.MTH File Format

Introduction

An .MTH file is a utility file for Derive, the computer algebra system for DOS made by Soft Warehouse of Honolulu. It is a plain text file of definitions and expressions, such as the functions ELLIPTIC_F and FIBONACCI, written in Derive’s own expression syntax. Derive’s Transfer Load and Merge commands read one, and Transfer Save writes one, so it is how a set of definitions is kept between sessions and handed to others.

Derive came with a library of them (VECTOR.MTH, ODE1.MTH, BESSEL.MTH and about twenty more, each described in the DERIVE.HLP help file), and users made their own. A file that sets out a walk through some mathematics, to be played rather than loaded, uses the .DMO extension instead.

Structure

A file is lines of ASCII text, each ending in a carriage return and line feed, and the last line is followed by a single 1A byte (Ctrl-Z, the old DOS end-of-file mark). All 34 different files found for this page end that way. There is no signature and no header block.

"File ELLIPTIC.MTH, (c) 1990 by Soft Warehouse Inc."

ELLIPTIC_F(phi,m):=INT(1/SQRT(1-m*SIN(t_)^2),t_,0,phi)

ELLIPTIC_E(phi,m):=INT(SQRT(1-m*SIN(t_)^2),t_,0,phi)

Lines

Each line holds one expression of one of three kinds, and a blank line separates it from the next (the library files have one after every expression).

Line continuation

A line that does not fit is broken after 78 characters of text, and a ~ is put at the end of the physical line, which makes it 79 long. The next physical line carries on from the next character, so the break can fall anywhere, even inside a name or a number. To read the line, remove each ~ and its line break and join the pieces. In the .MTH files on this Mac every physical line that ends in ~ is 76 to 79 characters long, and no line is longer than 79. (A .DMO demo is not wrapped.)

CATALAN(n):=COMB(2*n,n)/(n+1)

FIBONACCI(n):=IF(n>=0 AND FLOOR(n)=n,ELEMENT(ITERATE([ELEMENT(v,2),ELEMENT(v,1~
)+ELEMENT(v,2)],v,[0,1],n),1),1/SQRT(5)*(((1+SQRT(5))/2)^n-((SQRT(5)-1)/2)^n*C~
OS(pi*n)))

Expression syntax in the files

Derive’s syntax is not specified on this page. These are the forms met in the library files.

• Function and variable names are letters, digits and underscores. Functions built into Derive (SIN, INT, VECTOR, ELEMENT, LIM and so on) are written in capitals in the library files.
• The library files end the names of dummy variables in an underscore, such as t_, k_ and m_, so they do not clash with a name the user already has. This is a habit of the files, not a rule of the syntax.
• Constants: pi and inf by name, #e (the base of natural logarithms) and #i (the imaginary unit) with a hash. A leading @ and a number, as in @1 in LIM2, stands for an arbitrary integer.
• Operators: + - * / ^, = and the comparisons, AND and OR, ! for factorial, . for the dot product of vectors and matrices, and a back quote after a matrix for its transpose. Vectors and matrices are written in square brackets, a matrix being a vector of vectors: [[1,0],[0,1]].
• A line may carry bytes above 127: GRAPHICS.MTH has a parameter named with byte E9, the capital theta of the DOS character set (code page 437). The viewer shows it as the same byte in Windows-1252.

A worked example

The first 0x70 bytes of ELLIPTIC.MTH. The first line is a text expression, then a blank line, then the start of the first definition. Every line break is 0D 0A.

00000000: 2246 696c 6520 454c 4c49 5054 4943 2e4d  "File ELLIPTIC.M
00000010: 5448 2c20 2863 2920 3139 3930 2062 7920  TH, (c) 1990 by
00000020: 536f 6674 2057 6172 6568 6f75 7365 2049  Soft Warehouse I
00000030: 6e63 2e22 0d0a 0d0a 454c 4c49 5054 4943  nc."....ELLIPTIC
00000040: 5f46 2870 6869 2c6d 293a 3d49 4e54 2831  _F(phi,m):=INT(1
00000050: 2f53 5152 5428 312d 6d2a 5349 4e28 745f  /SQRT(1-m*SIN(t_
00000060: 295e 3229 2c74 5f2c 302c 7068 6929 0d0a  )^2),t_,0,phi)..

The last bytes of the file are 29 0d 0a 1a: the final bracket, the line break and the Ctrl-Z.

In the file viewer

The viewer shows the text coloured: names the file defines, Derive’s built-in functions, operators, constants, numbers and text lines each have their own colour, and a word broken by a ~ is coloured as one word. The Overview tab lists every definition in a table: its name, whether it is a function or a variable, its parameters, its body (shortened) and its line; a click goes to that line. Only text that reads as Derive is taken, so another format using the extension is left to the viewer that knows it.

Related files

• .DMO: a Derive demonstration, the same text syntax with ; comment lines.
• DERIVE.HLP: Derive’s help file, which lists each utility file and the functions it defines.

Not described

This page is a partial reference, read from the Derive 2 library files (28 different .MTH files, each found in five copies on this Mac) and nothing else.

Links