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Text File  |  2003-02-09  |  3.8 KB  |  102 lines
  1.  
  2. title(exp):=block(clearscreen(),disp(dpart(exp)))$
  3. (title("A CLASSICAL TEXTBOOK EXAMPLE OF DIFFERENTIATION"))$
  4. X^X^X;
  5. DIFF(%,X);
  6. (title("DIFFERENTIATION OF A NESTED FUNCTION"))$
  7. ERF(TAN(ACOS(LOG(X))));
  8. DIFF(%,X);
  9. title("EXPANDING AND FACTORIZING A UNIVARIATE POLYNOMIAL")$
  10. (X-1)*(2*X-1)*(3*X-1)^7;
  11. EXPAND(%);
  12. FACTOR(%);
  13. title("FACTORIZATION OF CYCLOTOMIC POLYNOMIALS - WHICH FORM OF AN EXPRESSION IS MORE SIMPLE?")$
  14. X^600-1;
  15. FACTOR(%);
  16. title("FACTORIZATION OF A MULTIVARIATE POLYNOMIAL")$
  17. (Y^3-X^2)^4*(X+Y+Z)^2;
  18. EXPAND(%);
  19. FACTOR(%);
  20. title(" ALGEBRAIC SIMPLIFICATION EXAMPLE")$
  21. (SQRT(R^2+A^2)+A)*(SQRT(R^2+B^2)+B)/R^2
  22.  -(SQRT(R^2+B^2)+SQRT(R^2+A^2)+B+A)/(SQRT(R^2+B^2)+SQRT(R^2+A^2)-B-A);
  23. RATSIMP(%);
  24. title(" ALGEBRAIC SIMPLIFICATION EXAMPLE")$
  25. (Z^5-Y*Z^4+X*Z^4-2*Y*Z^3-6*X*Z^3+2*Y^2*Z^2+4*X*Y*Z^2-6*X^2*Z^2+Y^2*Z+
  26. 6*X*Y*Z+9*X^2*Z-Y^3-5*X*Y^2-3*X^2*Y+9*X^3)/(-Z^2+Y+3*X)^2;
  27. RATSIMP(%);
  28. title("INTEGRATION OF A NON-TABULATED FUNCTION")$
  29. 1/(X^3+A*X^2+X);
  30. INTEGRATE(%,X);
  31. DIFF(%,X),RATSIMP;
  32. title("LOGARITHMIC SUBCASE OF RISCH'S INTEGRATION ALGORITHM")$
  33. (LOG(X)-1)/(LOG(X)^2-X^2);
  34. INTEGRATE(%,X);  
  35. title("TAYLOR SERIES EXAMPLE")$
  36. SIN(X+A*X^3);   
  37. TAYLOR(%,X,0,19);
  38. title("TAYLOR SERIES EXAMPLE - PUISEUX")$
  39. SQRT(LOG(1+X)+SIN(X));
  40. TAYLOR(%,X,0,17); 
  41. title("MACSYMA to FORTRAN conversion - optimized routine not yet available")$
  42. EXP:-GAMMA^5+DELTA*GAMMA^4+2*DELTA^2*GAMMA^3-ALPHA^3*GAMMA^3-3*ALPHA^2*GAMMA^3
  43. -3*ALPHA*GAMMA^3-GAMMA^3-2*DELTA^3*GAMMA^2+3*ALPHA^3*DELTA*GAMMA^2
  44. +9*ALPHA^2*DELTA*GAMMA^2+9*ALPHA*DELTA*GAMMA^2+3*DELTA*GAMMA^2
  45. +ALPHA^2*GAMMA^2-2*ALPHA*GAMMA^2+GAMMA^2-DELTA^4*GAMMA-3*ALPHA^3*DELTA^2*GAMMA
  46. -9*ALPHA^2*DELTA^2*GAMMA-9*ALPHA*DELTA^2*GAMMA-3*DELTA^2*GAMMA
  47. +2*ALPHA^2*DELTA*GAMMA-4*ALPHA*DELTA*GAMMA+2*DELTA*GAMMA+DELTA^5
  48. +ALPHA^3*DELTA^3+3*ALPHA^2*DELTA^3+3*ALPHA*DELTA^3+DELTA^3+ALPHA^2*DELTA^2
  49. -2*ALPHA*DELTA^2+DELTA^2+ALPHA^5+ALPHA^4-2*ALPHA^3-2*ALPHA^2+ALPHA+1;
  50. FORTRAN(%);
  51. FACTORSUM(EXP);
  52. FORTRAN(%);
  53. title("BIGNUM ARITHMETIC AND ARBITRARY PRECISION FLOATING POINT ARITHMETIC")$
  54. 6427752177035961102167848369364650410088811975131171341205503;
  55. %^5;
  56. 2535301200456458802993406410751;
  57. %TH(3)/%;
  58. SQRT(%PI),NUMER;
  59. FPPREC:50;
  60. BFLOAT(SQRT(%PI));
  61. /* at the moment this runs pretty slowly but would be a nice example of bignums
  62. title("LARGE NUMBERS - THE LARGEST KNOWN PRIME NUMBER")$
  63. 2^(44497)-1; */
  64. title("VANDERMOND'S MATRIX")$
  65. MAT1:MATRIX([1,X,X^2,X^3],[1,Y,Y^2,Y^3],[1,Z,Z^2,Z^3],[1,W,W^2,W^3]);
  66. FACTOR(DETERMINANT(MAT1));
  67. MINOR(MAT1,4,4);
  68. %^^-1,FACTOR;
  69. title("SOLVING ALGEBRAIC EQUATIONS")$
  70. Q^2*X^2+P^2*Q*X-P*Q*X-P^3=0;
  71. SOLVE(%,X);
  72. title("APPLICATION OF CUBIC FORMULA")$
  73. (BREAKUP:FALSE,EQ:4*X^3+A*X+10*B= 0);
  74. H:SOLVE(EQ,X)$
  75. FIRST_ROOT:FIRST(H);
  76. SECOND_ROOT:PART(H,2);
  77. THIRD_ROOT:LAST(H);
  78. title("SOLUTION OF SET OF SIMULTANEOUS LINEAR EQUATIONS")$
  79. [3*A+5*B+7*C+11*D+13*E=17*R,19*A+23*B+29*C+31*D+37*E=41*S,43*A+47*B+53*C+59*D+61*E=67*T,
  80. 71*A+73*B+79*C+83*D+89*E=97*X,101*A+103*B+107*C+109*D+113*E=127*Y];
  81. SOLVE(%,[A,B,C,D,E]);
  82. title("SOLUTION OF SET OF SIMULTANEOUS NON-LINEAR EQUATIONS")$
  83. [X*Y*Z = 42,-Z+Y+X = -2,-3*Z+2*Y+3*X = -9];
  84. SOLVE(%);
  85. title("FINDING EIGENVALUES")$
  86. MATRIX([0,6,-10,-8],[6,0,8,10],[-10,8,15*A,6],[-8,10,6,15*A]);
  87. SOLVE(CHARPOLY(%,L),L);
  88. title("TWO DIMENSIONAL PLOT")$ 
  89. PLOTNUM:100$
  90. PLOT(X*SIN(X^2),X,0,4,PLOT(X*SIN(X^2),X,0,4));
  91. title("TWO DIMENSIONAL PARAMETRIC PLOT")$
  92. PLOTNUM:400;
  93. PARAMPLOT(S*SIN(S),S*COS(S),S,0,80,PARAMPLOT(S*SIN(S),S*COS(S),S,0,80));
  94. title("THREE DIMENSIONAL CARTESIAN PLOT OF A BESSEL FUNCTION")$
  95. PLOTNUM:20$
  96. PLOT3D(J0(SQRT(X^2+Y^2)),X,-12,12,Y,-12,12,PLOT3D(J0(SQRT(X^2+Y^2)),X,-12,12,Y,-12,12));
  97. title("THREE DIMENSIONAL POLAR PLOT OF THE SAME BESSEL FUNCTION")$
  98. PLOT3D(J0(R),TH,0,2*%PI,R,0,12,POLAR,PLOT3D(J0(R),TH,0,2*%PI,R,0,12,POLAR));
  99. title("THREE DIMENSIONAL PLOT OF X*EXP(-X^2-Y^2)")$
  100. PLOT3D(X*EXP(-X^2-Y^2),X,-2,2,Y,-2,2,PLOT3D(X*EXP(-X^2-Y^2),X,-2,2,Y,-2,2));
  101.  
  102.