%***  INTEGER ARITHMETIC EXAMPLES  ***%

% INTEGER ADDITION & SUBTRACTION %

32 + 15 - 24;
@: 23


? % MULTIPLICATION & UNARY MINUS %

5 * -12;
@: -60


? % USE OF PARENTHESIS % 

436 * (123 - 57);
@: 28776


? % RAISING TO A POWER %

100^3;
@: 1000000


? % ASSIGNMENTS TO A VARIABLE %

FOO: (3*8 - 16)^2;
@: 64


? % USE OF ASSIGNED VARIABLE % 

3*FOO^5;
@: 3221225472


? % SAVE INTERMEDIATE RESULTS %

SEC#PER#YR: 365*24*3600;
@: 31536000


? IN#PER#MI: 5280*12;
@: 63360


? % USE OF INTERMEDIATE RESULTS %
% TO FIND INCHES TO ALHPA CENTAURI %

4 * 186000 * SEC#PER#YR * IN#PER#MI;
@: 1486601994240000000


? % EXACT, INFINITE PRECISION % 

99^99;
@: 
3697296376497267726571879056288054405956687642817411
0243025997242355257045527752342141065001012823272794
0978889548326540119429996769494359451621570193644014
418071060667659301384999779999159200499899


? 
%*** RATIONAL ARITHMETIC EXAMPLES  ***%

% REDUCE FRACTIONS TO LOWEST TERMS %

56/77;
@: 8 / 11


? % FIND COMMON DENOMINATOR % 

5/6 - 3/4;
@: 1 / 12


? % RATIONAL SIMPLIFICATION % 

3 * (1/2 + 1/6);
@: 2


? % FLOATING POINT NOTATION %

POINT: 10$

? 1/3;
@: 0.3333333333


? 
%***      VARIABLE RADIX BASE      ***%

% SET FOR HEXADECIMAL ARITHMETIC %

RADIX (16);
@: 0A


? % USE AS A HEX CALCULATOR %

7C80 - 2*12EF + 0A3C;
@: 60DE


? % ASSIGNMENT TO A VARIABLE %

EG: 10000;
@: 10000


? % RETURN TO BASE TEN ARITHMETIC %

RADIX (0A);
@: 16


? % FIND EG IN BASE TEN %

EG;
@: 65536


? % BASE TWO ARITHMETIC %

RADIX (2);
@: 1010


? % BINARY ARITHMETIC CALCULATOR %

101101110 * EG;
@: 1011011100000000000000000


? % RETURN TO BASE TEN ARITHMETIC %

RADIX (1010);
@: 2


? 
%***  EXPONENTIAL SIMPLIFICATIONS  ***%

% FRACTIONAL POWERS %
8 ^ (2/3);
@: 4


? 12 ^ (1/2);
@: 2 * 3^0.5


? % POWERS OF THE IMAGINARY NUMBER %

#I^2;
@: -1


? #I^-7;
@: #I


? % COMPLEX EXPONENTIALS % 

#E ^ (#I*#PI);
@: -1


? 
%***           FACTORIALS          ***%

5!;
@: 120


? 50!^2;
@: 
9250170652825079190134707232358836823494868074219019
8770613927101881057071736043444238321314044821530214
4000000000000000000000000


? % BINOMIAL COEFFICIENTS [12:30] % 

N: 30;
@: 30


? M: 12;
@: 12


? N! / ((N-M)!*M!);
@: 86493225


?   
%***    BASIC ALGEBRA EXAMPLES     ***%

% AUTOMATIC ALGEBRAIC SIMPLIFICATION %

% COMBINES SIMILAR TERMS AND FACTORS %

3*X - X;
@: 2 * X


? Y^3 * Y^(R+1);
@: Y ^ (4+R)


? 
% EXPLOITS IDENTITIES AND ZEROS %

0 + X;
@: X


? 1 * Y;
@: Y


? Z * 0;
@: 0


? X^1;
@: X


? Y^0;
@: 1


? 1^X;
@: 1


? % MULTIPLE SIMPLIFICATIONS %

5*X^1*Y + Y^2*-3*X/Y + W^(Z^2 - Z*Z);
@: 1 + 2*X*Y


? % POLYNOMIAL MULTIPLICATION % 

(3*X - 2*Y) * (Y^2 + 4*X);
@: -8*X*Y + 3*X*Y^2 + 12*X^2 - 2*Y^3


? % POLYNOMIAL POWERS %

(X+1)^2;
@: 1 + 2*X + X^2


? (X+5) * (X^2-2*X+3)^2;
@: 45 - 51*X + 38*X^2 - 10*X^3 + X^4 + X^5


? % CONTENT FACTORIZATION % 

FCTR (6*X^3*Y + 15*X^2*Y);
@: 3 * X^2 * Y * (5+2*X)


?   
%***  LOGARITHMIC SIMPLIFICATIONS  ***%

% NATURAL LOG OF ONE %

LN (1);
@: 0


? % COMMON LOG OF 1000 %

LOG (1000, 10);
@: 3


? % EXPAND THE LOG OF A PRODUCT %

LN (X*Y);
@: LN(X) + LN(Y)


? % EXPAND THE LOG OF A POWER %

LOG (Z^3, 10);
@: 3*LN(Z) / LN(10)


? % MULTIPLE SIMPLIFICATIONS % 

LN(X^2*Y) - 2*LN(X);
@: LN (Y)


? % INTER-BASE SIMPLIFICATIONS %

LOG(X,10) * LOG(10,#E);
@: LN (X)


? % LOGARITHMIC POWERS %

#E ^ LN(X+5);
@: 5 + X


? 
%*** TRIGONOMETRIC SIMPLIFICATIONS ***%

% ELEMENTARY ANGLE VALUES %

COS (0);
@: 1


? SIN (#PI/2);
@: 1


? SIN (37*#PI/3);
@: 3^0.5 / 2


? % EQUIVALENT FUNCTIONS %

TAN(X) * COS(X);
@: SIN (X)


? % MULTIPLE ANGLES EXPANSION %

SIN (2*X);
@: 2 * COS(X) * SIN(X)


? COS(3*X);
@: 4*COS(X)^3 - 3*COS(X)


? % ANGLE SUMS EXPANSION %

COS (X-Y);
@: COS(X)*COS(Y) + SIN(X)*SIN(Y)


? % COMBINATION EXPANSIONS %

EG: SIN (2*X+Y);
@: 2*COS(X)^2*SIN(Y) + 2*COS(X)*COS(Y)*SIN(X) - SIN(
Y)


? 
%***      REPRESENT EQUATIONS      ***%

EQN: 2*X+7 == A^2 - X^2/X - 3;
@: 7+2*X == -3-X+A^2


? % STEP BY STEP SOLUTION FOR X %

EQN: EQN + X - 7;
@: 3*X == -10+A^2


? EQN: EQN/3;
@: X == (-10+A^2)/3


? 
%***      CALCULUS OPERATIONS      ***%

% FIND DERIVATIVES %

DIF (3*X^2 + 5*X - 4, X);
@: 5 + 6*X


? DIF (LN(X)^2, X);
@: 2*LN(X) / X


? DIF (#E^X^2, X);
@: 2 * #E^X^2 * X


? DIF (P*SIN(X) + X^2, X);
@: 2*X + P*COS(X)


? % FIND INTEGRALS %

INT (2*X - 1/X, X);
@: X^2 - LN(X)


? INT (X * #E^X^2 * SIN(#E^X^2), X);
@: -COS(#E^X^2) / 2


? INT (LN(LN(X))/X, X);
@: LN(X)*LN(LN(X)) - LN(X)


? 
%***     PROGRAMMING IN MUSIMP     ***%

% TAYLOR SERIES EXPANSION FUNCTION %

FUNCTION TAYLOR (EXPN, X, A, N,	
% Locals: % J, C, ANS, NUMNUM, DENNUM),
  NUMNUM: DENNUM: 30,
  J: ANS: 0,
  C: 1,
  LOOP
    ANS: ANS + C * EVSUB (EXPN, X, A),
    WHEN J=N, ANS EXIT,
    EXPN: DIF (EXPN, X),
    J: J + 1,
    C: C * (X-A) / J,
  ENDLOOP,
ENDFUN ;
@: *** REDEFINED: TAYLOR
 TAYLOR


? % TAYLOR SERIES EXPANSION %

TAYLOR (#E^X, X, 0, 6);
@: 1 + X + X^2/2 + X^3/6 + X^4/24 + X^5/120 + X^6/
720


? TAYLOR (SIN(X), X, 0, 8);
@: X - X^3/6 + X^5/120 - X^7/5040


? TAYLOR (#E^SIN(X), X, 0, 4);
@: 1 + X + X^2/2 - X^4/8


? 
MOVD ('CRLF, 'NEWLINE)$

?  RDS ()$

? ^C