muMATH-80

Do some experiments like I propose. Do not forget semicolon at the end of each

command and type the commands in uppercase:



1) Arithmetic:



Look how many digits you can have in your calculations



200!+99^99;



See the result of 381 digits.

Fractions can be reduced

16384/6144;

The computer will tell you that it is 8/3.

SIN (#PI/3);

answer is 3^(1/2)/2

but

SIN (2)+2*SIN(2);

will be displayed as 3*SIN(2), because it is not rational number





2) Simple algebra

Now try

(x+x)/(a*x);

You will get

2/a as a result. Wow! Symbolic manipulations.

SOLVE (x^2-3*x==a*x,x);

It will find two solutions

X==3+a and X==0

It understands complex numbers, try

#I*#I;

answer is -1

MuMath knows the relation which joins three symbols that came from three

different branches of mathematics: calculus, algebra and geometry

#E^(#I*#PI);



3) Matrix symbolic operations

Add twp arrays

[a,2]+[-a,b];

Try to invert the matrix (symbol shift with F,G,U,Z for brackets and braces)

{[a,b-2],[c,d]}^-1;



4) Calculus

Program knows about sums

SIGMA (J^2,J,0,N-2);

or limits

LIM (X^2 / SIN (A*X) , X, 0);

(remark the additional questions in case of ambiguities)

And finally some derivations and integrals



DIF ((X^3-2)/(2*X+1),X);

INT ((X^3-2)/(2*X+1),X);



5) Transcendental functions

Program knows many trigonometry transformations. Try

TRGEXPD (SIN(2*X+Y), -15);

Repeat the previous example by changing second parameter (but keep it negative)



6) Commands

try

OBLIST () ;

to get a full list of commands. The language Musimp is crossover of Algol and

Lisp.

-----------------

Can we make 48 K version? Maybe. There is version for 48 K TRS-80, assembled

from address #5200. Although the part of the program will be in video memory

this means that it can fit into RAM memory.