include text and fractions, square roots, chemistry, or other technical material for distribution to your sighted students, instructors, and colleagues.
If any item is missing, please call our Business Office at 608-257-9595 immediately!
For clarity, we use these techniques:
yr brl 5try is %[n l ?. In the braille
edition, full cells bracket the exact cells and spaces you enter. Don't
type the full cells themselves. In the inkprint edition, the braces
enclose the "screen braille" characters and spaces in the Courier
typefont. Don't type the braces themselves. When you read _ @l
it means you type five characters: dots 4-5-6, space, dot 4, dots
1-2-3, space. The Section 2 Tutorial and BEX Appendix 1 provide more
information on screen braille.
The Computer Prompts: Your Response. The
braille edition uses the Computer Braille Code so you know the exact
characters. In inkprint, you see bold Palatino type in text, and Courier
type for extended computer dialogs.
<space> <control-S>:
Represent a single character each. You make a <CR> by pressing the
"Return" key. When it's crucial that you press the spacebar when dealing
with the computer, we show this with <space You can create the single
<control-S> character in BEX's Editor by pressing
control-C S.
Before you turn on the computer and start playing with MathematiX, we urge you to read all of Section 1. You'll find out what MathematiX can and can't do, what equipment you need, and how to set up BEX to work with MathematiX. Then you'll be ready for Section 2, which takes you on a guided tour of all MathematiX's functions. To understand why and how you separate literary and mathematical braille in your MathematiX chapters, read Section 3. Section 4 explains how you and MathematiX work together to format your inkprint. When you need to know which Nemeth symbols to use to express a particular inkprint sign, check Section 5, Appendix B (Supported Symbols in Transcriber Order), or Appendix C (Supported Symbols in Alphabetical Order).
Raised Dot Computing wants you to make best use of
MathematiX. When you run into problems, check Section 8 to see if the
answer's here in the MathematiX Manual, and the KNOWN MATHEMATIX
BUGS chapter on the MathematiX Sample Data disk. If you're still
boggled, please get in touch with us. To help us help you better, we ask
that you:
MathematiX adds a new Math Menu to your BEX program. The Math Menu lets you get verbal and regular print mathematical output from BEX chapters containing Nemeth Code braille. MathematiX does not translate inkprint into Nemeth Code. We urge you to read all of this Section before you turn on the Apple. As we explain in Part 1, to use MathematiX, you must already know something about the Nemeth Code system. Read Part 2 to see where MathematiX is different from Nemeth Code. MathematiX is not a separate program, it's an additional module for BEX. Parts 3 and 4 explain the BEX skills you need for MathematiX.
MathematiX's main purpose is to prepare inkprint documents with technical symbols like fractions, exponents, square roots, etc. as well as text. MathematiX can only create regular print output, through a limited group of dot-matrix printers and interface cards--the same restrictions that apply to BEX's large print. MathematiX lets you prepare documents for distribution to your sighted instructors, students, or colleagues.
MathematiX can also be used to proofread the accuracy of Nemeth Code, with either verbalization through a voice synthesizer or regular print characters on the Apple screen. The blind user can check to make sure that what's entered will be accurately interpreted by MathematiX when it comes time for print output. The sighted transcriber can use MathematiX's screen preview to check the accuracy of Nemeth Code data entry of informal material for classroom use.
When you use option B - Back translate from Grade 2, BEX expands the contractions of literary braille to their inkprint equivalents. When you use option P - Print chapters, BEX makes hard copy by breaking your text into lines and pages while obeying the format indicators and commands in your chapter. When you use option M - Math output on the Math Menu, MathematiX does both tasks: it expands mathematical symbols into inkprint signs; it expands literary braille into inkprint letters; and it organizes all this information onto output pages. Throughout this manual, we use the verb tix to describe this combination of back-translation and formatting. When you use MathematiX, you can tix a chapter to a dot-matrix printer for regular print, or to a voice synthesizer or the screen for proofreading.
This manual won't attempt to teach you Nemeth Code. We recommend you get a copy of the Nemeth Braille Code for Mathematics and Science Notation, which is available from: \\address
Print Catalog No.: 7-8743
Braille Catalog No.: 5-8743
American Printing House for the Blind
1829 Frankfort Avenue
Louisville KY 40206
Telephone: 502-895-2405 \\endaddress
In order to create a particular inkprint sign, you'll need to know the corresponding Nemeth Code symbol. This manual also makes no attempt to teach the subjects that are represented in Nemeth Code. In Appendix A, the Glossary provides brief definitions of the technical vocabulary we use to describe various inkprint signs. To really understand what those symbols mean and how to use them correctly, consult your math or science teacher.
The Nemeth Braille Code for Mathematics and
Science Notation defines how to represent a wide variety of
inkprint signs through the use of specific braille
symbols. Some braille symbols are just one cell long:
+ (dots 3-4-6) shows the inkprint plus sign. Other braille
symbols require several cells: $%33o (dots 1-2-4-6, 1-4-6,
2-5, 2-5, 1-3-5) represents a single down arrow sign in inkprint. But
technical materials aren't all arrows and operators: the Nemeth Code uses
literary (Grade 2) braille for the text. Nemeth Code was designed to be
read by humans, not by computers. Humans handle ambiguity better than
computers, since we can pick up clues from context. In particular,
MathematiX cannot "know" the difference between math and literary braille.
That's why MathematiX requires you to explicitly
distinguish between literary and math material
in your tix-ready chapters. The Nemeth braille reader depends on context
to decide when ,* (dot 6, dots 1-6) is representing the
literary word Child and when it's the Nemeth symbol for the
inkprint therefore sign. MathematiX, on the other hand,
always assumes that ,* is therefore unless you
tell it otherwise. Similarly, context lets the braille reader decide when
dot 2 is representing a digit and when it's showing the literary comma. In
addition to marking the boundaries between literary and math in your
chapters, you also have to tell MathematiX the difference between
punctuation and digits--details appear in Section 3.
A Nemeth Code transcription is based on the appearance of the inkprint, not its mathematical meaning. Since Nemeth Code includes symbols and indicators describing the spatial relationship of inkprint signs, MathematiX can use Nemeth to create inkprint output. However, Nemeth was not designed as a means of writing inkprint mathematics, and MathematiX needs some additional inkprint-specific information to tix correctly. To obtain intelligible inkprint, you have to write braille that does not conform to standard Nemeth Code. Section 4 discusses the issues of spacing, superimposing, and enlarging characters. MathematiX supports many but not all Nemeth symbols: Section 5 provides step-by-step guidance for how to enter the supported symbols, as well as a list of the unsupported ones.
We've attempted to make MathematiX's regular print output as clear as possible. Dr. Caryn Navy used MathematiX to produce hundreds of math handouts for her university courses. Not only did the sighted students find them easy to read, her sighted colleagues were jealous of her ability to make printed, as opposed to hand-written, materials. While MathematiX output is suitable for homework, papers, and rough drafts of theses for the technical typist, it's definitely not publication quality.
MathematiX requires an Apple II with at least 128K memory. An Apple IIgs or an Apple IIc always have at least 128K memory; you must install an extended 80-column card in an Apple IIe to get the memory up to 128K. (Details in BEX Interface Guide 1:2). An Apple II Plus can only have 64K memory, so you can't run MathematiX on an Apple II Plus. If you're not sure how much memory your Apple has, use option W on BEX's Starting Menu to find out.
You need at least two disk drives to run MathematiX; one of these drives must be a 5.25-inch floppy disk drive. At the Master Level, you can establish "extended disk systems" that include 3.5-inch disk drives, RAM drives, and/or the Sider hard disk system. As long as your configuration has more than one disk drive (5.25 inch, 3.5 inch, RAM memory, or Sider hard disk) you can use MathematiX. Using RAM drives and 3.5-inch disk drives requires BEX 3.0; you can load the MathematiX software on RAM drive.
BEX uses a particular set of programming techniques to make large print output. When MathematiX tixes to a printer, it uses those same programming techniques to make regular print that includes math. Although MathematiX output is not large print, MathematiX requires that your dot-matrix printer and interface be compatible with BEX large print. This means you need:
connected to your Apple through:
See the BEX Interface Guide Section 4 on Printers for details.
MathematiX is an add-on to BEX. Before you can use MathematiX, you have to know how to use the base program. This manual assumes that you've read through at least the BEX User Level: you know what BEX chapters are, and how to select, edit, and print them. We won't explain how to do all these things here--the MathematiX Manual is long enough. Instead, we just point your way to relevant sections of the BEX Dox for crucial facts.
Your BEX version must be 2.2 or later to work with MathematiX--use option U - Update date on the Starting Menu to check your BEX version. If you own BEX 2.1, contact us for update or upgrade information. Beginning with BEX 3.0, BEX works well on the Apple IIgs (taking advantage of expansion memory and doing large print through a built-in port.) Throughout this manual, we show samples of MathematiX and BEX screen output. The BEX samples are based on BEX version 3.0; if you're using an earlier version, the wording of the prompts will vary slightly.
While you can enter braille in BEX's Editor, a stand-alone braille computer is the best environment for writing braille materials. When you write your material on an external device like the VersaBraille or Braille 'n Speak, you must know how to transfer the data into BEX chapters. The BEX Interface Guide gives the nitty gritty details of cabling and switch settings, and the BEX User Level has procedural instructions. User Level Section 11 describes BEX and the VersaBrailles; User Level Section 12 describes Input through Slot, which lets you create a BEX chapter by sending characters in to the Apple through a serial port. The RDC Newsletter April/May 1988 issue has Robert Carter's article detailing the Braille 'n Speak interface.
As always, your BEX configuration describes your equipment preferences. At a minimum, your MathematiX configuration must:
MathematiX won't run at the Learner Level of BEX. While MathematiX output is regular print, it uses the same programming techniques as BEX large print. When you ask MathematiX to tix in inkprint, MathematiX must find a large print printer in your configuration in order to access your printer's graphics capabilities. If you can make large print, you can make MathematiX output. If you're having trouble making large print, check Section 4 of the Interface Guide. If you're still boggled, please call Raised Dot Computing's technical helpline at 608-257-8833 so we can get you in business.
Once you include a large print printer in your configuration, MathematiX can make math output. All MathematiX cares about is that you've configured one large print printer; when it's tixing inkprint MathematiX completely ignores the font size, line spacing, carriage width, and form length values you supply. However, you can also get large print output from this device by using option P - Print on the Math or Main Menus. When you're printing, your configuration values do affect output. When you're tixing, they don't--more on this topic in Section 4.
Here are two possible configurations that work with MathematiX, as they'd appear when you use option V - View a configuration on the Starting Menu.
This ADA user has a switch box attached to slot 2, so
she can connect both her VersaBraille and her VersaPoint to a single Super
Serial Card. She prepares tix-ready chapters on her VersaBraille, and
transfers them to the Apple through slot 2; when she wants hardcopy
braille, she prints it to the VersaPoint in that slot. Her ImageWriter in
slot 1 plays three roles. When she prints, she can specify it as printer 1
for large print or printer 2 for regular print output. (The printer 2
set-up sequence starts with a software reset command
<Esc>c that clears out lingering graphics spacing,
followed by an eight-character left margin.) When she uses option M - Math
output on the Math Menu, MathematiX tixes to the same ImageWriter in
regular print.
The ImageWriter is interfaced through the Apple IIgs's built-in serial port, and is referenced twice in the configuration: printer 1 is a regular print specific printer, while printer 2 is BEX large print. MathematiX can tix inkprint thanks to the printer 2 definition. Master JOHN has a Braille 'n Speak to prepare his tix-ready chapters. He installed a Super Serial Card in the IIgs's slot 2 (and set the Control Panel to "your card") so he can transfer files between the Braille 'n Speak and BEX. He uses Input through slot to get material from the Braille 'n Speak to the Apple, and prints to the "Paperless brailler" (printer 3) to send Apple text to the Braille 'n Speak. The Apple IIgs has one 5.25-inch disk drive (virtual drive 2), one 3.5-inch disk drive (virtual drives 3 and 4), and 512K memory. John loads both the Main side of BEX and the MathematiX software on RAM drive--more details on why he numbered the RAM drives this way in Section 10.
With MathematiX, you can prepare inkprint materials that include text and math, chemistry, and scientific notation. The starting point for MathematiX is BEX chapters containing a modified form of Nemeth Code braille. You can create these chapters with BEX's Editor. Writing and editing braille is even easier on a braille-oriented device like the VersaBraille; you can prepare the data on another device and then bring it in to BEX with From VersaBraille or Input through Slot. If you're in doubt about how you transfer information from another device into BEX chapters, please see BEX User Level 11 for how to proceed.
Once you have BEX chapters, there are two steps to the MathematiX process. You proofread the chapters to check for structural errors, with feedback in spoken words or as screen graphics. You can fix any errors you find in the BEX Editor. When you know the chapters are correct, you output this data to a dot-matrix printer. This tutorial Section demonstrates exactly how you use MathematiX to accomplish these tasks.
The best way to learn about MathematiX is to actually follow along with every step in this Section. Before you begin, you need to establish a BEX configuration that's compatible with MathematiX. As detailed in Section 1, Part 4 this means you configure at the User or Master Level, and you define at least one large print printer. When you ask MathematiX to produce regular-print inkprint, MathematiX must find a large print printer in your configuration in order to access your printer's graphics capabilities. Two sample configurations that work with MathematiX are shown in Section 1, Part 4. We suggest you interface and test the large print output first, so you can focus on learning about MathematiX in this tutorial.
Once you have established and tested this configuration, here's what you need for the tour:
Boot BEX, specify your MathematiX-compatible configuration by name, and get to the Starting Menu. To ensure that you always have access to MathematiX, we urge you to make a working copy of the two disks in the MathematiX package: the MathematiX Menu Disk and the MathematiX Sample Data disk. Floppy disks can be easily destroyed. Once you make working copies, store the original disks in a different location. If you didn't make working copies and misfortune rendered your original disks useless, RDC would charge you $25 to replace them.
The MathematiX disks are not copy-protected, but they are copyrighted by Raised Dot Computing, Inc. RDC's copyright for MathematiX is identical to the BEX copyright. You may use MathematiX with BEX on any one computer at one time. You may not make multiple copies of BEX or MathematiX to use on more than one computer at a time. When you want to use MathematiX on more than one computer simultaneously, contact RDC for special "pack" discounts.
Employing option C - Copy disks on BEX's Starting
Menu, make working copies of both MathematiX disks on to the two
high-quality blank disks. (Don't copy the two master disks on to both
sides of one flippy disk--you'll see why this wouldn't work in Part 3.)
Insert the MathematiX Menu Disk in drive 1, one high-quality blank disk in
drive 2, and press C at the Starting Menu. BEX describes the
copying process and prompts you to press Return--do so and then sit back
for around two minutes. Repeat this process with the MathematiX Sample
Data disk. Label your working copies, then remove your original MathematiX
disks to a safe place. That way, if a working copy is damaged in the
future, you can make a new one from the original.
Now that you have working copies of the MathematiX disks, you can explore MathematiX. The MathematiX Menu Disk is not a bootable program disk. Instead, it adds a new menu, the Math Menu, to your existing BEX program. You must be at BEX's Main Menu to move to the Math Menu. Insert your BEX Main Disk in drive 1 and press the spacebar to move from the Starting Menu to the Main Menu.
At the Main Menu, remove the Main Disk from drive 1
and replace it with the MathematiX Menu Disk. Press the spacebar to move
from the Main Menu to the Math Menu--there's a short pause while BEX reads
software from the disk and then you're presented with the Math
Menu: prompt. (When you've configured at the Master Level, the
prompt is shortened to simply Math:.)
If your configuration wouldn't work with MathematiX, then you get an error message describing what's lacking. Read BEX User Level Section 3 on how to establish a new configuration that includes a large print printer, and please do so before proceeding with the rest of the tutorial.
Like all BEX menus, you can list your choices by
pressing <CR> at the Math Menu prompt. Press <CR>
now and you'll see many familiar options. The heart of MathematiX is
option M - Math Output, which we demonstrate in detail real soon. The
other options work more or less identically to their cousins on the Main
and Second Menus--full details in Section 6.
The Second and Page Menus aren't directly accessible
from the Math Menu--you have to go to the Main Menu first. To move from
the Math Menu to the Main Menu, you insert the BEX Main Disk in drive 1
and press J. To go from the Math Menu to the Starting Menu,
you insert the BEX Boot Disk in drive 1 and press spacebar. To get from
the Starting Menu back to the Math Menu, you must first move to the Main
Menu.
Try it out! Place the BEX Main Disk in drive 1 and
press J. There's a brief disk access and BEX presents the
Main Menu prompt. Now put the MathematiX Menu Disk in drive 1 and press
spacebar, and you're back at the Math Menu. Press spacebar, and MathematiX
asks you to confirm that you want to move to the Starting Menu. Place the
BEX Boot Disk in drive 1 and press <CR Now put the MathematiX Menu Disk
back in drive 1 and press spacebar again--BEX reminds you that the Math
Menu is only accessible from the Main Menu. Swap disks to get to the Main
Menu, then swap again to get to the Math Menu. These disk swaps will
become second nature after a little experience--you can refer to the chart
on the MathematiX Reference Card for guidance.
You have learned the basics of navigating the MathematiX Menu Disk. Keep in mind:
You're ready to actually use the Math Menu.
Get back to the Math Menu, swapping disks as needed.
Insert the MathematiX Sample Data disk in drive 2. Like all BEX menus, the
Math Menu has option D - Disk catalog. Press D and then
<CR> to see the chapters on the disk. For your convenience, we
supply several chapters to use in the tutorial: Some were written on a
VersaBraille, and some were created in the BEX Editor.
When you use Math Output, MathematiX expands mathematical symbols into inkprint signs and literary braille into inkprint letters. Math Output also organizes all this information onto output pages. We use the verb tix to describe this combination of back-translation and formatting. The chapters that end in the number sign character are tix-ready chapters, containing the modified Nemeth Code that MathematiX requires for correct output. Math Output provides three tix destinations: hardcopy regular-size inkprint on your printer; screen preview for sighted users; and verbal preview of the content of the chapter.
Let's see what Verbalize does. You may wish to switch
to expanded speech at this point by issuing the command control-E
E. Now with your MathematiX Menu Disk in drive 1 and the MathematiX
Sample Data disk in drive 2, do this:
Entering question mark gives you an on-line reminder
of the three tix destinations. Once you answer V <CR>
for the Verbalize destination, MathematiX reads briefly from both disks,
and then starts the tix scratch to tell you it's working.
Whenever you use Math Output, MathematiX must read software from the
MathematiX Menu Disk. (This is why MathematiX requires two disk drives,
and why we advised you not to copy the MathematiX disks onto a flippy
disk.) When the tix scratch and disk access is finished, MathematiX starts
verbalizing.
For Verbalize, Math Output sends the
HELLO chapter to your voice synthesizer and the 40-column
screen. Literary material is spoken as words, while mathematical material
is spelled out sign for sign and letter by letter. BEX format commands are
also spelled out, not executed. Verbalize provides a way to proofread the
structure and content of a tix-ready chapter; it does not preview the
format.
When the screen is full, output pauses and you hear a
low boop. You can use screen review to examine what's been said. Press the
spacebar when you're ready for more output. You quickly get to the end of
the sample information in the HELLO chapter; press the
spacebar once more to return to the Math Menu prompt.
If you can see the 40-column screen, you can check
both the content and the format of the HELLO chapter. Follow
this sample:
The word tixing ... on the screen
accompanies the tix scratch. The format commands in the HELLO
chapter are executed. Because the chapter begins with $$np,
you see Page 1 at the bottom of the first screen. When the
screen is full, you hear a boop; press spacebar for the next screen.
This quick sample has shown you the basic pattern when using Math Output:
It's time to find out what makes a chapter "tix-ready."
The THREE Q chapter on the MathematiX
Sample Data disk contains three review questions and solutions for the
dreaded Imaginary MathematiX Aptitude Test. The Math Menu duplicates the
Editor option from your Main Menu. You can use all and any of the Editor
commands explained in BEX User Section 5. Edit the THREE Q
chapter, and then issue the command control-S L to lock out
changes. Now any Editor command that would add or delete text just beeps,
so you can review the contents of the chapter without changing anything.
When you read a braille chapter in the Editor, the
screen and your voice synthesizer show the information in the screen
braille system. As detailed in BEX Appendix 1, each braille cell
has a unique ASCII inkprint equivalent. For example, the @
at-sign is the same as dot 4. Many important cells are shown with
punctuation, so be sure to request "most" punctuation from your voice
device. The MathematiX Reference Card includes a chart of the screen
braille characters. To make it easier to examine this chapter, we provide
a hard-copy version below. Sighted users can request braille dot patterns
on the screen by entering the command control-S S B.
THREE Q page 1The next paragraph shows all the characters in the
first BEX page of the THREE Q chapter, exactly as they appear
in the Editor (or on a VersaBraille display).
@l $$np $$h ,ma? ,review = ,,imat $p ,sample #a3
,a4+ ,rates $$i0$$ml0 $p ,frank takes @m ?2/3# @l h\rs 6pa9t a po/1 :ile
,nancy c pa9t ! po/ 9 @m ?3/4# @l h\rs4 ,if !y "w tgr 6pa9t "o po/1 h[ _m
m9utes w x take !m 6f9i% ! job8 $$ml6 $p ,,solu;n3 ,! orig9al data is giv5
9 @m ?hours/post#_1 @l b x is easi] 6"w ) po/s p] h\r4 ,frank c pa9t @m
?3/2# @l po/s p] h\r1 & ,nancy c pa9t @m ?4/3# @l po/s p] h\r4 ,if !y
"w tgr = an h\r1 !y c pa9t @m ?3/2#+?4/3# .k ?9/6#+?8/6# .k ?9+8/6# .k
?17/6# @l po/s p] h\r4 ,? -b9$ rate ( @m ?17/6# @l po/s p] h\r c al 2
express$ z @m ?6/17# @l h\rs p] po/1 or @m #0.353 @l ( an h\r4 ,ea* m9ute
is @m 1_/60 @l ( an h\r4 ,use @m #60 @* 0.353 @l 6f9d ! total m9utes =!
job--approximately #ba4 $$ml0 $f @l ,sample #b3 ,"r ,triangles $p ,a
triangle ) "o @m #90^.* @l angle is call$ a ."r triangle4 ,! side t is
opposite ! "r angle is call$ ! hypot5use4 ,! ,py?agor1n !orem tells u t !
squ>e (! l5g? (! hypot5use is ! sum (! squ>es (! o!r two sides4 ,if
y h a "r triangle ) "o side ( @m #6''_1 @l & ano!r side ( @m #8''_1 @l
:at is ! l5g? (! hypot5use8 $$ml6 $p ,,solu;n3 ,9 ma!matical not,n1 !
,py?agor1n !orem is /at$ z3 @m x^2"+y^2 .k z^2_4 @l ,s9ce y "k ! l5g? (
two sides1 & nei is /at$ 6be ! hypot5use1 all y d is solve = ;z3 @m
z^2 .k #6^2"+8^2 .k 36+64 .k 100_4 ,since #10^2 .k #100_1 @l ! hypot5use
is @m #10''_4 @l ,alt]natively1 y c "w ! pro#m ? way3 @m $p z .k
>x^2"+y^2"] .k >6^2"+8^2"] .k >36+64] .k >100] .k #10
$$ml0
Unlike standard Nemeth Code, MathematiX requires you
to explicitly distinguish between literary and
math material in your tix-ready chapters. The human reader
uses context to decide when ,* (dot 6, dots 1-6) means
Child and when it's the Nemeth symbol for the inkprint
therefore sign. But unless you tell it otherwise, MathematiX
assumes that ,* is always therefore. In other
words, MathematiX always begins in math mode.
Press control-G to go ahead one word: the
first four characters in THREE Q are space, at-sign,
lowercase l, space. This is the tix translation tool that
turns on MathematiX's literary mode. Let's jump ahead to some math
material, by locating for other tix translation tools.
Press control-L to begin the locate
command, then type <space> @, then press
control-A to advance the cursor. You land at character
92--you can hear the math mode tix translation tool by pressing
control-G. You must alert MathematiX to math material with
the four characters space, dot 4, lowercase m, space. Press
control-G to hear the math material: it's the simple fraction
two-thirds, spoken as question mark, two, slash, three, number sign. The
next "word" is the literary mode tool, followed by the grade 2 words
hours to paint a post. When you use option M - Math output,
the four-character tix translation tools become one space. In Section 3,
Part 2 we explain two other tix translation tools, which don't create a
space when output.
You've seen that a tix-ready chapter contains literary
and math braille, with tix translation tools marking their boundaries. In
addition, you can use familiar BEX format tools to control the inkprint
output. Just like BEX, you show a new paragraph with space, dollar sign,
lowercase p, space. Prove it to yourself: Issue the command
control-A control-P to advance to the next paragraph
indicator. Now press control-R to hear the previous word.
It's the BEX format command $$ml6 which establishes a left
margin of six characters. The problem statements use the full width of the
page, while the solutions have a six-character left indent. Two
control-G commands move over the paragraph indicator, and
another control-G gets you the grade 2 word
SOLUTION followed by a colon. You can use many, but not all,
of the BEX format commands to control inkprint output with
MathematiX--details in Section 4.
Punctuation symbols are another area where MathematiX
requires more information than standard Nemeth. MathematiX can't use
context to know when dot 2 is representing the digit 1 and when it's
showing the literary comma. Repeat the control-L control-A
command to place your cursor at character 278, another math mode tix
translation tool. Use control-G to read the next two "words."
After the space, at-sign, m, space, there's a simple fraction followed by
a comma. This is spoken as question mark, hours, slash, post, number sign,
underline, 1. The underline is the Nemeth Code Punctuation Indicator, dots
4-5-6. As detailed in Section 3, Part 2, MathematiX requires you to use
the punctuation indicator in math mode with eleven symbols.
There's one more interesting thing about this fraction: its numerator and denominator are words, not digits. Because this fraction is in math mode, no contractions are taken in the numerator hours and the denominator post. You can't write any literary contractions in MathematiX's math mode. Although you can tell by context when dots 3-4 means "st" and when it means "fraction line," MathematiX is not that clever.
To see what else a tix-ready chapter can contain,
let's check out the second problem. We begin each problem with
$f to force a page break. Locate for these four characters to
advance to character 736, where Sample 2 begins. The format command
$$ml0 appears right before the new-page indicator, cancelling
the six-character left margin used for the solution to Sample 1. Advance
to the next paragraph with control-A control-P, and move
through the first sentence with control-G. The first four
words are in literary braille. The math mode tix translation tool comes
next, followed by the Nemeth for ninety degrees. Then there's
the literary mode tool, followed by four more words. Now you find the BEX
underline begin command , the literary word right, and the
underline finish command . The underlined word is italicized in
braille--it begins with dots 4-6, the period in screen braille. MathematiX
ignores the presence of italics signs--when you want your literary
material underlined, use the BEX format commands. MathematiX won't
underline any material in math mode.
Now you have a general idea of what's in the
THREE Q chapter. Issue the Editor command control-S
L to toggle off the lock out changes mode, and then enter
control-Q to Quit the chapter.
The important things to remember about tix-ready chapters are:
Let's see how Verbalize handles the material you've just reviewed.
THREE Q
ChapterWith your MathematiX Menu Disk in drive 1 and the MathematiX Sample Data disk in drive 2, proceed like this:
MathematiX always begins in math mode. The first
characters in the chapter are @l, which turn on literary mode
and create one space when tixed. Therefore, the first thing you hear is
space. Since the first three paragraphs are in literary mode,
MathematiX verbalizes the material in words. The first math mode tix
translation tool appears after the second "dollar sign, p" and the words
"Frank takes." Because you're still in literary mode, you don't hear the
output "space" that results when this @m is tixed. The
problem statement switches between literary and math modes several times.
When MathematiX verbalizes the solution paragraph for
sample 1, you hear more of the "picky" style used for math mode. The
fraction that's composed of words is spelled out letter for letter: you
hear start fraction h o u r s fraction line p o s t end fraction
comma. When the screen is full and the synthesizer's finished
talking, you hear a low boop. Press the spacebar for more data.
Sample 2 begins most of the way down the second screen of data. After you press spacebar a second time and move to the third screen, you hear one of the many instances where MathematiX can't express the exact mathematical meaning of the inkprint signs. Instead, MathematiX uses the most general term, leaving the interpretation up to you.
Where the THREE Q chapter has @m
#6''_1 @l, the verbalized version is 6 double prime comma
space. The inkprint "double prime" sign is used in several
contexts. In this case, double prime means "inches." When you're writing
about degrees, minutes, and seconds, you use the same "double prime"
symbol for the seconds. And when you're writing about variations on a
variable name, you use the same symbol to literally convey the concept
"double prime." Once you start using MathematiX, you will be verbalizing
material that you have written. This will make it easier to interpret the
meaning when MathematiX offers generic terms like "double prime."
There's another example of generic vocabulary on this
third screen. You can find it with Screen Review. After the low boop that
means the screen is full, press control-L to begin Screen
Review, then press the letter K to read the 11th screen line.
You hear: stated as: x squared plus y squared. Press the down
arrow to hear the next line, which is equals z superscript 2
baseline period space. In the THREE Q chapter, this
material appears as /at$ z3@mx^2"+y^2 .k z^2_4@l. MathematiX
attempts to say "squared" when it sees the digit 2 as an exponent.
However, MathematiX can't always meet this goal, so the right-hand side of
this equation is verbalized in more generic terms as "z followed by an
exponent of 2."
Verbalize allows you to check the contents and meaning
of your tix-ready chapters, but it doesn't provide a preview of the
format. You can use BEX $$ commands and format indicators to control final
inkprint format. When you Verbalize, the commands themselves are parrotted
back to you. For easier listening, MathematiX uses a special vocabulary
for the basic format indicators in math mode: "new paragraph" means
$p, "new line" means $l or a hard <CR>,
and "new page" means $f. Check out lines V and W on the
current screen to see an example. The source material is way3@m$l z
.k, and it's verbalized as way: new line z equals.
When you're in literary mode, MathematiX doesn't use this special
vocabulary.
That's enough close work for now. If you're still using Screen Review, press the <Esc> key to exit. You can continue to Verbalize the rest of the chapter on your own, or you can stop verbalizing early. All you do to cancel Verbalize is press the <Esc> key. If Verbalize has paused for a full screen, you may hear the next word before you return to the Math Menu prompt.
Verbalizing a chapter lets you know how MathematiX interprets your braille material:
You're ready to make an inkprint version of the
THREE Q chapter.
Tixing inkprint is very similar to verbalizing: you
use option M - Math Output for both. The only difference is you specify
the I destination instead of the V destination.
Before you begin, load the paper into your dot-matrix printer and set the
top of form. Make sure that the printer is "on-line," ready to receive
data from the Apple. With the MathematiX Menu Disk in drive 1 and the
MathematiX Sample Data disk in drive 2, follow these prompts:
If your BEX configuration doesn't include a large print printer definition, MathematiX will complain with an error message at this point. Please read Section 1, Part 4 to find out how to make a MathematiX-compatible configuration.
The printer won't start immediately--MathematiX has to
go through the same tixing process as when you verbalize. MathematiX reads
software from disk, makes the tix scratch, reads more software from disk,
and then starts sending graphics to your printer. Once MathematiX has
tixed all the data in BEX page 1, it goes through the same process for BEX
page 2. The final result is three inkprint pages long, because we began
samples 2 and 3 with the $f form-feed indicator.
You have just seen how the MathematiX process goes when everything's perfect. One of the big advantages of using a computer is that you don't have to be perfect the first time: you can find and correct your errors. A tix-ready chapter must have a particular structure or MathematiX won't create the results you want.
The WRONG chapter on the MathematiX
Sample Data disk is an incorrect version of Sample 1 from the THREE
Q chapter. We've introduced six small errors that result in some
interesting mayhem. See what happens when you do this:
Some of the errors we introduced in WRONG
are so blatant that MathematiX can't create legible inkprint. That's why
you hear the Please use Verbalize error message after the tix
scratch. Verbalize provides greater detail about the structure
errors that triggered this error message. Verbalize also helps you
confirm that MathematiX can correctly interpret what you have written.
WRONGAs we analyze what verbalize says, you will learn how to recognize the most common kinds of errors. Then we will step you through finding and fixing them. Put on your thinking cap, and follow along:
The first few format commands sound reasonable enough,
but things quickly degenerate. Instead of hearing Math Review for
IMAT as words, the information is spelled out letter for letter and
space for space. That's a sure sign that you are in math mode. As we have
stressed, MathematiX can't cope with literary material when it's in math
mode. The first error in this WRONG chapter is that we
deleted the initial @l that turns on literary mode.
Very quickly, you hear ERROR: fraction not
finished in chapter WRONG# page 1 paragraph 0, all spoken in an
emphatic high pitch. This is one of MathematiX's structure
error messages. MathematiX knows that fractions follow a pattern:
they start with ?, have a fraction line / in the
middle, and end with . Because MathematiX is in math mode, it reads the
literary "th" contraction from the word Math as "start
fraction." When MathematiX reaches the end of the paragraph, it checks to
see if the fraction has been completed. Since the heading doesn't happen
to use the "st" or "ble" contractions, MathematiX can't find all the
elements in a well-structured fraction, and emits the error description
Fraction not finished.
Verbalize provides location information to help you
track down errors. MathematiX uses paragraph $p indicators to
check for structural problems in chunks and it reports errors with
paragraph numbers. This problem showed up before the first paragraph
indicator in the BEX page, so it's located as Chapter WRONG# page 1
paragraph 0.
After the first paragraph indicator, that missing
literary translation tool continues to influence Verbalize's vocabulary.
The sample number followed by a literary colon gets mangled to a
subscript 3 baseline space. When MathematiX finally encounters
another literary translation tool (it's after the two-thirds fraction
halfway down this screen) then literary material is pronounced
appropriately.
The next problem pops up right at the end of the first
screen. You hear the same error description, "fraction not finished," but
this one refers to paragraph 2. MathematiX complains because we removed
one of the end fraction indicators in the problem statement paragraph.
MathematiX uses natural divisions to break your material into "chunks,"
and checks for structural integrity at the end of the chunk.
In addition to paragraph $p indicators, MathematiX recognizes
hard <CR>s, new-line $l indicators, new-page
$f indicators, and the end of each BEX page as "chunk"
boundaries. The upshot is that some structure errors are only reported
after the next "chunk."
The next problem shows up on the second screen. You
hear that fraction composed of words as start fraction h o u r s
fraction line p o s t end fraction 1 space. What's that digit 1? It
should be a comma. This is the third error in WRONG: we
deleted the dots 4-5-6 punctuation indicator that MathematiX requires to
recognize dot 2 as a comma. As you verbalize material, keep your ears
peeled for digits that pop up where punctuation should be. Section 3, Part
2 and the MathematiX Reference Card list the eleven cases where you must
use the punctuation indicator.
The bottom half of the second screen is devoted to a
reduction of four fractions with equals signs between them. Lines P and Q
show the result of ?9/6#+?8/6#.k. You get the Greek letter
kappa instead of equals. This is the fourth
error we introduced in this chapter: omitting the space on both sides of
this .k equals sign. Without the initial and final space
MathematiX sees dot 4-6, dots 1-3 as lowercase Greek kappa. MathematiX
also requires spaces before and after the greater-than and less-than
signs.
On to the third and final screen of the
WRONG chapter! The first few lines are fine, but then you get
a "new fraction finished, but ..." error. When MathematiX sees the start
of a fraction, it immediately checks to make sure that you have finished
the previous one. This error popped up because we omitted an end fraction
indicator in the middle of this paragraph.
Finally, things get strange again after the words
cross space 0 point 3 5 3 space. When you verbalized the
correct version in Part 5, there sure weren't any subscripts or integrals
in Sample 1. 6 f subscript 9 base line d space integral is
MathematiX trying to interpret the cells 6f9d! as math
braille. Thanks to your human intelligence, it's obvious that those cells
are representing the literary braille words to find the.
Remember, MathematiX is only a software program. As you've probably
guessed by now, the sixth error is a missing literary translation tool
after the #60 @* 0.353.
You've seen how Verbalize gives you a MathematiX perspective on exactly what's in a tix-ready chapter.
Let's clean up the problems in this chapter.
In this Part, we demonstrate using BEX's Editor to correct the six errors we found in Part 7:
WRONG chapter,
there's a literary translation tool missing.
Use option C - Copy chapters on the Math Menu to
copy the WRONG chapter to the name RIGHT on the
MathematiX Sample Data disk. (This preserves the errors in
WRONG in case you or someone else wants to repeat this
tutorial.) Edit the RIGHT chapter. If you're comfortable with
screen braille, you can make your changes by typing on the full Apple
keyboard.
When you're still learning the screen braille
equivalents, you may find it easier to use BEX's braille keyboard mode.
(If you have an Apple IIgs with a detached keyboard, then you can't use
braille keyboard mode.) You turn on braille keyboard by clicking down the
Caps Lock, then issuing the command control-S K B. Now use
the S-D-F and J-K-L keys as a standard six-key braille entry system. In
addition to the Control key method, you can chord your Editor
commands by depressing the space bar at the same time as the command
letters. For example, to go ahead one word, press space and dots 1-2-4-5
simultaneously.
To fix the first problem, you need to insert the
literary mode translation tool right at the start. Begin the insert with
control-I, type space, dot 4, dots 1-2-3, space, then finish
the insert with control-N.
In the second paragraph, you need to find a fraction
that's missing its final . Enter the command control-A 2
control-P to advance the cursor to the second paragraph indicator.
With braille keyboard, you enter this as dot 1-space, dots 2-3, dots
1-2-3-4-space. Unfortunately, you can't ask BEX to locate for something
that's not there, but you know that this faulty fraction
does have the ? at the start. In other words,
you can find the start of a fraction by locating for space, dots 1-4-5-6.
Begin the search by entering control-L
<space> ? control-A. The braille version is dots
1-2-3-space space dots 1-4-5-6 dot 1-space. You land at character
94: read the fraction with control-G. The result is
question mark, two, slash, three, number sign. All signs
accounted for here! Enter control-L control-A to repeat the
locate: you arrive at character 151. When you read this word,
you only hear question mark, three, slash, four and you have
found the problem. Press control-I to insert, then type one
number sign (dots 3-4-5-6), and finish the correction with
control-N.
The remainder of the errors showed up in the third
paragraph. Enter control-A control-P to get to its start. The
missing punctuation indicator showed up after the fraction with the word
hours in the numerator. Move to this spot by entering
control-L ?hou control-A. You braille the locate command with
dots 1-2-3-space, 1-4-5-6, h, o, u, dot 1-space. Now press
control-G to hear the word: it's ?hours/post#1.
The digit 1 needs dots 4-5-6 before it: press left arrow (or
control-H) until you hear one. Type
control-I _ control-N to insert the punctuation indicator.
On to the questionable equals sign. Use the
control-L .k control-A command to locate for the meat of the
symbol. You land at position 460. Press control-R to go back
and hear the entire word: you'll hear point k. Since a BEX
"word" by definition has a space on both sides, you know that this equal
sign is correct. Type control-L control-A to repeat the
locate, then control-R again: this time, you hear
question mark 9 slash 6 number sign plus and so forth
finishing up with point k. Since the initial space is
missing, you hear the entire fraction plus the vagrant kappa. Use right
arrow (or control-U) to place your cursor on the period, type
control-I <space> control-N to insert the space.
You can use the technique described above to find the
missing end fraction indicator in this paragraph: combine locating for
<space> ? with control-G to check the
fraction's completeness. You will find the problem fraction begins at
character 529--insert dots 3-4-5-6 after the digit 6.
The last error is a missing literary translation tool,
which revealed itself in Verbalize as 6 f subscript 9 base line
d. Locate for dots 2-3-5, 1-2-4, 3-5, 1-4-5 and you land at
position 679. Press left arrow to move to the space before, then insert
the @l literary mode tool. You're done. Before you quit the
Editor, it's a good habit to restore the keyboard mode to normal. Enter
control-S control-K control-N then unclick the Caps Lock key.
Now you can press control-Q to save your changes.
Congratulations!
In addition to verbalizing every symbol in your
tix-ready chapter, you can also ask MathematiX to verbalize selected
portions of the data. The HUSH chapter on the MathematiX Menu
Disk contains one of the tix verbalization tools that control
what's spoken. With the MathematiX Menu Disk in drive 1 and the MathematiX
Sample Data disk in drive 2, try this out:
When you faithfully followed along and made all the
corrections, you'll hear the tix scratch and disk access and then return
back to the Math Menu prompt. The HUSH chapter contains the
eight characters @notalk, which tell MathematiX to suppress
speech output during Verbalize unless it encounters a structure error.
Find out more about the other verbalization tools and structure error
messages in Section 7.
As you're developing your MathematiX skills, it's a
good idea to verbalize a corrected chapter again to make sure you have
caught your errors. As you've seen, MathematiX does not understand the
material in your chapter. While some problems result in explicit structure
errors, other defects are verbalized without incident. When you tix to
inkprint, any data that would cause a Verbalize structure error halts
output entirely. But there are many problems that MathematiX won't
recognize as such. For example, when you've omitted a punctuation
indicator, MathematiX blithely tixes the digit instead of the punctuation.
When your data contains ?hours/post#1 then the inkprint shows
the digit 1 instead of a comma.
Good work! You have reached the end of the MathematiX Guided Tour. With this basic understanding of MathematiX, you're ready to use the program for your own materials. Sections 3 through 8 in the MathematiX Manual provide in-depth reference material on the topics we have briefly explored here. Once you have used MathematiX for a short time, you'll want to browse through Section 9, where we have collected many hints and tips for making the most of MathematiX. Here's an overview of where to look for more details:
We hope that you find MathematiX a useful and enjoyable tool.
In order for MathematiX to create the math output you
desire, your chapters must be tix-ready. This Section
provides an overview of what a tix-ready chapter contains. Section 5
details how to enter specific math symbols for predictable inkprint
output. As MathematiX tixes, it creates the spatial math format based on
time-honored rules. You can also use $$ commands and tix
format tools to control the output format--more information on this
appears in Section 4.
There are several ways you can write your Nemeth chapters. The easiest tool for braille readers is a device with both braille input and braille display--like the tape-based or disk-based VersaBraille. The next best thing is a device that at least allows braille input, such as the Braille 'n Speak, Eureka, or the braille keyboard mode of BEX's Editor. The drawback to BEX's Editor is that the voice feedback uses screen braille characters: the Nemeth Code for the square root of x over y sounds like "question mark, greater-than, x, ready, slash, y, number sign." As detailed in Section 7, you can Verbalize your tix-ready chapter to proofread the content as words, not graphics. If you have a braille embosser, you can make paper braille copies periodically to help you proofread your input in a natural way.
Because MathematiX expands your data
significantly while it's tixing, you must limit each BEX
page to no more than 2500 characters. (When you're doing very
graphic-intensive material--more than three levels of hypercomplex
fractions or calculus--keep each BEX page to 2000 characters or less.) In
the Editor, use control-W C to check the character count of
the current page. You can use option F - File list on the Page Menu to
check the size of every BEX page in a chapter, and option A - Adjust Pages
on the Second Menu to make a copy of one or more BEX chapters with
different page boundaries (Learner Level Section 11). If you didn't obey
these character limits, you would get a spirited audio reminder. When
MathematiX doesn't have enough room to tix a BEX page, it emits the
overflow shriek. Press <Esc> to cancel Math output, and then use
Adjust Pages or control-C control-P in the Editor to ensure
each BEX page has 2500 or less characters.
When you prepare your tix-ready chapters on an external device, you must get the data into BEX chapters before you can tix it. When you're working with a tape-based VersaBraille, you use option F - From VB to bring your data into BEX chapters. For all other devices, you use option I - Input through Slot. For your convenience, both of these options are available on the Math Menu. The Math Menu versions are slightly different than the Main and Second Menu counterparts. One important change in the Math Menu options is From VB and Input through Slot create smaller BEX pages to help you avoid overflow problems. Other minor changes are described in Section 6.
MathematiX allows you to specify any chapter name when
you choose the Math Output option. Just as BEX allows you to
back-translate an inkprint chapter, resulting in incomprehensible data,
you could specify an inkprint or literary braille chapter to tix,
resulting in "garbage." As introduced in Section 2, we suggest that you
name tix-ready chapters with the number sign character at the end. This
lets you immediately identify the chapters as tix-ready. You can enter
/# <CR> at the chapter prompt to selectively scan a
disk, and BEX presents a numbered list restricted to the chapters that end
with the number sign character. See BEX User Level Section 4 for a full
explanation of selective scanning with the slash.
In standard Nemeth Code, you can (within limits)
intermix mathematical expressions and literary contractions. For example,
the four cells f>m] (dots 1-2-4, 3-4-5, 1-3-4, 1-2-4-5-6)
can mean either the literary word farmer or the mathematical
expression "f times the square root of m." However, MathematiX can't
discriminate between literary and mathematical Nemeth on its own.
MathematiX always starts out in math mode, where
f>m] gets tixed as "f times the square root of m."
MathematiX assumes all material is math unless you inform it otherwise.
Your tix-ready chapters must contain explicit information for MathematiX
to understand the data it's processing.
The tix translation tools are plain text characters that tell MathematiX how it should interpret the braille characters in your chapters:
@l -- (space, dot 4, l, space) turns on
literary mode; becomes one space in your final output
_@l -- (dots 4-5-6, space, dot 4, l, space)
turns on literary mode without creating space in final output
@m -- (space, dot 4, m, space) turns on math
mode; becomes one space in your final output
_@m -- (dots 4-5-6, space, dot 4, m, space)
turns on math mode without creating space in final output
These tix translation tools are slightly different from the Translator Controls explained in BEX User Level Section 9. With BEX's Grade 2 translation and Back from Grade 2, the dot 4 (at-sign) TCs are residual: they remain in the translated chapter. With Math Output, the four-character tix translation tools become one space in the final output while the five-character tools disappear entirely.
It's your responsibility to keep the modes "pure":
after you turn on literary mode, MathematiX won't interpret any characters
as math until you turn math mode on again by entering @m or
_@m. Each time you choose Math Output, it's as if your
chapter starts with _@m. Be sure you have a space on both
sides: only then will MathematiX switch translation. In math mode,
@l or @l gets tixed as "pounds sterling;" in
literary mode, it's tixed as simply "at-sign, l." For both math and
literary modes, @m or @m get tixed as "at-sign,
m."
The tix translation tools are extensively demonstrated
in Sections 5 and 9; here's a quick sample. To tix the inkprint for
"three-eighths is smaller than three-fourths," you can enter either:
#4 3_/8@lis small] ?an@m#4 3_/4 or #4 3_/8 is smaller
than #4 3_/4. To tix a fraction with a numerator of 5 and a
denominator of the word "hours," you can enter either: ?5/_
@lh\rs_@m or ?5/hours.
These tools function completely differently than their Grade 2 and Back from Grade 2 counterparts. For the literary braille translator, space, dot 4, dots 3-6 space turns off translation entirely. You cannot turn off translation when tixing. You must use either the literary or math braille codes to write all your material.
To facilitate creating tix-ready chapters with the Grade 2 translator, MathematiX provides an alternative way to signal math translation:
@- -- (space, dot 4, dots 3-6, space)
turns on math mode; becomes one space in your final output
_@- -- (dots 4-5-6, space, dot 4, dots 3-6,
space) turns on math mode without creating space in final output
Section 9 discusses preparing tix-ready chapters with the assistance of the Grade 2 translator.
Because standard Nemeth Code allows mixing of mathematical and literary material, three braille indicators help the reader when context alone doesn't make things clear. In addition to requiring you to explicitly distinguish math and literary material, the use of the English Letter, Numeric, and Punctuation indicators in MathematiX is not standard Nemeth.
The English letter sign plays a similar role in grade 2 and Nemeth: it identifies isolated letters that are not contractions. In MathematiX's math mode, contractions are never allowed: dots 1-3-4-5-6 is always the letter y, never the word you. Generally, the letter sign is optional for math mode; your output will be fine whether it's there or not. (See Section 5, Part 10 for the single exception, forming boldface characters.)
However, in literary mode, MathematiX
requires the use of the English letter sign in some contexts where good
grade 2 does not. (This limitation is shared with BEX's option B - Back
from grade 2.) Whenever you want an isolated letter in your
inkprint, precede it with the dots 5-6 letter sign--it won't ever cause an
"extra" letter sign to be tixed. When you want to abbreviate the compass
direction in the short sentence, Go west, young man! you must
write @l ,g ;,w41 "y man6. If you used @l ,g ,w41 "y
man6, the result would be Go Will., young man!.
In standard Nemeth Code, all numbers are shown with lowered letters, except the page numbers on the title page and on each braille page. Rule 2 in the Nemeth Braille Code for Mathematics and Science Notation details the requirements for the Numeric Indicator, dots 3-4-5-6.
In math mode, always use Nemeth digits (dropped
letters). MathematiX lets you be sloppy when it comes to the Numeric
Indicator: you can follow the code book to the dot or you can leave it out
almost entirely. (See Section 5, Part 10 for the exception, boldface
digits.) Don't use Nemeth digits in literary mode. Instead, follow
standard grade 2 practice: use the Numeric Indicator and the letters
a through j. The three phrases: #4 tigers
4 tigers @l#d tig]s@m are tixed as 4 tigers 4 tigers 4
tigers.
In standard Nemeth Code, the same braille cells are used for common punctuation or digits. As detailed in Rule 6, sometimes context is enough to determine which is which; the Punctuation Indicator, dots 4-5-6, resolves ambiguity. You never use the Punctuation Indicator in literary mode for MathematiX. You must always use it for math material. Eleven symbols require use of the Punctuation Indicator:
_'
_0'
_0
_3
_6
_1
_,8
_8
_4
_8
_2
Yes, you do enter the same two cells for question
mark and closing outer quotation: MathematiX is smart enough to use
context to tell the difference and tix the appropriate sign. As detailed
in Section 5, Part 13, MathematiX doesn't recognize the standard
_0 Nemeth Code empty set symbol. You use @_0
instead to distinguish empty set from closing outer quotation.
Math Output is a unique hybrid of translation and
format. MathematiX is largely in control of how many characters appear on
each output page--details in Part 1. As stressed in Part 2, where you put
spaces in your tix-ready chapter dramatically influences whether
MathematiX can tix at all. Like BEX, you can control tix format through
$$ commands and four-character format indicators like
$p--see Part 3.
In many situations, the inkprint format is controlled
through your choice of standard Nemeth symbols. When you enter
#100_/900 Math Output creates a linear fraction, while
?100/900 results in a spatial fraction, with an appropriate
length fraction bar centered vertically between the numerator and
denominator. For samples of how you enter particular symbols in your
tix-ready chapter, consult Section 5 or the alphabetical list of symbols
in Appendix C. In this Section, Part 4 discusses the few special cases
where you create correct inkprint format with non-standard Nemeth. Part 5
explains the tix vertical tools that let you determine
inkprint vertical spacing, if you really want to. With those exceptions,
MathematiX makes most format decisions unilaterally: you can't change the
size and relative spacing of the characters MathematiX creates.
Regular inkprint output is a cooperative process between BEX and your printer. It's an entirely different story when MathematiX tixes inkprint. A little background on just what happens will help you understand how many characters can fit on one output page.
For regular inkprint, you define the basic page size
with carriage width and form length--in your configuration, or with
$$w and $$f commands in your chapters. Within
this framework, BEX's formatter breaks your text into lines and pages,
sending the printer a stream of characters plus spaces, <CR>s, and
form feeds. What happens then depends largely on the printer. Important
details like the depth of a single "line," the size of the characters, and
the spacing between them are the printer's department. You can generally
control these features through "escape sequences"--control characters,
letters and numbers that instruct the printer to do something special,
like double-wide characters.
On the other hand, the Math Output option controls
just about everything. Instead of sending your printer the letter
a, for example, MathematiX tells the printer to make 13 dots
that together draw an a. Based on the graphic capabilities of
your printer, MathematiX itself determines the maximum number of
characters that fit on one line horizontally: 76 for the ImageWriter and
58 for the Epson. You can narrow the text and increase the white space on
the left and right with the BEX margin commands $$ml and
$$mr, but you can't change the carriage width.
MathematiX overrides any value you supply in your large print printer
definition, and ignores any $$w command in your tix-ready
chapters.
MathematiX is also completely in control of form
length. Like regular print, the default vertical spacing is one <CR>
for hard and soft <CR>s and two <CR>s for paragraphs. However,
the height of the material on each line determines the exact vertical
distance between one line and the next. An output line that only contains
text and linear math requires much less vertical space than an output line
containing a hypercomplex fraction. MathematiX makes sure that your
output's readable by adding a little extra to the tallest sign on each
line. MathematiX ignores the form length value in your configuration and
any $$f commands because MathematiX isn't counting
lines. The constant factor for tixed inkprint is that around
700 dots fit on each page vertically. The default single line spacing is
deeper than the six lines per inch common to most regular printers. A
hypothetical tix-ready chapter containing only literary material would
output with 43 lines per page on both ImageWriter and Epson.
In a regular print or literary braille chapter, the
space character plays several roles. It defines a "word" so readers can
understand what's meant: therapist and therapist
are two different concepts! BEX's translator creates correct grade 2 based
in part on where spaces appear. When it comes time to output the text,
BEX's formatter requires periodic spaces to divide the document into
output lines. Finally, you must space your format commands, format
indicators, and translator controls correctly so the translator and
formatter can recognize them.
Spaces similarly play several roles in your tix-ready chapters. For math mode, where spaces appear is crucial for meaning. Various tix spacing tools let you modify the space as a word boundary, provide good places to break the output into lines, and differentiate between characters-as-commands and characters-as-data. Except for the special cases covered in this Part, the spaces you enter in your tix-ready chapters result in spaces on the tixed page. MathematiX does not afford you total control over the spacing of each sign on the page; remember, the goal of MathematiX is readable, draft mathematics.
MathematiX is unforgiving of Nemeth shortcuts: for
predictable output, use spaces exactly as the Nemeth Code dictates. For
example, a space following a superscript or subscript means a return to
the baseline. x^2+y means "x squared plus y." When tixed in
inkprint, the "x," "plus," and "y" share a common baseline while the "2"
exponent floats higher. When you don't have a space on both sides of the
plus sign, x^2+y means "x raised to the 2 plus y power." The
inkprint floats an unspaced "2 plus y" above the "x" at the baseline. See
"Using the Sticky Space," below, for how to include an output space in a
super- or subscript.
MathematiX and Nemeth depend on spaces to
differentiate between several meanings of the same braille symbol. Here's
just one example: Space, dot 5, k, space represents the less-than sign:
-n "k n says "negative n is less than n." When you want the
less-than sign, you must put spaces on both sides. -n
"kn<:] means "negative n followed by n overbar." If MathematiX
encountered -n "kn, it returns a structure error, thinking
you'd started a modified expression with dot 5 and neglected to finish it.
(Section 7 lists all the structure errors and how to recover.)
These tools let you precisely control whether a space appears in your output.
_ dot 4-5-6, space is the
disappearing space: Treated as space for word-by-word
editing on VersaBraille or in BEX. Valid as "space" for any math sequence
or tix translation tool. No output space is produced when tixed; not a
legal place to break the line.
@ dot 4, space is the discretionary line
break: like a space, gives MathematiX permission to move to a new
output line at that spot if needed. No output space is produced when
tixed.
<control-S> sticky space:
Not seen as a space in a math sequence. Always produces output space when
tixed; not a legal place to break the line.
The _ dot 4-5-6, space facilitates
creating tix-ready chapters and better inkprint output. Editing very long
math expressions on the 20-cell VersaBraille display can be awkward: use
the disappearing space to break them up into more manageable "words." When
MathematiX encounters _ in your tix-ready chapter, it
recognizes that a space is present for the purpose of translating the
math. Yet when it tixes a disappearing space, no space appears in the
output.
The disappearing space allows you to suppress inkprint
spaces to better follow math conventions. Suppose you wish to show three
variables inside parentheses, separated with commas but no spaces. You
can't use (a,b,c), because the dot 6s are seen as
capitalization indicators: the tixed result would be (aBC).
Entering (a,_ b,_ c) does the trick. (As an alternative, you
could use literary commas:
(a_1b_1c) also results in (a,b,c)).
The dissappearing space is also useful when writing
signs of comparison in upper or lower limits. When you write
x.k1 then MathematiX tixes an output space on either side of
the equal sign. When you write x_.k_1 then the "x", equals
sign, and "1" are unspaced. More on this topic in Section 9, Part 5. The
dissappearing space lets you tix a Hebrew aleph or bet that's immediately
followed by an English letter. ,,ax would result in
"uppercase A, uppercase X," while ,,a_ x results in "aleph,
lowercase x."
The five-character tix translation tools
_@l and _@m are a special use of the
disappearing space: they signal the change between literary and math modes
while producing no spaces in the output.
As MathematiX tixes, it uses spaces to divide your
material into output lines. The program knows that some spaces are not
good places to break the line: it won't move to a new output line if a
space is inside a fraction, square root, or modified expression. If you
entered very long expressions without any spaces, then MathematiX wouldn't
know where to divide the output lines. In the grip of this dilemma,
MathematiX can respond in two ways. You may get overprinted and illegible
output, or the program may crash. In the latter case, you should press
control-Reset to get the BASIC prompt. Then type RUN START
<CR> (in all caps) and fix up the chapter.
To ensure pleasant sailing, you must provide
MathematiX with places to break the line. Either type a space every 50 or
so inkprint signs, or use the discretionary line break, @ dot
4, space. This gives MathematiX permission to break a line at that spot if
needed. When MathematiX doesn't need to break the line, then the dot 4
space is suppressed and no space appears in the output.
BEX supports a different discretionary line break
system: after you enter the format command $$sd to enable it,
BEX recognizes the <ASCII 30> control character as an acceptable
place to break a line. MathematiX does not recognize
<ASCII 30> as a discretionary line break.
As introduced in BEX, the sticky space is a "hard" or
non-breaking space. In terms of translation, MathematiX does
not consider <control-S> a "space." The
sticky space allows you to include output spaces in subscripts or
superscripts. While a real space means "return to baseline," the
<control-S> doesn't. When MathematiX encounters a
sticky space in your tix-ready chapter, it always creates an output space
but won't break the line at that spot.
These samples demonstrate the difference between a sticky space and a regular space:
x^2 + y -- x squared plus y
x^2+y -- x raised to the 2 plus y power, no
spaces in inkprint "2 plus y"
x^2<control-S>+<control-S>y -- x
raised to the 2 plus y power, inkprint appears as 2, space, plus, space,
y.
However, those are nonsensical samples. A more
realistic application of the sticky space is for function names in
subscripts or superscripts. The sticky space allows you to write "y to the
sin x power:" y^sin<control-s>x. (Since MathematiX
won't allow you to transfer control characters from a
tape-based VersaBraille, you can also repeat the superscript indicator,
entering y^sin ^x for the same result.)
There are four Nemeth symbols that could be confused
with format indicators or tix translation tools. When you want the
inkprint sign tixed with spaces on both sides, you must use the tix null
tool, "] dot 5, dots 1-2-4-5-6 to interrupt the command
sequence:
$l"] parallel to (instead of a new-line
indicator)
$p"] perpendicular to (instead of a paragraph
indicator)
@l"] pounds Sterling (instead of turn on
literary mode)
.k"] kappa with spaces on both sides (instead
of equals sign)
When you write the perpendicular to symbol without spaces on either side, then MathematiX knows you mean perpendicular to, and tixes the correct sign. But if you want spaces on both sides of the inkprint sign, you must use the tix null tool to tell MathematiX that you don't want a new paragraph. You can't put the null tool between the dots 1-2-4-5-6 and the p, because MathematiX wouldn't see the "perpendicular to" symbol at all.
When you tix to the screen or inkprint, option M -
Math Output can interpret some $$ format commands in your
chapters. Because of the complexity of inkprint mathematical output, it
was not possible to implement every one of the $$ commands
supported by option P - Print chapters on the Main or Math Menus. This
Part examines four groups of commands:
$$ commands that only
work for Math Output.
$$ commands that work a little
differently for Math Output than for Print.
$$ commands that function the
same with both Math Output and Print.
$$ commands that won't work with
Math Output at all.
$$ CommandsThese commands only work when you tix with Math Output. If you use option P - Print on the Math or Main Menus with a tix-ready chapter containing these commands, the command letters appear in your output.
$$o -- overprint # times for each line of
output. The more overprinting you specify, the darker your output--and the
more time required for final printing. The default is $$o1
(one printing pass). Beyond two or three passes, you begin to punch holes
in the paper.
$$kb and $$kf -- keep together,
begin and keep together, finish. These commands work as a pair to prevent
MathematiX from breaking a long math expression into two output lines.
When the material between the $$kb and $$kf
commands won't fit in the current output line, MathematiX moves to a new
line and tixes it there. If the material between the $$kb and
$$kf commands is too long to fit on any single
output line, then MathematiX crashes. Press control-Reset to get the BASIC
prompt. Then type RUN START <CR> (in all caps) and fix
up the chapter, inserting spaces or discretionary line breaks to enable
MathematiX to tix correctly.
$$ CommandsFor each command, we state how it works in MathematiX, and then the differences from Print.
$l, or $p to next soft <CR Default carriage
width is 76 for ImageWriter and 58 for Epson. For Print, you have
multi-line, "smart" centering: your text continues to center until the
next hard <CR>, $l, or $p.
$$h -- In literary mode, center and
underline one line of text from previous <CR>, $l, or
$p to next soft <CR In math mode, the line of text is not
underlined, only centered. For Print, you have multi-line headings that
are both centered and underlined.
-- begin underlining if you're in literary mode. When you're in math mode, this command is ignored for inkprint although it's verbalized. For Print, this always underlines.
-- finish underlining if you're in literary mode. When you're in math mode, this command is ignored for inkprint although it's verbalized. For Print, this always finishes underlining.
<CR>$$vh1 [running header text]$p
-- For each output page, repeat the "running header text" on line 1 and
skip line 2. Use other $$ commands to position the header
horizontally; the "running header text" can contain math
material. With Print, you skip line 2 with the $$vs2 command,
and it doesn't matter whether you end the header with <CR>,
$l, or $p.
<CR>$$vh1 [running header
text]<CR> -- For each output page, repeat the "running header
text" on line 1 but don't skip line 2.
<control-S> -- Sticky space token:
always make a space here in the output and never break the line at this
spot. With Print, you must also enter $$ss in your chapter to
enable the use of <control-S sticky spaces are
always enabled with MathematiX.
$$ CommandsConsult BEX User Level Section 7 for details on how these commands work.
$p -- begin new paragraph (space, dots
1-2-4-6, p, space). Number of spaces to indent set by combination of
$$i and $$ml; number of <CR>s set by
$$s; default is $$ml0 $$i5 $$s2.
$$s -- establish number of <CR>s for
paragraph $p indicators
$$i, $$i-, $$i+ --
establish or adjust indent for paragraph $p indicators,
relative to left margin.
$l or <CR> -- begin new output line
(space, dots 1-2-4-6, l, space) at current left margin. Default is single
spacing, $$l1
$$l -- establish line spacing for new-line
$l indicators and hard or soft <CR>s.
$$ml, $$ml+, $$ml-,
-- establish left margin numerically; default $$ml0
$$ml* -- establish left margin at current
position on the output line
$$mr, $$mr+, $$mr-,
-- establish or adjust right margin numerically; default
$$mr0
$f -- begin new output page (space, dots
1-2-4-6, f, space).
$$np -- number pages with word
Page centered at bottom
$$n - set the next output page number to #
<Del> -- (delete character); page number
token in running header
$$p -- place the following text at # position
horizontally on current output line
$$p+ or $$p- -- place subsequent
text # characters to left or right of current position on output line
$$tc -- clear all tabs
$$t -- establish tab position numerically
$$t*, $$t-, $$t+ --
establish tab based on current position on output line
$$d -- reset Math Output to default: no page
numbering, no header, $$ml0 $$mr0 $$l1 $$s2 $$i5
$$ Commands That
Don't Work in MathematiXIf you include these commands in your tix-ready chapter, they won't do a thing. They are verbalized as "not supported." When you tix to inkprint or the screen, these commands are completely suppressed.
$$f -- set form length to # lines per
page.
$$w -- set carriage width to # characters per
line.
$$mt -- set top margin to # lines.
$$vf [text]<CR> -- running footer of
"text" on bottom line of each output page.
$$vh2, $$vh3, etc. -- running
head on line 2, 3, etc. You can only have a running head on line 1 with
MathematiX.
$$vs -- skip line # on each output page.
$$vo -- restore line # to text, clearing a
header or skip command.
<control-T> -- "touching token" to
replace initial or final space in BEX $$ commands.
<ASCII 30> -- Discretionary line break:
if needed, place a soft <CR> here. Use @ dot 4, space
instead.
<ASCII 31> -- Discretionary hyphen: if
needed, print a hyphen and place a soft <CR> here.
$$sd - Enable use of <ASCII 30> and
<ASCII 31> as discretionary characters.
$$a - advance to line # on the output page.
$$vn - go to a new page unless that would make
a blank page.
$$vl - move to a new page when fewer than #
lines remain on current output page.
$$vi - finish current line, then move to a new
page when fewer than # lines remain on current output page.
$$r -- Flush right text from previous
$p, $l, or <CR> to next $p,
$l, or <CR
$$b or $$b -- stop and beep #
times
$$eX -- "escape code" commands for specific
printer features, like boldface, superscript, etc.
$$sp -- suppress underlining of trailing
punctuation.
$$su -- force uppercase only output.
$$vg -- switch to Roman numeral page
numbering.
$$vk -- cram a BEX word against the right
margin.
$$vrX -- fill the current output line by
repeating any character X.
$$z -- zap formatter; output all
$$ commands as they appear in the Editor.
In some situations, MathematiX requires non-standard Nemeth entry in order to create correct inkprint output.
While Nemeth provides various ways to show two
inkprint signs are on top of each other, MathematiX takes a different
approach. You use the general pattern of multipurpose indicator, first
symbol, termination indicator, second symbol. For example, to get a plus
sign superimposed on a circle, enter "$c]+. Once you
understand how MathematiX interprets this pattern, you can use it to
superimpose any symbols.
The multipurpose indicator " tells
MathematiX to save its current output location. The termination indicator
tells MathematiX to restore that location. When MathematiX tixes the
sequence "$c]+, it goes through this reasoning: "OK, I'll
save my position, print a circle, restore the remembered position, print a
plus, and then get ready to print the next sign." The result is a plus
printed on top of a circle.
MathematiX lets you specify "regular-sized" and "enlarged" symbols of enclosure, such as parentheses, brackets, braces, and vertical bars. When the expression you're enclosing includes a spatial fraction or other material with more than two vertical levels, your inkprint will be easier to read if you use the non-standard enlarged versions.
,,\,??24/8#+2,/?64/8#+2,#,,\ .k
,\?3+2/8+2#,\
,\,??24/8#+2,/?64/8#+2,#,\ .k ,\?3+2/8+2#,\
.,(?1/2#, ?1/3#, '''.,)
.(?1/2#, ?1/3#, '''.)
?1/3#,(?>x+y]/2#,)
?1/3#(?>x+y]/2#)
These enlarged symbols are twice as high as a standard MathematiX character; they straddle the reference baseline. Half of their "extra" height is placed below the baseline, and half goes higher than the top-of-caps line. More details in Section 9, Part 6.
While MathematiX does a good job of making draft
quality output, it ocassionally makes some poor choices. In Section 9,
Part 6, we detail exactly how MathematiX places characters on the page.
Here we just discuss a "cookbook" solution to the most common problem.
When tixing spatial fractions, MathematiX automatically "drops down" the
denominator to ensure legibility--when a denominator includes a radical,
for example, there's adequate space between the horizontal fraction bar
and the top of the radical sign. MathematiX doesn't handle the placement
of numerators as elegantly. For example, when ?x2/7 is tixed,
the bottom stroke of the subscript digit 2 is superimposed on the
horizontal fraction line.
The simple way to solve this problem is to make your
fraction more complex! When tixing inkprint, MathematiX puts more vertical
space in a complex fraction than a simple fraction. When you have
something tall in a numerator of a simple fraction, you'll get better
results if you write it as a complex fraction. The subscript in
,?x2,/7, is perfectly legible. When your numerator with a
subscript is already in a hypercomplex fraction, then you can control the
vertical spacing manually with a tix vertical tool--details below.
Larger inkprint versions of two Greek letters have
conventional meanings in higher math. While a regular-sized sigma is just
a sigma, the sigma that shows summation is twice as high. Similarly, a
larger pi represents a product. In order for MathematiX to make the
proper-size inkprint Greek letters, use .,,s for the
summation and .,,p for the product. If you neglect to request
these enlarged operators, the print reader won't recognize the sigma and
pi as operators.
While Nemeth Code simply says, "this stuff is above, this stuff is below," the traditional inkprint presentation centers the limits below and above the central operator--an enlarged sigma or pi, or a standard intersection or union. MathematiX can't center the limits automatically. If both your lower and upper limits are one or two characters (inkprint signs) long, then you can't control centering anyway. But when either limit is three signs or longer, you must add spaces inside the modified expression.
MathematiX outputs these spaces, centering the elements by brute force. Each space after the above symbol, dots 1-2-6, nudges the upper limit to the right, while each space after the below symbol, dots 1-4-6, nudges the lower limit to the right. Each space you put after the initial dot 5 nudges the central operator one character to the right. Several examples of these techniques appear in Section 9, Part 5.
The tix vertical tools let you tell
MathematiX exactly how to space your inkprint output vertically. Each
MathematiX inkprint "character" is built up from individual dots on the
screen or your printer. (These dots are called "pixels" when refering to
the screen--we'll use this term to avoid confusion with the dots in the
braille cell.) The basic size of a MathematiX character is 7 pixels wide
by 8 pixels high. You can't control horizontal spacing at the pixel level:
use BEX $$ commands to move horizontally in character-chunk
(7 pixel) increments. (As detailed in Section 9, Part 6, some "tall"
inkprint signs are composed of several "characters;" the enlarged sigma
.,,s for example, is two characters stacked vertically.)
Each tool is composed of three cells: Dots 2-4-6
[, followed by a direction shown with above >
or below %, followed by a lowercase letter code for distance
moved. (A list of the fourteen valid combinations appears on the
MathematiX Reference Card.) The code letters are:
q
h
o
x
d
t
f
For example, [%o means "move down
one character (eight pixels)" while [<q means "move up a
quarter of a character (two pixels)." You can get intermediate values by
entering several tools in a row: [<q[<h moves up
three-quarters of a character or six pixels.
Where you use the tix vertical tools determines the
duration of the change in vertical position. You can enter a tix vertical
tool immediately after one of the five Nemeth indicators that imply
vertical movement: opening simple fraction indicator ?,
opening complex fraction indicator ,?, opening hypercomplex
fraction indicator ,,?, directly-over indicator
<, or directly-under indicator %. At this
point, MathematiX is about to make its own vertical spacing decision; it
sees the tix vertical tool as modifying the vertical value. When
MathematiX encounters a tix vertical tool after one of these five
indicators, the change in vertical position only affects the following
element.
Alternatively, you can take complete responsibility
for the duration of the tix vertical tool's effects. Recalling the
discussion of superimposition in Part 4, MathematiX interprets a dot 5
" as a command to remember the current position on the page,
and ] dots 1-2-4-5-6 as a command to restore the current
position. (Although the same symbols are used for modified expressions,
MathematiX doesn't alter the spacing in that case.) Combining
the tix vertical tools with superimposition, you can save your current
position, move up or down a specified amount, print something, and then
get back to your starting location.
Before we get down to samples, there are several
important cautions. Remember that MathematiX is a tool for draft
mathematics and not a typesetting program. In all cases,
MathematiX attempts to space the inkprint appropriately. When you use the
tix vertical tools, you are in effect overriding MathematiX's automatic
spacing decisions, which requires you to a) know what inkprint math
should look like and b) think like a software program. As
with $$ commands, Verbalize doesn't provide feedback on the
format created by the tix vertical tools: a sharp-eyed sighted assistant
is a necessary peripheral. A brailler graphics program like RDC's pixCELLS
can produce tactile versions of MathematiX's screen display to help
interpret the tix vertical tool's effects--see Section 9, Part 4 for how
to do this.
As mentioned earlier, when a numerator in a spatial fraction drops below the normal baseline, the inkprint result can be illegible. Don't attempt to use tix vertical tools to adjust a denominator, because MathematiX will override your adjustments.
You can intervene with a tix vertical tool when the
numerator of a fraction goes further than a quarter of a character under
the baseline. A subscript moves down half a character. Moving the
numerator up by four pixels yields a more legible result: use
?[<hx2/7 instead of ?x2/7. If the numerator
of a fraction contains a summation sign with material above and below it,
you need to raise the numerator by one and a half characters:
?[<x".,,s%i_.k_1<,=] i^-5"/4.
The prohibition against denominator-fiddling doesn't
rule out numerators that are in the denominator of a complex fraction.
With ,?[<h?1/x2#,/?[<hy2/567#,, for example, the
subscript digit 2s are much more legible. Notice that the tix vertical
tools here are not "superimposed" within a dot 5, dots
1-2-4-5-6 pair. That's because the tool immediately follows the opening
fraction indicator. When MathematiX encounters the tool, it only changes
the vertical position of the numerator.
By superimposing shifted signs, you can generate an
almost unlimited number of shapes and scribbles. The superimposition
syntax is "save position, base symbol, restore position, overprinted
symbol." To shift and superimpose, this becomes: "save
position, tix vertical tool, base symbol, restore position, overprinted
symbol." In chess notation, for example, the bishop is represented with a
stylized mitre. A recognizable version of the bishop sign can be created
with "[<q$p]$c. MathematiX tixes this as: save position,
move up 2 pixels, draw a perpendicular to sign, restore position, draw a
circle shape. The dot 5 save and dots 1-2-4-5-6 restore bracketing the tix
vertical tool are crucial: if you omitted them, then you'd shift the
baseline of all subsequent text. Other examples of the tix vertical tools
appear in Section 9, Parts 6 and 7.
This reference Section gives general guidelines and samples for how you enter the math part of your document, beginning with symbols used in elementary school and working up to calculus, chemistry, and post-secondary topics. While we've tried to illustrate all the common symbols, these samples are not exhaustive. When you need to find a particular symbol, check the transcriber order list in Appendix B or the alphabetical order list in Appendix C.
We've tried to make MathematiX understand Nemeth Code,
but Nemeth wasn't designed as an inkprint typesetting system. Most
importantly, MathematiX requires you to use @l and
@m to explicitly show the boundaries between
literary and math braille. MathematiX
requirements for the Numeric, English Letter, and Punctuation Indicators
are neither exactly standard Nemeth nor standard grade 2. These deviations
from standard Nemeth are constant no matter what math symbols you're
entering in your tix-ready chapters--see Section 3, Part 2 for a complete
explanation of what's required.
In this Section, we draw your attention to the other instances where you must enter non-standard Nemeth to get correct inkprint. The exact placement of spaces in your tix-ready chapter is very important: so crucial, in fact, that we devote an entire Part to it--see Section 4, Part 2. In the many samples that follow, take careful note of where spaces do and don't appear.
With those exceptions, in general, the more perfect your Nemeth Code, the better the MathematiX result. Many Nemeth users develop their own shorthand for personal materials, but this will only create structure errors in MathematiX. As you're learning MathematiX, take frequent advantage of the Verbalize feature (Section 8) to discover where MathematiX would choke on shorthand.
#1 "1 #2 ;2 #3 "1 #6
(10+2)./3 .k #4
#7@0 of @s3.00 is #21@c
#3@*(3_/4) and #3*(3./4)@l>e two ways 6write !
same expres.n4
#5 - #2 "k #4_1 but #5 + #2 .1 #4_4
Since sample 3 is all in math mode, the
of contraction isn't used. Sample 4 doesn't use the
and contraction; literary text only appears after the
@l translation tool. This also shows uses of _/
to write the slash in an in-line fraction; Part 3 explains
writing spatial fractions. Notice the use of the _
Punctuation Indicator for the comma and period in sample 5; MathematiX
always requires its use before ten common punctuation characters in math
mode.
Nemeth and MathematiX both require spaces on either
side of the equals, greater than, and less than signs of comparison. In
some inkprint situations, you may wish these three signs to appear
unspaced: use the disappearing space _ to suppress the output
space--details in Section 4, Part 2. Unlike standard Nemeth Code,
MathematiX recognizes any other sign of comparison even if it's not
preceded and followed by a space.
@l,: is grt]3@m?3/4# or ?5/6#_8
@l,a c's spe$ is f.d )@m?miles/hours#_4
@l,a c's spe$ is f.d
)@m?miles/_@lh\rs_@m#_4
#4_?3/8_#@lis small] ?an@m#4_?3/4_
#4 3_/8 is smaller than #4 3_/4
You don't use the Numeric Indicator within a spatial fraction, since is the closing simple-fraction indicator. Notice the Punctuation Indicator before the final question mark in sample 1. Sample 2 shows the two ways MathematiX can cope with literary braille appearing within a math expression. 2.a keeps to "pure" math mode: the contraction is not taken in the denominator. 2.b encloses the contracted word hours within the five-character disappearing tix translation tools.
Sample 3 uses the standard Nemeth Code for an in-line mixed fraction but MathematiX tixes this spatially, with the three-eighths and three-fourths written vertically. To get in-line mixed fraction output, you must use the non-standard Nemeth shown in sample 4.
x^2 + y^2 .k z^2
x1+x2 .k y"1-y"2
e^x^^2 "k e^x^;2
q^e^^5+n^^;1
x;n-1, x;n[1
?x^2"/y^2"
?x^1_/2"/2
y^sin ^x
y^sin<control-s>x
As seen in sample 2, Nemeth and MathematiX
interpret a number immediately following a letter as a subscript. To write
a number that immediately follows a letter at the baseline, use the dot 5
multipurpose indicator, ", as shown. Nemeth Code and
MathematiX support 14 superscript and subscript levels. Sample 4
demonstrates that you can combine up to three superscript ^
and subscript ; symbols. Sample 5 shows the [
used for a comma within a subscript or superscript.
Samples 7 and 8 show the non-standard Nemeth that
MathematiX requires for some superscripts and subscripts. In a spatial
fraction, any fractional superscript or subscript must be linear (or
decimal). If you used ?x^?1/2#"/2 instead of sample 7,
MathematiX generates a structure error.
In standard Nemeth, the space following a function
name in a superscript or subscript doesn't return you to the baseline.
MathematiX always sees a space or dot 5 " as the
return to the baseline from a superscript or subscript. You have two ways
to correctly write "y to the sin x power." You can repeat the superscript
symbol after the space, as shown in sample 8.a. Alternatively, follow
sample 8.b and use the <control-S> sticky space between the "sin"
and the "x". <Control-S> always creates a space in the output, but
it's not interpreted as a space by MathematiX as it tixes--more on this
topic in Section 4, Part 2.
,??24/8#+2,/?64/8#+2,# .k ?3+2/8+2# .k ?5/10# .k
?1/2
,,?1,,/,?1,/?1/7#,#,,# .k ,?1,/?7/1#,# .k
?1/7
?x^3_/2"/7
A complex fraction contains a spatial fraction in its numerator or denominator. A hypercomplex fraction contains a complex fraction in its numerator or denominator. In-line fractions don't count when determining complexity or hypercomplexity. MathematiX doesn't permit spatial fractional exponents (Part 4). Since Sample 3 uses an in-line fractional exponent, it's "simple," not complex.
>2]
<3>8] .k #2
>20+.>25.]] .k >20+5] .k >25] .k
#5
>x^2"+y^2"]
>?x+y/2#]
?>x+y]/2
$t ,a,b,c has $[ ,a,c .k #90^.*
$r "1 $4 ;2 $e "1 $c
>area $4 ,x] .k #5
$a
- $'
$[3333
$<33o$l$%33o
$<33o $p"] $o
$[o$p$<[o
$*33o
$[33.*
#0$.*33*1
Nemeth Rule 16 describes a wide variety of
shapes: MathematiX only supports the shapes shown here. MathematiX can't
draw pentagons, rhombuses, trapezoids, specialized angles, specialized
triangles, or modified shapes. For example, in standard Nemeth code,
$q means quadrilateral and $t.i] means isosceles
triangle: MathematiX would output a plain q for the former
and a structure error for the latter. When you need to express these
concepts, use words instead of Nemeth symbols.
Sample 6 shows an unspaced parallel to
symbol, which MathematiX interprets correctly. If you used standard Nemeth
by writing spaces on both sides of this sign of comparison, you would need
to use the tix null tool to prevent MathematiX from seeing $l
as a new-line indicator. That's why the "] appears where it
does in Sample 7. BEX interprets the four characters space, dots 1-2-4-6,
lowercase p, space as a paragraph indicator. Only when you
interrupt the sequence with the null dot 5, dots 1-2-4-5-6 can MathematiX
"see" a perpendicular to symbol--this also applies to a spaced pounds
sterling symbol and a spaced Greek kappa.
The Nemeth Braille Code for Mathematics and Science Notation discusses arrows in Rules 14 and 21. MathematiX only supports the Rule 14 arrows, as illustrated in Samples 5 through 11. Here's the MathematiX perspective on the six steps in arrow construction outlined in Rule 21:
$.
[,
solid dot *, or hollow dot .*.
33 shaft indicators. Each 33 you add gives
another "character chunk" of shaft. For example,
$[33333333333333333333 yields an arrow as long as 11 letters.
o,
solid dot *, or hollow dot .*.
MathematiX recognizes the contracted as well as
the uncontracted arrow symbols. For vertical arrows, the inkprint result
is identical. For contracted right arrow, $o makes a shorter
inkprint arrow than $33o.
#3.54:
x:+y:
"x:+y:<:]
""x .k y%:]%:]
""x+y%:]<:]
MathematiX doesn't support modified expressions
of the second or higher order: "x+y<:<<a .k #3] just
gets you a structure error when tixed. As seen in Sample 5, repeating the
basic underbar or overbar structure yields multiple parallel lines. Sample
6 shows the non-standard MathematiX requirements for simultaneous overbar
and underbar: if you entered the correct "x+y%:<:] the
tixed result would only show an overbar.
.1: .1.k
:.1 .k.1
"k: "k.k
:"k .k"k
,a @:@: ,b_1 ,a .k@: ,b_1 ,a @:.k ,b
:@+.k .k_.1 .+:
"$[33*<$.*33o]
"$3333o<$[3333]
$33o $[33
Nemeth and MathematiX allow scores of combinations--see Rule 20 for a list. In Samples 1 and 2, we recommend using the "a" versions rather than the "b" versions, when possible. This is especially important when the sign appears above or below the baseline, because MathematiX produces a single character for the "a" versions. For the "b" versions, MathematiX builds up several characters, which can throw off the spacing of other elements when included in a subscript, superscript, fraction, radical, or modified expression.
In standard Nemeth Code, when one arrow follows
another, you assume they are stacked vertically. If you really want one
arrow followed horizontally by another arrow, you do something special. As
shown in Samples 6 and 7, MathematiX reverses these assumptions. To stack
two arrows vertically, you need to use the directly over or directly under
modified expression. Two arrows next to each other create one arrow
followed horizontally by another. The standard Nemeth for Sample 6 would
be $[333$333o, while the standard Nemeth for Sample 7 would
be $o"$[.
x+_;,b
@;,r^2
_#1_#2 .k _;,l_;,m_;,n
?_#1_#2/x
MathematiX supports neither italic nor sans serif type; only boldface English letters, boldface digits, and script English letters are available. In sample 1, the English Letter Indicator is required where shown to differentiate a boldface English letter from a German letter (Part 11). In sample 3, notice that every character in a special typeface requires its own indicator. MathematiX does not support the indicators to change the typeface for an entire phrase. As demonstrated in sample 4, you do use the Numeric Indicator for boldface digits in a fraction, which is the single contradiction to our Numeric Indicator prohibition in Part 3.
.a+.b+.g
@l,we see t@m#4.k .k #2.,k when .k"] .k #5 and .,k
.k #10_4
_,a-_,b
,,a0
,,a_ x ,,xy,,a
MathematiX does not support any Russian letters. You can't combine a special typeface with a non-Roman alphabet: MathematiX won't make a boldface kappa or a script German S.
In Sample 2, notice the tix null tool "]
(Section 4, Part 2) in the second lowercase kappa. MathematiX always
interprets space, dots 4-6, k, space as an equal sign. The tix null tool
"breaks up" the sequence, allowing MathematiX to recognize the dots 4-6, k
as a kappa.
MathematiX only supports two Hebrew letters: aleph and
bet. Two dot 6s can be either the Hebrew letter indicator or the double
capitalization indicator. When double dot 6 precedes two or more letters,
MathematiX interprets ,, as the double capitalization
indicator. In sample 5, we use the _ disappearing space
(Section 4, Part 2) to break up the first expression so that the aleph can
touch the lowercase x.
,h2,s,o4
,s,o;4^-2
,c_3],c
,n_7],n
,n_=],n
2,h2+,o2 $[33o 2,h2,o
The source of the single, double, and triple bond
symbols is "Report of the Chemistry Braille Workshop" (Von E. Eulert,
1985). While these symbols are not found in the Nemeth Code Book, they are
widely accepted. In Section 9 we demonstrate using BEX $$p
commands to create spatially molecular diagrams.
"lim%x$o0] ?1/x# .k ,=
"$c]+
"!%:]
@b(n%k)
" .,,s%i_.k_1< ,=] ,(?1/i^5"#,)
?@dx/@dz# .k q''
@& y @=\;x \ xy .k -xy
!;0^,="f(x, n) dx .k n&
,a .% ,b .k @_0 ,* ,a /.k ,b @/ ,a and ,b /.k
@_0
.,(?1/2#, ?1/3#, ?1/4#, ?1/5#, '''.,)
"x<_<] .1@.1] y:
Samples 2 and 3 demonstrate MathematiX's
non-standard approach to superimposition (printing two inkprint signs on
top of each other). In MathematiX, the pattern is multipurpose indicator,
first symbol, termination indicator, second symbol, while Nemeth uses
first symbol, dot 4, second symbol, termination indicator. The proper
Nemeth for Sample 2 would be $c_$+], meaning "take a circle
shape and fill-in with a plus shape." MathematiX does not recognize the
standard Nemeth %! for an integral sign with an underbar. The
MathematiX "!%:] literally tells the software: "modify an
integral sign by placing an underbar." Section 4, Part 4 explains how you
can use this technique to superimpose just about any inkprint signs, while
Part 5 addresses a special use to exercise fine control of vertical
spacing.
Standard Nemeth for Sample 4 would be
(n%k). In MathematiX, you must start a binomial
expression with @b(.
Sample 5 shows the special techniques for summation
signs. The standard Nemeth would be ".,s%i.k1<,=]
,(?1/i^5"#,). The double dot six makes an enlarged capital sigma.
The extra spaces inside the modified expression make the upper limit, the
operator, and the lower limit center correctly in inkprint. The
disappearing spaces that bracket the equal sign ensure correct inkprint
output. See Section 4, Part 4 for an explanation and Section 9 for more
samples.
Sample 9 shows your entry for the empty set sign.
MathematiX always interprets _0 as closing double quote: only
when you add the dot 4 will MathematiX create the empty set sign.
Sample 10 uses enlarged braces to enclose tall inkprint. This deviates from standard Nemeth, where enlarged braces are only used when the enclosed inkprint comprises several independent lines. MathematiX printed output looks best if you use enlarged signs whenever they enclose more than two levels--more samples in Section 4, Part 4.
MathematiX can't tix inkprint from every possible Nemeth symbol. With reference to the rule numbering in Nemeth Braille Code for Mathematics and Science Notation, here's what MathematiX can't do:
$$ commands to format your inkprint spatially, MathematiX
can't tix spatially arranged braille. If you follow Rules 24
and 25 in the Nemeth Code to create spatially arranged arithmetic, for
example, you are making braille that MathematiX simply chokes on.
\ for a tally mark.
The MathematiX disk adds a fifth menu to your BEX program. This Section details how the Math Menu options function. The Math Menu shares many qualities common to all BEX menus. Follow the instructions in User Level Section 4 for naming and selecting chapters. Press <CR> to get the list of options. To choose an option, press just its initial letter.
Since MathematiX came after BEX, its Math Menu isn't completely integrated into the BEX menu structure. The Math Menu is only available from the Main Menu. MathematiX won't let you move from the Starting Menu directly to the Math Menu. Moving between the Math Menu and the Main and Starting Menus requires swapping disks. Here's the drill:
To move from the Math to the Second or Page Menus, you must first switch disks and get to the Main Menu. If you're storing either the BEX Main side or the MathematiX software on RAM drive or the Sider, some disk swapping is still required to move from the Starting Menu to the Math Menu--please see Section 10 for details.
Most of the Math Menu options are borrowed from BEX's Main and Second Menu: details in Parts 3 and 4. The heart of MathematiX is option M - Math Output. The Math Output process, which we call tixing, is a combination of translating and formatting. For each BEX page, MathematiX loads two software modules from the MathematiX disk. So unlike any other BEX option, the MathematiX Menu Disk must stay in the drive throughout the process--this is why MathematiX requires a two-drive Apple system. (Because of this double disk access, you may wish to consider investing in extra memory for your Apple and BEX 3.0. Then you can run MathematiX from a RAM drive, which is much faster.)
Once you press M on the Math Menu,
MathematiX prompts for the chapter to tix. You specify one or more
chapters by name or by scanning, and then Math Output prompts tix
where:. For a reminder of your choices, type ?
<CR> at this prompt. By typing the first letter and pressing
<CR>, you choose one of the three destinations:
S -- Screen preview is appropriate for
sighted users wishing to proofread a tix-ready chapter. The material is
printed to the 40-column screen. When the screen fills, you hear a low
boop--press the space bar for the next screen.
V -- Verbalize allows both blind and sighted
users to proofread the content and structure of a tix-ready chapter.
MathematiX interprets the material, expressing it in words, not graphics.
When MathematiX detects a mathematical expression with a faulty structure,
it presents an error message accompanied by its approximate location in
the BEX chapter. Section 7 describes the tix verbalization tools you can
use to control what's spoken and the meaning of the structure error
messages.
I -- Inkprint hard copy creates the regular
print mathematical output. MathematiX tixes to the first large print
printer you've defined in your configuration.
If you don't want to tix after all, press
<CR> alone at the Tix where: prompt to get back to the
Math Menu. You can cancel tixing at any point by pressing <Esc For
screen or verbalize destinations, <Esc> halts tixing immediately.
When you're tixing inkprint hard copy, it can take up to five seconds for
MathematiX to return you to the Math Menu.
Once you type a destination letter and press
<CR>, MathematiX reads some software from the MathematiX program
disk. Then it reads the first BEX page of the tix-ready chapter and starts
to tix it: the scratchy noises you hear mean the software's working. The
last step before output is to read some more software from the MathematiX
disk. This process is repeated for every BEX page of the chapter or
chapters you've specified. If you didn't leave the MathematiX disk in the
program drive, you would get BEX's standard Program segment could
not be loaded error and return to the Math Menu.
Three kinds of problems with your tix-ready chapters can prevent MathematiX from completing the Math Output process.
control-C control-P in
the Editor to reduce the number of characters on each BEX page. For
general material, your BEX pages must contain 2500 or fewer characters;
for graphic-intensive material like calculus, keep your pages under 2000
characters.
SYNTAX ERROR IN 1045 or OUT OF
MEMORY ERROR IN 900. The tix-ready chapter includes very long math
expressions that exceed the maximum characters per line. Since you haven't
provided MathematiX with an acceptable place to break the line, it's
"crashed." Press control-Reset, depress the Caps Lock, and type RUN
START <CR>. You must edit the chapter and insert spaces or
discretionary line break @ characters--see Section 4, Part 3
for details.
Option P - Print chapters on the Math Menu lacks a few features found in its Main Menu counterpart. The options that let you bring tix-ready data from other braille devices have been modified to work better with MathematiX.
When you print a BEX chapter, the formatter creates output pages using the printer's carriage width and form length and any format commands in your text. You can print a tix-ready chapter to a brailler to proofread it in hard copy. The tix tools, math, and literary braille appear just as you entered them: all format indicators and commands are executed. MathematiX only tixes when you use option M - Math Output.
The Main and Math Menu's Print option format text
identically: the difference lies in your range of printing destinations.
On the Math Menu, you can only print to the screen or one of the numbered
printers defined in your configuration. You can't use +V to
add voice output; you can't type N <CR> to define a new
printer on the fly; and you can't specify L <CR> to
mean the last printer used. Multi-function print on the Main Menu lets you
restart a printout on a specified page or make more than one copy of a
document. Multi-function print is not available on the Math Menu: switch
disks and go to the Main Menu when you need those features.
Because MathematiX greatly expands your data as it
tixes, option I - Input through slot on the Math Menu creates BEX pages
with a maximum of 2500 characters. In addition, the Math Menu's Input
through Slot has one new feature. User Level Section 12 explains how you
finish the transfer process by pressing Q on the Apple
keyboard: this closes the current BEX page and builds a chapter directory.
On the Math Menu, you have an alternative way to end the transfer: place
the single <control-Z> character at the end of the data
you're sending. When the Math Menu's Input through slot sees a
<control-Z> in the file, it acts like you've pressed Q
on the Apple keyboard.
The Math Menu version of option F - From VB creates BEX pages of 2500 or fewer characters, to minimize overflow errors during Math output. Unlike its Main Menu cousin, the Math Menu's From VersaBraille doesn't ask you if you want control characters. Since math material makes heavy use of dots 4-5-6 and dot 4, trying to transfer control characters from the VB would result in massive confusion. All the symbols that control format in MathematiX are printing characters, so you shouldn't need to use control characters anyway.
After you press F, the only prompt is
Do you want V B page indicators? N. As explained in full in
User Level Section 11, most of the time you press <CR> to accept the
No default. Then you'll enter chord-X H at the VB chapter
name to begin the transfer of data.
Seven of the Math Menu options are identical to their counterparts on your Main and Second Menus. We duplicated them on the Math Menu for your convenience, so you wouldn't have to constantly switch disks. These "all-stars" are:
When you use option M - Math Output, you have three
destinations for your tixed data. This Section focuses on the Verbalize
destination. Once you type V <CR> at the Tix
where? prompt, MathematiX tixes your data in words to the 40-column
screen and your voice synthesizer. Part 1 explains what happens during
verbalization and how to interpret what you hear. Part 2 discusses the tix
verbalization tools that control what's printed to the screen and spoken.
Part 3 of this Section is relevant to sighted as well as blind MathematiX
users. MathematiX can't tix a series of math symbols that don't conform to
its guidelines. If a structure error occurs while tixing to the screen or
printer, MathematiX halts output entirely. Verbalize provides all users
with detailed information about these structure errors before you tix
inkprint. In the Section 2 Guided Tour, Parts 7 and 8 provide a
step-by-step sample of using Verbalize and understanding its vocabulary.
Verbalize doesn't provide you with a preview of the
final inkprint format. As explained in Section 4, MathematiX itself is in
charge of most inkprint format decisions. When MathematiX encounters any
$$ commands in the chapter during Verbalize, it simply
parrots them back to you. As detailed in Section 4, Part 3, MathematiX
ignores format commands that it doesn't support. When you verbalize a
command like $$vl8, MathematiX tells you that it's not
supported. Like BEX, MathematiX allows you to enter nonsensical format
values. Even if you set left and right margins larger than the carriage
width with $$ml100$$mr100, Verbalize won't complain. However,
MathematiX may crash when you attempt to tix to inkprint. When it comes to
Math Output of format commands, garbage in, garbage out.
What Verbalize does well is tell you the inkprint result of the data you've entered. Verbalize uses a "picky" style for math material, and a more "conversational" approach for literary text. Every space, digit, symbol, letter, and punctuation mark is announced individually in math mode. MathematiX does its best to conventionally read the math aloud. However, MathematiX doesn't understand the underlying meaning of the symbols you've entered, so it can't always read things as a person would. In many cases, MathematiX simply announces the name of the signs that would appear in inkprint, leaving the interpretation up to you. You can check Appendix A, Verbalize Vocabulary, for the meaning of any unfamiliar terms.
After you turn on literary mode by typing
@l, you hear full words and no explicit spaces or
capitalization. Set the voice device for "Most" punctuation mode when you
want to check your literary punctuation. Use this change between "picky"
and "conversational" styles to check the accurate placement of the tix
translation tools. It's easy to recognize if you've neglected to precede
literary material with @l, since MathematiX attempts to
interpret the literary contractions as math symbols. You'll hear patent
nonsense that quickly degenerates into a structure error. Similarly, if
you neglect to switch back into math mode with @m, then your
math is verbalized as a hodgepodge of unrelated contractions.
Here's a quick demonstration of the "picky" and
"conversational" styles. A tix-ready chapter containing just: 3./8
is smaller than 3./4 is verbalized as 3 divided by 8 space i
s space s m a l l e r space t h a n space 3 divided by 4. Since the
entire sample is in math mode, you hear every letter and space in the
phrase is smaller than.
On the other hand, consider a tix-ready chapter
containing: $p#4_?3/8_#@l is small] ?an@m#4_?3/4_#_4. When
you verbalize this, you hear:
In this case, the phrase is in literary mode, so it's
pronounced as words. If you omitted the @m that turns math
mode back on, you'd hear:
And if you remembered the @m but omitted
the @l, you'd hear:
Part 3 explores structure errors in great detail.
When you verbalize a chapter, you may not wish to hear the entire text. You determine what's spoken with the three tix verbalization tools:
@talk -- Begin speech and screen output,
pausing when the screen fills. (Default)
@express -- Begin continuous speech and screen
output
@notalk -- Suppress speech and screen output
unless there's a structure error during verbalization
For inkprint or screen destinations, all the tix
verbalization tool characters are suppressed: you don't get
@talk in your output. You can type one space after these
tools to make them "words;" if you do, it disappears when tixed. On the
other hand, a space before the tool is significant. The following three
samples tix identically: ,a_4 #2 "k #3 ,b_4 #2 "k @talk #3 ,c_4 #2
"k @talk#3.
When you answer V <CR> to the
Tix where: prompt, MathematiX always begins in regular "talk"
mode. When the Apple's screen is full of verbalized words, you hear a low
boop. You can use screen review to go over what's been said, or you can
press the spacebar to continue. When you want to save wear on your thumb,
use the "express" talk mode. To freeze output and enter screen review for
proofreading, press control-L.
The "notalk" lets you zero in on a portion of a
chapter for close review. It's also handy when you need to confirm that
you've corrected an error found previously. When you verbalize one or more
perfect tix-ready chapters that start out with @notalk, then
you only hear the tix scratch and disk access. When you return to the Math
menu, you know that all is well.
You can use BEX's Editor to add the
@notalk tool where you want it--remember, it's entirely
suppressed when you tix to your printer. Alternatively, you can specify
the HUSH "set-up" chapter as first in your list of chapters
to tix. The HUSH chapter just contains the
@notalk tool--it's on your MathematiX Menu Disk.
Several mathematical expressions require the use of
more than one sign in a particular order. For example, a simple fraction
must begin with ?, include a fraction line /,
and end with . When MathematiX reports a structure error, it
means that one or more of these signs is missing or present in the wrong
order.
When MathematiX notices a structure error while tixing to the screen or the inkprint printer, output halts. You hear a beep, followed by:
MathematiX replaces the NAME with the
actual BEX chapter name, and the page with the specific BEX page number.
During Verbalize, MathematiX announces structure
errors in greater detail (even when you're in @notalk mode):
Check below for the meaning of the error descriptions.
To emphasize the error, MathematiX raises the pitch of your synthesizer.
MathematiX uses the actual BEX chapter name and BEX page number.
MathematiX lists the paragraph number by counting $p
indicators in your chapter. When the error occurs before the first
$p in a BEX page, you hear paragraph 0.
After the error message, MathematiX restores the pitch
to normal and continues tixing. If you were in "notalk" mode, the
structure error message acts like a @talk tool: you hear all
the material up to the next @notalk tool. You can cancel
tixing by pressing <Esc> and go fix the error immediately, or you
can continue through the list of chapters, noting all errors to hunt them
down later. When you're configured at the Master Level, you can use the
control-B P command to get a hard-copy version of the entire verbalize
screen output--details in Section 9, Part 1.
In the following list, we present all the error messages in alphabetical order. For each one, there's a brief summary of the data pattern that causes MathematiX to emit the message. As discussed further below under "Hints for Interpreting Errors," the fact that MathematiX mentions "fractions" doesn't necessarily mean that the problem lies with a fraction in your material. There will be times when an error message seems completely unrelated to what you're writing. To help you track down problems, use BEX's Locate command to move to the first item in the data pattern.
@b( not
followed by ).
, not
preceded by ,/ whether or not preceded by ,?.
,? not
followed by ,/ and ,.
,/ not
preceded by ,?.
<3> not
followed by ].
] that
does not match an appropriate starting indicator. MathematiX may add
further location information, such as "Extra termination sign in numerator
of complex fraction." One cause is neglecting to place the "
at the beginning of the modified expression; it can also mean a radical
that lacks its initial >.
? followed by but
with no intervening /.
? followed by
/ but not followed by
? followed by a chunk
boundary (explained below) or structurally incorrect radical or modified
expression.
,, not
preceded by ,,/ whether or not preceded by ,,?.
,,? not
followed by ,,/ and ,,.
,,/ not
preceded by ,,?.
]
preceded by < with no intervening >.
< and
> not followed by ].
% not
preceded by ".
" not
followed by ].
,? or ,,? preceded by ,?.
,,? preceded by ,,?.
? or ,? or ,,? preceded by
?.
> or
<2> not followed by ].
By definition, a complex fraction's numerator or
denominator (or both) contains a simple fraction, while a hypercomplex
fraction includes a complex fraction in its numerator and/or denominator.
However, MathematiX does not check to see if your complex and hypercomplex
fractions strictly satisfy these definitions. When you enter
,?a;4,/45, to allow room for a subscripted numerator,
MathematiX tixes the inkprint with more vertical space than if you entered
the standard Nemeth ?a;4/45.
MathematiX can't know what you mean to write; when the conditions listed above are met, you get the error message. When you intend to write a hypercomplex fraction and omit one of the required symbols, then the error messages are self-explanatory. However, there will be times when an error message seems completely unrelated to what you're writing.
The most common cause of structure errors is writing
grade 2 contractions in math mode. You must introduce all
literary material with either the one-space @l or
disappearing _@l tix translation tool. When you don't, every
th or st sign causes a fraction-related error,
while ar and gh generate radical-related errors.
In addition to missing translation tools, missing spaces can cause havoc.
The spaces around dot 5 are crucial to its meaning: If you slipped a space
in the middle of the "less than" "k you'd get an "Modified
expression not terminated" error.
Several Editor commands can help you track down
problems. (Section 2, Part 8 demonstrates a host of techniques.) Let's say
you intended to write /,* "it does not follow that," yet you
reverse the position of the dots 3-4 and dot 6. You get a message
Complex fraction not started in chapter JUNK page 1 paragraph
4. Edit page 1 of the JUNK chapter. Then enter
control-A 4 control-P to advance four $p
indicators. Checking the error message list, you see that this message
happens when MathematiX finds ,/ that's not preceded by
,?. Once you're in the fourth paragraph, type control-L
,/ control-A to zero in on the problem data.
MathematiX checks the structural integrity of your
material in chunks, one BEX page at a time. To decide where an expression
ends within each BEX page, MathematiX can use hard <CR>s, new line
$l, new paragraph $p, and new page
$f indicators. MathematiX's "chunking" techniques can
influence the timing and placement of structure errors. For some
expressions, the error description pops up immediately. But generally,
MathematiX works backwards from the chunk boundary, reporting the problems
in reverse order. A chunk boundary in the middle of an expression can
cause several, accumulating structure errors.
For example, suppose you verbalize a
LOUSY chapter containing: ,?24,/>?$p1/2#],.
You would hear:
When MathematiX encounters the paragraph indicator in
the middle of this otherwise correct complex fraction, it
first reports a ? that's not followed by
/ and . Then it checks to see what else has been started in
this paragraph. Working backwards, it complains about the
> that's not followed with ], and finally the
,? that's not followed by ,/ and ,.
When MathematiX announces the new paragraph, it's completely finished with
the first chunk.
That's why 1/2 is announced as "one slash
two" instead of "one fraction line two." When MathematiX gets to the
termination indicator ], it realizes that nothing has been
started, so it reports "Extra termination sign." Finally, it reaches the
BEX page chunk boundary, and complains about the , which has
not been preceded by ,\.
Structure errors are reported with paragraph numbers, so liberal use of paragraph indicators makes your material easier to navigate. When you use Input through slot, it's possible that BEX would move to a new page in the middle of an expression, causing structure errors in correct material. Use the clipboard to copy the material from the end of one page to the start of the next. When you hear a spate of error messages in a row, you need to peel back layers of the onion to locate the culprit. Until you're a MathematiX expert, we recommend you confirm that you have located and fixed all problems by verbalizing again after you hear and correct errors.
When you encounter problems using MathematiX, check
here to see if there's a simple solution. Next, take a look at the
KNOWN MATHEMATIX BUGS chapter on the MathematiX Sample Data
disk to see if we have supplied a workaround. If not, please see the end
of this section for how to contact us for help!
control-C control-P in the Editor or
Adjust pages on the Second Menu. Details in Section 3, Part 1.
V <CR> at the Tix
where: prompt, all I hear is the tix scratch.
@notalk tool at the start of the
chapter, and your material contains no structure errors.
@notalk and delete it, then try
again.
I <CR> at the Tix
where: prompt but I don't get inkprint output.
I
<CR> at the Tix where: prompt.
@. Read more in Section 3, Part 2.
SYNTAX ERROR IN 1045 or OUT OF MEMORY ERROR IN
900.
$$mr100 would create an effective
carriage width of zero, because the right margin is larger than the entire
carriage width.
RUN START <CR>. Check for places needing spaces or
discretionary line break @ characters. Make sure your format
commands make sense. Sometimes the program crashes so badly, you have to
reboot.
control-D at the Math Menu to
load the RAM drive, the program hangs.
* as a drive number to
access the Main Side RAM drive--details in Section 10, Part 2.
To help us help you better, we ask that you:
In this Section we have gathered together an interesting miscellany of hints, tips, and techniques. Part 1 discusses three BEX Master Level features that supercharge MathematiX. In Part 2 we describe how to produce more closely-conforming Nemeth braille from your tix-ready chapters; Part 3 explains how to enlist the aid of the Grade 2 translator in creating the literary parts of a tix-ready chapter. One way that blind users can be come more familiar with the appearance of inkprint mathematics is detailed in Part 4. Calculus users will find Part 5 of particular interest. As Parts 6 and 7 briefly demonstrate, you can use MathematiX to output very complicated materials. RDC wants you to make best use of MathematiX. If you're unsure how to create a particular format, please get in touch so we can work together to figure out if it's possible.
You can take advantage of a number of BEX Master Level features to make your MathematiX use more enjoyable. First and foremost is RAM drives, discussed in Section 10. The section numbering in the BEX Master Level changed dramatically from version 2.2 to version 3.0, so we just refer to section titles here.
Both BEX 2.2 and 3.0 provide a special BEX chapter
that's in memory, not on disk. In BEX 2.2, it's called the Zippy chapter
and its name is the single <Del> character. In BEX 3.0, the same
thing is known as the Ready chapter, referred to with the single
] right bracket character. Whichever version of BEX you have,
Verbalizing goes much faster when your tix-ready chapter is stored in this
Zippy/Ready chapter.
The Master Level control-B I/O commands
let you send data to more than one channel at a time. You can take
advantage of this to get a simultaneous hardcopy record of what shows on
the screen during Verbalize. This can be very helpful when you're trying
to track down thorny structure errors. For example, when your
configuration defines printer 4 as a paperless brailler, issue the command
control-B P 4 immediately before you press V at
the tix where: prompt. From that point on, all the
information that goes to the voice channel is also sent to the paperless
brailler. When Verbalize is finished, use control-B P D to
turn the printer channel off again.
control-B PThere are two points to keep in mind when you use this
trick. As always, the speed of the slowest channel determines the pace of
output. If you ask BEX to send the verbalize information to a Cranmer
Brailler, it will take a very long time. If you turn the
printer off-line, then you "freeze" BEX. To recover, simply turn the
device on-line again, then issue the command control-B P D.
Secondly, BEX has a disconcerting but minor bug that
you may encounter the first time you activate a printer
channel, depending on how the printer is configured. The first time you
issue the control-B P command, the program crashes into the Apple monitor.
You get random numbers like 00/378E: 00 24 and finally an
asterisk * prompt. Type control-C <CR> to
leave the monitor and get the BASIC prompt, then type RUN
<CR> to get back to the menu. Now you can issue the control-B
P command and it works fine.
Automatic procedure chapters, detailed in the BEX Master Level, let you perform multi-step operations unattended. You can establish an auto chapter that answers all the prompts for the three basic MathematiX steps:
To make sure that untixable data won't cause
havoc, when you run an auto chapter from the Math Menu, a Verbalize
structure error halts execution of the stored keystrokes. (As always, a
disk error also stops an auto chapter in progress.) The
@notalk tix tool can streamline the process: when your data
is free of errors, the Verbalize step is silent except for the tix
scratch. To ensure the presence of @notalk, you can specify
the HUSH chapter on the MathematiX Menu Disk as the first
tix-ready chapter you tix. (The HUSH chapter just contains
the eight characters @notalk.)
Here's a step-by-step example of how you could create an auto chapter that performs those three steps. While the sample uses Input through slot, it works equally well for From VB.
In order to include Input through slot in the auto
chapter, you must type a <control-Z> character at the end of the
file in your external braille device. Since the auto chapter always uses
the name HOMEWORK for the received file, if you repeat the
procedure with the same data disk, you overwrite the chapter each time.
When you want to save an earlier version, simply rename the chapter before
repeating the process.
The TIX HOMEWORK-A chapter that's saved
on the program drive contains all the keystrokes needed to duplicate the
process at a later time. To use the auto chapter, put the MathematiX Menu
Disk in drive 1, a data disk with sufficient room in your default data
drive, get your external device and printer ready, and press control-A at
the Math: prompt. MathematiX prompts you for the auto chapter
name: type 1DO HOMEWORK-A <CR> and sit back and relax.
The T2B-T transformation chapter on the
MathematiX Menu Disk helps you change a tix-ready chapter to more standard
Nemeth Code. T2B-T finds the MathematiX-only symbols like
@m or _ and replaces them with nothing. Once
this replacement is complete, you can emboss the modified chapter, using
option P - Print chapters on the Math or Main menus.
Suppose you have a chapter named LESSON2
on a data disk in drive 2. Here's how you prepare a hard-copy braille
version without any of the MathematiX-only symbols.
You hear some interesting clicks and pops as the
MathematiX symbols are deleted. Notice that the target chapter has a
different name! If you entered the same name for the target chapter, you
would no longer have the tix-ready version. You're now ready to proofread
the LESSON2X chapter. When you are satisfied, you emboss it
by specifying the printer number for your brailler.
While MathematiX is geared towards the production of inkprint from braille input, it can also be used to assist in the production of Nemeth braille. Sighted people can tix to the Screen to quickly check the accuracy of Nemeth Code entry. This technique works best when the document you're transcribing is mostly literary, but makes some use of Nemeth Code. (Many of the samples in this Manual were prepared this way.)
@l. When
you switch to manual Nemeth entry, start off with @-. (As
introduced in Section 3, Part 2, MathematiX interprets @- and
@m identically.) You must follow all the guidelines in
Sections 3 and 5 when it comes to entering the math symbols. This is your
ORIGINAL chapter.
ORIGINAL chapter, creating a ORIGINAL2 chapter.
Grade 2 translation will only occur between the @l and
@- controls.
ORIGINAL2 to the Screen. Use option M -
Math Output to proofread, specifying the Screen tix destination.
ORIGINAL2. If any
problems pop up when proofing, edit the chapter, fix them, and proof again
to confirm.
At this point, you have a tix-ready chapter. Use
option N - Name change on the Second Menu to rename ORIGINAL2
as HOMEWORK or whatever.
When you want to prepare a more standard Nemeth
braille hardcopy of this data, follow the instructions in Part 2 on the
use the T2B-T transformation chapter.
As mentioned in Section 3, Part 2, MathematiX needs
more letter signs in literary mode than good grade 2 requires. Option G -
Grade 2 translator adheres more closely to the grade 2 rules. You can
force the Grade 2 translator to place a letter sign by preceding the
letter with . Lettered outlines are an example. Grade 2
doesn't require a letter sign before an isolated letter that is followed
by a period. When you enter @lb. GENERAL REACTION:@- ,a + ,b $o
,,ab@l then the translator creates: @l b4 ,,g5]al ,,reac;n3
@- ,a + ,b $o ,,ab @l. When you tix this, the initial letter
becomes but..
Slip before the letter to force the translator to
place a letter sign: @lb. GENERAL REACTION:@- ,a + ,b $o
,,ab@l. Don't do this in math material--if you want an English
letter sign or any other braille character, you have to enter it yourself.
When you specify the Screen preview tix destination, Math Output produces inkprint on the Apple's HI-RES screen. Using the techniques described here, you can save one screen's worth of output as an Apple HI-RES graphic file. You can then use RDC's pixCELLS software (or Lorin Software's Illustrations program) to send this graphic file to an embosser, providing a tactile image of MathematiX's graphics output. Each brailler dot in the tactile graphic corresponds to one inkprint dot in MathematiX. This can show blind users the MathematiX version of a specific inkprint sign, as well as the spacing decisions that MathematiX makes.
pixCELLS makes one brailler dot from every lit pixel on the Apple HI-RES screen; a full screen requires six braille pages. Whether the graphics file requires one or two brailler pages vertically depends on how much information is in your tix-ready chapter. When you tix to the screen, MathematiX uses an effective carriage width of 40, which would require more than one braille page horizontally.
Use a right margin command to narrow MathematiX's
output so that it fits within one braille page horizontally. When you're
embossing the graphic on a VersaPoint, Ohtsuki, or Romeo, begin your
tix-ready chapter with $$mr25. For a Cranmer Brailler, use
$$mr26. Since less information fits on each screen line, very
long math expressions won't be accurately represented.
You can only save one screen's worth of information at
a time. This means that after you type S <CR> at the
Tix where: prompt, you should hear one low boop after the tix
scratch. When you press the spacebar after this boop, you return to the
Math Menu. If you hear another low boop, it means there's more than one
screen worth of stuff.
We supply an automatic procedure chapter on the
MathematiX Menu Disk named PIXGRAB-A which issues the
commands that save the graphics file. To use it, you must have two floppy
disk drives--see below for how to cope when you don't.
Prepare a short tix-ready chapter that begins with the
appropriate $$mr command. Tix the chapter to the Screen
preview destination to make sure that it's just one screen long. The
GREEK chapter on the MathematiX Sample Data disk is an
example; it contains all of MathematiX's Greek characters. You must have a
data disk in drive 2 with at least 34 free sectors. Now you're ready to
go:
You hear the tix scratch, followed by brief silence and a low boop. Press the spacebar to return to the Math Menu. You're ready to run the auto chapter:
Now BEX goes through the process of saving the last
HI-RES image under the name MATH.IMAGE on the data disk in
drive 2. Once the file is saved, you are back at the Math Menu.
When you don't have two floppy disk drives, then the
PIXGRAB-A chapter won't work. But you can still issue the
appropriate commands manually. Once you have tixed to the screen and
pressed space, here's what you do:
You must type the address A$2000,L$2000
exactly as shown: this captures the HI-RES image. You can substitute any
name you prefer where we show MATH.IMAGE. When you wish to
save the image on a different disk drive, change the in S#,D.
(When you're comfortable editing auto chapters, you can copy
PIXGRAB-A and modify the disk drive references there.)
If you repeat this process with the same data disk,
the new MATH.IMAGE file replaces the old. When you want to
capture a series of graphics, use the DOS RENAME command
after each "grab." Suppose you're capturing two images. You automatically
or manually save the first image, then do this:
Now when you capture the second image, the
IMAGE.1 file is preserved.
In Section 4, Part 4, we discuss how MathematiX positions the upper and lower limits around a central operator in a modified expression. MathematiX can't center the limits automatically. If both your lower and upper limits are one or two characters (inkprint signs) long, then you can't control centering anyway. But when either limit is three signs or longer, you must add spaces inside the modified expression. Each space after the above symbol, dots 1-2-6, nudges the upper limit to the right, while each space after the below symbol, dots 1-4-6, nudges the lower limit to the right. Each space you put after the initial dot 5 nudges the central operator one character to the right.
In the following samples, we use "n" to stand in for any lower limit, and "x" to stand in for any upper limit. The operator is always shown as the sigma, but the techniques hold true for other operators as well. Take special notice of where spaces appear:
".,,s%n<x] ".,,s%nn<x] ".,,s%n<xx]
".,,s%nn<xx]
".,,s%nnn<x] ".,,s%nnn<xx]
".,,s%nnn<xxx]
".,,s%n<xxx] ".,,s%nn<xxx]
".,,s%nnn<xxx]
".,,s%n<xxxx] ".,,s%nn<xxxx]
".,,s%nnn<xxxx]
Sample 1 doesn't use any "padding" spaces, because the lower and upper limits are two or fewer characters. In the other samples, you always pad the sigma. Of course, when your limit produces an even number of signs, no amount of tweaking can create perfectly balanced centering.
MathematiX requires spaces on both sides of the equals, greater than, and less than signs of comparison. For correct inkprint, signs of comparison in the upper and lower limit must not be spaced. It's important to use the disappearing space for signs of comparison in a limit, and to only enter "padding" spaces exactly where we show them. The following chart shows what can go wrong:
" .,,s%n_ .k_ #0< ,=]a;n
".,,s%n_ .k_ #0<,=]a;n
".,,s%n .k #0<,=]a;n
".,s%n .k #0<,=]a;n
The tix vertical tools let you get deep into MathematiX's format. As we stressed when we introduced them in Section 4, Part 5, the tix vertical tools override MathematiX's automatic spacing decisions. For success, you need to know what inkprint math should look like and be able to think like a software program. Thanks to long lists of exceptions deep inside MathematiX, 97% of your output will be just swell. This Part provides the background so diligent users can fix up that last three percent; Part 7 explains how we use these techniques in the chapters from MathematiX Sample Data disk. Verbalize doesn't provide feedback on the format created by the tix vertical tools. Either a sharp-eyed sighted assistant or a graphics program like pixCELLS (see Part 4) is required to see the tools' effects.
While MathematiX does a good job of making draft quality output, it occasionally makes some poor choices. If you desire to improve the output, you need to know how MathematiX places characters on the page. Some parts of MathematiX make smarter decisions than others.
For the relative vertical placement of many expressions, MathematiX takes into account the actual width and height of the signs involved. No manual intervention is required when MathematiX creates:
For example, when you tix >67^3"]
MathematiX raises the top line of the radical so that it doesn't obscure
the cube exponent. When you tix "!<:], MathematiX keeps
track of the height and width of the integral sign. When it places the
overbar, it's clearly above the integral.
On the other hand, sometimes the vertical placement of signs is based on MathematiX's assumption that the enclosed character is "normal size." When the enclosed character is taller, then the relative position is too close together. (A list of the tall characters appears below.) You can use tix vertical tools or other techniques to improve the presentation of:
When creating spatial fractions, MathematiX always
places the horizontal fraction bar at the same position relative to the
baseline. The denominator material is automatically dropped down as
needed. MathematiX assumes that the lowest character in the numerator does
not drop below the baseline. One way to make room for droopy numerators is
to write the fraction as complex, even if it's simple. Or you can use the
tix vertical tools. When the numerator has a subscript, raise the
numerator one-quarter character with [<q. When the
numerator has a modified expression with one sign printed below, raise the
numerator one character with [<o.
When you tix .,,s:, MathematiX assumes
the summation operator is as tall and as wide as a capital letter. The
single character overbar appears too low, and follows the sigma. Since
MathematiX does an excellent job of placing overbars and underbars with
modified expressions, the simple solution is to write
".,,s:].
When positioning signs above or below a modified
expression, MathematiX generally assumes the central sign(s) are one
character high. The exceptions are the tall operators (summation, product,
intersection, and union) and the integral sign. Suppose you wish to print
a right-pointing arrow below a quantity enclosed within enlarged braces.
As the chart below shows, enlarged braces are two characters high,
straddling the baseline; they extend one-half character above and below
the baseline. To ensure legibility in the lower limit, drop it one full
character for a total of two characters below:
".,(?1/3#.,)%[%ox$o0].
MathematiX can't tix an indexed radical
in the upper or lower limit. Fortunately, there's an alternative math
notation that MathematiX can output correctly. Show the
indexed radical with a linear fractional exponent. To show an upper limit
of the cube root of two, use ".,,s%n_.k_#0<2^1/3"] instead
of ".,,s%n_.k_#0<<3>2]].
The majority of signs are a standard MathematiX "character": eight pixels high and seven pixels wide. There are a handful of "tall" exceptions, in three sizes:
! !! !!!
,,\
.,,s .,,p ,(
,) .,( .,) @,(
@,) ,\
.% .+
The CHARACTER SCALE chapter on the
MathematiX Sample Data disk contains a hairy collection of tix vertical
tools that tix a stack of horizontal lines at the left margin. You can
clipboard the contents of this chapter before any characters into a test
chapter. When output in inkprint or as brailler graphics (Part 4), the
scale helps you count the height of any character combination.
Unlike typeset mathematics, when MathematiX tixes superscripts or subscripts, it uses the standard-size character. It uses the following values to shift away from the baseline:
These values apply to many, but not all superscripts and subscripts. The exceptions are integral sign or a closing enlarged symbol of enclosure: in those cases, MathematiX increases these values automatically to ensure legibility.
You can take advantage of these exceptions to improve
the clarity of some superscripts and subscripts. For example, when you
want to show the quantity the fourth root of 89 cubed, enter
,(<4>89],)^3. When you use the right bracket notation
to evaluate an integral between the limits, use an enlarged right bracket,
not a standard right bracket: x^3"-2x+1@,);1^4 instead of
x^3"-2x+1@);1^4.
MathematiX can get cranky when asked to tix very long expressions without spaces or discretionary line breaks. The default carriage width is 76 characters for an ImageWriter and 58 for the Epson. When you're lining up material on two or more lines, you may need to know how long expressions are. In general, each Nemeth symbol stands for one inkprint sign, and produces one MathematiX character when tixed to inkprint. Most Nemeth indicators are interpreted as format information, and don't create a specific character when tixed. Here are the only exceptions:
$r
rectangle; $e ellipse; $a concave up arc;
$' concave down arc; .,,s summation operator;
.,,p product operator. The last two are also two characters
high.
+"- results in two characters: one
plus sign followed by one minus sign. +-, on the other hand,
results in a one-character-wide minus sign with a plus sign above it.
<18>478] is six characters.
3 and divide by two, rounding up. Then add the number of
arrow heads to find the total arrow length. $[33333 is four
characters: (5 divided by 2 rounded up is 3, plus one for the arrowhead);
$[33o is three characters (2 divided by 2 is 1 plus 2
arrowheads).
When you use tix vertical tools within a dot 5, save dots 1-2-4-5-6 restore pair, you must carefully plan both vertical and horizontal spacing. If you save and restore carelessly, you can end up never advancing horizontally.
Here's an example of how not to write a
short array: ,\"[<h,x]"[%h,x],\. In this version, the
closing vertical bar overwrites the two stacked X's. Here's why:
MathematiX outputs the first vertical bar and saves the position at one
character after the vertical bar at the baseline. The first tix vertical
tool moves up from the baseline to print the upper X. The termination
indicator takes you back to the baseline vertical position and the
post-bar horizontal position. This position is saved again, then
MathematiX goes down a half character and tixes the X, and finally
restores the position. Since both X's have been bracketed by "
], MathematiX has never advanced one character horizontally. When
it comes time for the closing vertical bar, it overprints the X's.
Here are two alternatives that tix correctly:
,\"[<h,x]"[%h,x],\ adds a space before the closing
vertical bar, advancing the horizontal position one character.
,\"[<h,x][%h,x[<h,\ is a little trickier. The first X
is bracketed with " ], resulting in no horizontal advance.
The second X is not bracketed: you manually move down a half
character, tix and advance the X, then manually move back up a half
character.
$$ Commands and Tix Vertical ToolsThe MathematiX Sample Data disk contains several tix-ready chapters that demonstrate a few of the many ways you can format your MathematiX output.
You can use MathematiX to print up chemical
structures. Take a look at the ACETIC chapter, which shows
the chemical structure of acetic acid. The trick is to work out the
structure in advance to ensure that the rows align. Since the braille and
inkprint versions of the chemical bond symbols are the same horizontal
width, you can check the accuracy by printing your trials in hardcopy
braille.
Because a chemical structure is very fluid, tabs are
not very useful. Instead, we use the absolute position command
$$p. Remember that the first character on the line is
$$p0. The sequence _// is an oblique double
bond. The sequence _3] is a horizontal bond. The character
\ is a vertical single bond.
The CALC chapter demonstrates a host of
the techniques enumerated here, as well as some others. You can emboss
this chapter to see how we handled the margins. We used a left margin of
five and a right margin of 10 for the problem statements; this makes it
easier for inkprint reader to distinguish between the problems and
solutions.
This chapter contains many long equations, where we
liberally use $$kb $$kf pairs. Notice that when showing an
integral with limits, it's clearer to place a space after the upper limit
and before the integrand. For example, !;3^4?1/x^2"# dx is
preferred to !;3^4"?1/x^2"# dx. To ensure that the integrand
appears on the output same line as the integral, use a
control-S sticky space.
When you want to present spatially arranged material
with MathematiX, you can use both tabs and tix vertical tools. We refer to
the TAB DEMO and TVT DEMO chapters from the
MathematiX Sample Data disk as we explain how you do it. The first sample
in TAB DEMO is a matrix with three rows and three columns.
The general approach for formatting matrices is also useful for
determinants, systems of simultaneous equations, and other spatial
material.
A matrix is an array of elements arranged in rows and columns, enclosed within a single pair of very large braces, brackets, or parentheses. In the standard inkprint notation, these very large symbols of enclosure span all the lines in the matrix. Printing a matrix in MathematiX presents two challenges: creating the very large symbols of enclosure, and aligning the elements in each column. As the chart in Part 6 shows, MathematiX's "enlarged" symbols of enclosure are only two characters tall. As a substitute for these inkprint symbols of enclosure, use MathematiX's enlarged symbols of enclosure at the beginning and end of each line. This legibly suggests the standard inkprint notation. If your inkprint readers will be encountering this for the first time, include a note alerting them to the substitution.
To align the material in each column, you use BEX tabs
and horizontal position commands. Here's the general approach we took for
sample number 1 in TAB DEMO. Before setting any tab stops, we
clear all previous tab stops with $$tc. We set all the tab
stops while entering the top row. Of course, the top row is not always an
ideal model for the remaining tab stops: some elements below the top
element may be longer. You must figure out the longest element in each
column and take this into account when establishing the columns.
To set the tab for a column, we place
$$t* right before the beginning of that column's material,
establishing a tab at the current horizontal position on the line. We set
the first tab stop for the position of the enlarged left bracket. We set
the other tab stops for one space beyond the longest element in the
previous column. To leave room for the longest element in a column, we use
$$p+ to skip ahead some number of characters. The # value is
equal to the number of additional characters in the column's longest
element. If the elements in the final column vary greatly in length, it
helps to set a tab stop for the close bracket, but we did not do that
here.
On subsequent lines we use a disappearing space
followed by a tab command _$$ (dots 4-5-6, space, dots
1-2-4-6, dots 1-2-4-6, space), to move to the beginning of a column. This
novel combination ensures that the tab command moves where you want it. If
the space after an element already brings you to the next tab stop, then
the standard $$ skips over to the next tab stop.
For example, when your input is: 5
Then the tixed result is: 5
This combination of the disappearing space and tab
command only works for Math Output. If you printed a tix-ready chapter
that includes _$$, you would see the single dots 4-5-6 or
underbar followed by however many spaces the tab stop creates.
In greater detail, the longest element in the first
column is two characters: -1. This appears in the second row,
not the top row where we're setting tab stops. That's why we put
$$p+1 to move ahead one character after the 3 in the first
column, top row. We then use $$t* to set the tab stop for the
second column. In the second column, the longest element is the
-5 in the top row--we don't need any $$p+
command to leave room for additional characters. We just leave one space
between the second and third columns, and then use $$t* to
set the tab stop for the third column. The longest element in the third
column is the -3 in the second row; since the element in the
first row has only one character, we leave a space before the enlarged
right bracket.
We move to the second line and then use
$$ to position the enlarged left bracket. _$$
takes us to the start of the second column and then the third column.
After the 2 in the second column, we do not really need the disappearing
space before the tab, as there is one space to spare. But because it does
not hurt, we use the disappearing space-tab combination everywhere to be
free from thinking about it. Since the -3 in the third column
has two characters, the length we allocated for the column, we don't need
to leave a space before the enlarged right bracket. The third row is
similar. Because the fraction in the third column has the width of just
one character and we allocated two characters for the third column, we
leave a space before the enlarged right bracket.
A determinant is written just like a matrix, except
the elements are enclosed by vertical bars instead of brackets. This is no
problem for MathematiX: begin and end each row with ,\, an
enlarged vertical bar. When you write systems of simultaneous equations,
you may want to line up the coefficients or the variables in each line.
You can use tab stops just as we did for lining up elements in a matrix.
Sample 2 in TAB DEMO demonstrates the use
of tabs in formatting a piecewise defined function, which gives different
rules for defining the function values on different parts of the domain.
In print each rule is written on a separate line, followed by a comma and
then the applicable part of the domain. The entire arrangement is enclosed
on the left by a very large left brace. In MathematiX we recommend
beginning each row in the pattern with the enlarged left brace
.,(. We clear out tab stops with $$tc, then set
a tab at the position of the first enlarged left brace. We write the top
row, then move down for the next row with $l. We use the
$$ tab command to position the enlarged left brace on the
second row, write the second row, and repeat it all again for the third
row.
Sample 3 in TAB DEMO shows an even
simpler approach to formatting the same thing. Since the definition
follows some introductory text, we used $$ml* to establish
the left margin at the position of the first enlarged left brace. Then we
write the top row and move down for the next row with $l.
Because the top row left margin has been established at the enlarged left
brace, we are in position to write the second and third rows without
messing with tabs at all. After the period at the end of the definition,
we reset the left margin to zero to correctly position the question on the
next line.
Sample 1 in TVT DEMO shows how to
construct the by-now familiar piecewise defined function with tix vertical
tools. This approach requires the extra work of deciding how much to move
up and down, since you are bypassing MathematiX's automatic routines that
ensure adequate vertical space between lines. However, tix vertical tools
make it possible to line up the arrangement with other text before and
after it.
Our goal was to align the preceding and following text with the middle row of the piecewise function definition. We begin with the introductory text. Then we save the current position (where the middle row will begin) and move up to place the top row. After we write the top row out, we restore the saved position--we're back at the middle-row starting point. Now we save it again, move down and write the bottom row. Then we restore the saved position to return to the beginning of the middle row. We then write this middle row and continue with a period and the next sentence. MathematiX is smart enough to leave room for the top and bottom rows when it positions the middle row and moves down for the line after the spatial arrangement.
In greater detail, just before the spatial arrangement we used a disappearing space after the equal sign so that we could save the position one space before the enlarged left brace. This improves the readability of the tix-ready chapter, as it allows us to begin each row in the arrangement with a space. Checking the chart in Part 6, we find that the top half of the middle enlarged brace and the bottom half of the top enlarged brace total two characters high. To add some gap between them for readability, we moved up two-and-three-quarters characters for the top row; this leaves enough room for the fraction in the top row. We did this movement in two steps, moving up three characters and then down one-quarter character. Similarly we moved down two-and-three-quarters characters for the bottom row, in two steps.
Using the tix vertical tools in this order requires you to write the actual math material out of order. There's another way to do it. Save the position at the middle row starting point, move up, write the top row, then restore. Back at the middle row, save the position, write the middle row, establish a tab stop at the end, then restore. Finally, back at the middle row one last time, save the position, write the bottom row, restore, then issue a tab command to take you past the end of the middle row. Establishing and using the tab stop is critical in this method, otherwise you won't advance horizontally. As we cautioned in Part 6, using the tix vertical tools within save-restore pairs requires planning to ensure that you actually move somewhere.
As discussed in Part 6, MathematiX places the fraction
line as if the numerator has nothing below its baseline. A numerator with
subscripts or with a directly below indicator requires special handling.
In TVT DEMO's Sample 2, the first fraction has a subscript in
the numerator. After the begin fraction indicator we use the tix vertical
tool [<h to move the numerator up one-half character, to
leave room for the subscript. Because we moved up inside of the numerator,
the fraction line restores the correct vertical position.
Similarly, in Sample 3 the last fraction has a
numerator which includes a directly below indicator. After the begin
fraction indicator we use a tix vertical tool to move the numerator up by
one character. This leaves room for the below expression--x, right arrow,
a--which requires the height of one character. Also notice the use of
$$kb $$kf pairs to ensure that this last equation is not
split between two lines.
As also mentioned in Part 6, when tixing an above or
below expression (other than an overbar or underbar), MathematiX places it
as if its height is one character. In Sample 4 the below expression has a
superscript and therefore has an extra half a character in its height.
Therefore, after the below indicator we use the tix vertical tool
[%h to move the below expression down by half a character.
Because we moved down inside of a below expression, the termination
indicator restores the correct vertical position.
The number line shown as sample 5 in TVT
DEMO uses tabs to line up the zeros of f'(x) with the
appropriate x values. To draw the number line at its proper length,
we use an underbar modified expression for the row of plus and minus signs
and zeros. We place an arrow head on both ends of this line by using the
tix vertical tools to move down three-quarters of a character (in two
steps).
You can use the Sider hard disk system, manufactured by First Class Peripherals, with both BEX 2.2 and 3.0. Beginning with version 3.0, BEX lets you use a variety of storage devices for the BEX software and your data. When your Apple has more than 128K memory, BEX 3.0 lets you configure the memory as super-fast electronic disks, or RAM drives. BEX 3.0 lets you store data on 3.5-inch disks, and you can also use these handy disks for MathematiX data. You can't copy the MathematiX software to a 3.5-inch disk.
There are several drawbacks to running MathematiX from a Sider volume. You must create an automatic procedure chapter that tells BEX where to look for the "program drive." Every time you boot BEX on the Sider, you have to use this auto chapter to get access to MathematiX. Since Sider disk access is no faster than floppy disk access, the main advantage of including the Sider in your use of MathematiX is not having to insert and remove floppy disks. If you can stand to run BEX from floppy disks, then simply define a BEX configuration that doesn't reference the Sider, and follow the floppy disk procedures for MathematiX. But if you insist, this Part explains how to do it.
The first step is copying every file from the MathematiX program disk to one Sider volume, using FID. Make note of the Sider volume number. For the sake of this example, you copy the MathematiX software on to Sider volume 9. When you copy the MathematiX software to a different Sider volume, substitute that number for the 9 in the samples that follow.
MTX Automatic
ProcedureBoot up from the Sider and get to BEX's Main Menu. In order to use MathematiX, you must create an automatic procedure chapter that tells BEX to go to the Math Menu when you press the spacebar. You only create the auto chapter once; you then use the auto chapter each time you want to run MathematiX from the Sider.
The auto chapter begins with a "magic character,"
which depends on your BEX version. Then comes the number 486, followed by
one <CR>, the Sider volume number, finished up with another <CR
For BEX 2.2, this "magic character" is control-6; here's the
step by step for creating the auto chapter:
For BEX 3.0, you use control-backslash as
your "magic character:"
The keystrokes you've stored in the MTX
chapter on virtual drive 1 tell BEX that pressing the spacebar means move
to the Math Menu on Sider volume 9. When you copy the MathematiX software
to a different Sider volume, substitute that volume number for the digit
9 in the sample above.
Every time you boot BEX from the Sider, you must run
the MTX auto chapter in order to get to the MathematiX
software. At the Main Menu, press control-A, then type
1MTX <CR> at the Auto chapter: prompt.
Here's a summary of how you navigate the BEX and MathematiX menus on the
Sider:
When you're at the Math Menu, virtual drive 1 is the Sider volume where the MathematiX software resides. To access the Sider volume where the Main side software resides, use the asterisk as a drive "number"--details below under "Redirecting Virtual Drive 1."
This feature requires BEX 3.0. As introduced in Section 6, during tixing, MathematiX must read software from the program disk twice for each BEX page. Since disk access to RAM drives is electronic, loading the MathematiX software on a RAM drive dramatically increases MathematiX's speed. To run both the Main side of BEX and MathematiX on RAM, you must have two RAM drives in your configuration. When you have just one large RAM drive from a slot 1-7 memory card, you must choose which set of programs to run from RAM: either the Main side or the MathematiX software.
In Section 1, we showed the "JOHN" configuration for an Apple IIgs 512K with three RAM drives, one 5.25-inch floppy drive, and one 3.5-inch disk drive. The virtual drives are set up like this:
In order to load the Main side software on RAM drive, virtual drive 1 must be a RAM drive, in this case, slot 3, drive 1. To also load the MathematiX software on RAM drive, all you have to do is define another RAM drive in your configuration. It doesn't matter what virtual drive number you assign to this drive: MathematiX looks for the second RAM drive in your list of virtual drives when it comes time to copy the software.
The numbering and size of your RAM drives depends on how much memory you've installed in your Apple. The final RAM drive--the highest number on the drive list--may be a little smaller than the others. You can't store the MathematiX software on the final RAM drive if you have 256K or 1024K of memory, since it holds only one-third as much.
In this sample configuration, the second RAM drive is slot 3, drive 3, which BEX addresses as virtual drive 5. Notice that the full addresses of virtual drives 5 and 6 are out of order. When you have 512K or 768K memory, then the last RAM drive holds two-thirds as much as a standard one, and you can copy the MathematiX software to it with room to spare. Since the second RAM drive always holds the MathematiX software, the "out of order" arrangement makes more room for data on virtual drive 6.
Control-DThe Main side software is automatically copied to virtual drive 1 when you move from the Starting to the Main Menus. The loading of the MathematiX software on to RAM drive doesn't happen automatically. You follow these four steps to copy the software:
control-D.
MathematiX begins copying all the files and chapters from the MathematiX disk to the RAM drive; when it's finished, you are switched over to the newly-copied software.
As you can see from the following table, moving between the Main and Math Menus is straightforward. However, you can no longer move directly from the Main Menu to the Starting Menu; you have to detour through the Math Menu:
control-D
Please note that you always use
control-D when you go from the Starting Menu to the
MathematiX RAM drive. If you don't use control-D after a trip
to the Starting Menu, then MathematiX uses the software from the floppy
disk. The first time you use control-D, MathematiX copies
software from disk. Until you turn off the Apple, subsequent times, you're
just telling BEX where to find the MathematiX software.
As stressed in Master Level Section 3, the current
program drive is always virtual drive 1. The Main side RAM drive is
virtual drive 1 when you're at the Main Menu. When you move to the
Starting Menu, BEX redirects virtual drive 1 to the floppy disk in slot 6,
drive 1. At the Starting Menu, you can catalog the Main Side RAM drive
with the letter M at the Which drive: prompt.
When you're at the Math Menu, the MathematiX RAM drive
becomes virtual drive 1. MathematiX introduces a new drive specification
to let you catalog or work with chapters on the Main Side RAM drive. When
you're at the Math Menu, use the asterisk * character to
refer to the Main side RAM drive. You can use asterisk alone for a
catalog, or as a "drive number" when scanning or naming chapters. For
example, *SAVE refers to a SAVE chapter on the Main side RAM
drive. Entering *A at the Naming method: prompt
would add the number sign character to chapters written on the Main side
RAM drive.