home *** CD-ROM | disk | FTP | other *** search
/ Enter 2004 January / enter-2004-01.iso / files / maxima-5.9.0.exe / {app} / share / maxima / 5.9.0 / tests / rtest5.mac < prev    next >
Encoding:
Text File  |  2003-02-09  |  2.6 KB  |  112 lines
  1. /*************** -*- Mode: MACSYMA; Package: MAXIMA -*-  ******************/
  2. /***************************************************************************
  3. ***                                                                    *****
  4. ***     Copyright (c) 1984 by William Schelter,University of Texas     *****
  5. ***     All rights reserved                                            *****
  6. ***************************************************************************/
  7.  
  8.  
  9. KILL(ALL);
  10. DONE$
  11. PARTITION(2*A*X*F(X),X);
  12. [2*A,X*F(X)]$
  13. PARTITION(A+B,X);
  14. [B+A,0]$
  15. 2*(A*LOG(X)+2*A*LOG(Y));
  16. 2*(2*A*LOG(Y)+A*LOG(X))$
  17. LOGCONTRACT(%);
  18. A*LOG(X^2*Y^4)$
  19. LOGCONTRACT(LOG(SQRT(X+1)+SQRT(X))+LOG(SQRT(X+1)-SQRT(X)));
  20. 0$
  21. ROOTSCONMODE:FALSE;
  22. FALSE$
  23. ROOTSCONTRACT(X^(1/2)*Y^(3/2));
  24. SQRT(X*Y^3)$
  25. ROOTSCONTRACT(X^(1/2)*Y^(1/4));
  26. SQRT(X)*Y^(1/4)$
  27. ROOTSCONMODE:TRUE;
  28. TRUE$
  29. ROOTSCONTRACT(X^(1/2)*Y^(1/4));
  30. SQRT(X*SQRT(Y))$
  31. ROOTSCONTRACT(X^(1/2)*Y^(1/3));
  32. SQRT(X)*Y^(1/3)$
  33. ROOTSCONMODE:ALL;
  34. ALL$
  35. ROOTSCONTRACT(X^(1/2)*Y^(1/4));
  36. (X^2*Y)^(1/4)$
  37. ROOTSCONTRACT(X^(1/2)*Y^(1/3));
  38. (X^3*Y^2)^(1/6)$
  39. ROOTSCONMODE:FALSE;
  40. FALSE$
  41. ROOTSCONTRACT(SQRT(SQRT(X+1)+SQRT(X))*SQRT(SQRT(X+1)-SQRT(X)));
  42. 1$
  43. ROOTSCONMODE:TRUE;
  44. TRUE$
  45. ROOTSCONTRACT(SQRT(SQRT(5)+5)-5^(1/4)*SQRT(SQRT(5)+1));
  46. 0$
  47. KILL(F,G,H,X,Y);
  48. DONE$
  49. DIFF(SIN(X)+X^3+2*X^2,X);
  50. COS(X)+3*X^2+4*X$
  51. DIFF(SIN(X)*COS(X),X);
  52. COS(X)^2-SIN(X)^2$
  53. DIFF(SIN(X)*COS(X),X,2);
  54. -4*COS(X)*SIN(X)$
  55. DERIVABBREV:TRUE;
  56. TRUE$
  57. DIFF(EXP(F(X)),X,2);
  58. %E^F(X)*'DIFF(F(X),X,2)+%E^F(X)*('DIFF(F(X),X,1))^2$
  59. 'INTEGRATE(F(X,Y),Y,G(X),H(X));
  60. 'INTEGRATE(F(X,Y),Y,G(X),H(X))$
  61. DIFF(%,X);
  62. 'INTEGRATE('DIFF(F(X,Y),X,1),Y,G(X),H(X))
  63.  +F(X,H(X))*'DIFF(H(X),X,1)-F(X,G(X))*'DIFF(G(X),X,1)$
  64. KILL(A,X,F,Y,T);
  65. DONE$
  66. DEPENDS(A,X);
  67. [A(X)]$
  68. DIFF(A . A,X);
  69. 'DIFF(A,X,1) . A+A . 'DIFF(A,X,1)$
  70. DEPENDS(F,[X,Y],[X,Y],T);
  71. [F(X,Y),X(T),Y(T)]$
  72. DIFF(F,T);
  73. 'DIFF(F,Y,1)*'DIFF(Y,T,1)+'DIFF(F,X,1)*'DIFF(X,T,1)$
  74. DEPENDS(Y,X);
  75. [Y(X)]$
  76. KILL(F,G,J);
  77. DONE$
  78. GRADEF(F(X,Y),X^2,G(X,Y));
  79. F(X,Y)$
  80. DIFF(F(X,Y),X);
  81. G(X,Y)*'DIFF(Y,X,1)+X^2$
  82. GRADEF(J(N,Z),'DIFF(J(N,Z),N),J(N-1,Z)-N/Z*J(N,Z));
  83. J(N,Z)$
  84. RATSIMP(DIFF(J(2,X),X,2));
  85. (J(0,X)*X^2-3*J(1,X)*X+6*J(2,X))/X^2$
  86. TEST(F):=BLOCK([U],U:INTEGRATE(F,X),RATSIMP(F-DIFF(U,X)));
  87. TEST(F):=BLOCK([U],U:INTEGRATE(F,X),RATSIMP(F-DIFF(U,X)))$
  88. TEST(SIN(X));
  89. 0$
  90. TEST(1/(1+X));
  91. 0$
  92. TEST(1/(1+X^2));
  93. 0$
  94. INTEGRATE(SIN(X)^3,X);
  95. COS(X)^3/3-COS(X)$
  96. KILL(Q);
  97. DONE$
  98. INTEGRATE(%E^X/(%E^X+2),X);
  99. LOG(%E^X+2)$
  100. INTEGRATE(1/(X*LOG(X)),X);
  101. LOG(LOG(X))$
  102. INTEGRATE(SIN(2*X+3),X);
  103. -COS(2*X+3)/2$
  104. INTEGRATE(%E^X*ERF(X),X);
  105. %E^X*ERF(X)-%E^(1/4)*ERF(X-1/2)$
  106. INTEGRATE(X/(X^3+1),X);
  107. LOG(X^2-X+1)/6+ATAN((2*X-1)/SQRT(3))/SQRT(3)-LOG(X+1)/3$
  108. DIFF(%,X);
  109. 2/(3*((2*X-1)^2/3+1))+(2*X-1)/(6*(X^2-X+1))-1/(3*(X+1))$
  110. RATSIMP(%);
  111. X/(X^3+1)$
  112.