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Text File  |  1996-10-11  |  1.6 KB  |  112 lines
  1. #LAPLACE
  2. #USEFLOAT=FALSE
  3. #USEERROR=TRUE
  4. #SIMPLIFY=TRUE
  5. #ERRBND=15
  6. #EXPDSP=6
  7. #PREC=4
  8. #F1=f(x)=
  9. #F2=g(x)=
  10. #F3=h(x)=f(x)/g(x)
  11. #F4=matrix(
  12. #F5=vector(
  13. #F6=diff(f)
  14. #F7=diff(g)
  15. #F8=diff(h)
  16. #F9=taylor(f,0)
  17. #F10=taylor(f,1)
  18. #F11=%(run type s:startup-sequence)
  19. #F12=
  20. #F13=
  21. #F14=
  22. #F15=
  23. #F16=
  24. #F17=
  25. #F18=
  26. #F19=
  27. #F20=
  28. ; complex numbers
  29. a=3+4*i,b=12+13*i
  30. arc(a)
  31. 2^a,a^2,a^b,b^a
  32. a*b,a/b,1/a
  33. abs(a),conj(a)
  34. ln(b),log(a),exp(a),sqrt(i)
  35. sin(a),cos(a),tan(a),cot(a)
  36. sinh(a),cosh(a),tanh(a)
  37. asin(a),acos(a),atan(a),acot(a)
  38. asinh(a),acosh(a),atanh(a)
  39.  
  40. ; set manipulation
  41. A=set(1,3,5,6,4,2,4,6,7)
  42. count(A),average(A),error(A),sigma(A)
  43. A+1, 1+A, A*2, 2*A
  44. B=set([1,2,3],[3,4,5],[5,6,6],[7,8,9])
  45. B+[1,3,5],B×[1,3,5],[1,3,5]×B
  46.  
  47. ; constants
  48. i^2,i^3,i^4,i^5
  49. ln(e),sin(pi),cos(pi)
  50. const(x)
  51. sin(x+pi),sin(x+2*pi),cos(x+pi),cos(x-pi)
  52.  
  53.  
  54. ; equations
  55. const(x)
  56. A=eq(x^2,2)
  57. sqrt(A),sin(A)
  58. A+1,1+A,2*A,A*2
  59. A^2,e^A
  60.  
  61. ; matrix
  62. A=[1,2,3;4,5,6;7,8,9]
  63. B=[4,7,5;1,8,9;7,5,1]
  64. A*B,B*A
  65. invert(B)
  66. det(B),spur(A)
  67. spur(A*B),spur(B*A)
  68. solve(A)
  69. rank(A)
  70. solve(B)
  71. rank(B)
  72. cvector(A,1),rvector(A,2)
  73. B'=orthogonal(B)
  74. cvector(B',1) *cvector(B',2)
  75. cvector(B',2) *cvector(B',3)
  76. cvector(B',1) *cvector(B',3)
  77. B''=norm(B')
  78. eval(cvector(B'',1) *cvector(B'',2))
  79. eval(cvector(B'',1) *cvector(B'',3))
  80. eval(cvector(B'',2) *cvector(B'',3))
  81. x=[10,20,30]
  82. A*x
  83. C=combine(B,x)
  84. solve(C)
  85.  
  86. ; functions
  87. f(x)=sin(x)*cos(x)
  88. f'(x)=diff(f,x)
  89. f''(x)=diff(f',x)
  90. f''(x)=diff(diff(f,x),x)
  91. g(x)=diff(x^2,x)
  92. h(x)=diff(cos(x)*tan(x)/sqrt(x),x)
  93. a(x)=cos(x)
  94. a(x)=taylor(a,x,0,6)
  95. b(x)=taylor(ln(x),x,0,2)
  96.  
  97. ; error distribution
  98. a=10±2, b=20±2.4
  99. a*b,a+b,a*a,a^2
  100. eval(atan(a))
  101.  
  102. ; references
  103. a:=3
  104. f(x)=a*x^2
  105. a=4
  106. eval(f(a))
  107. f(2)
  108. f(a)
  109. a:=3
  110. f(a)
  111.  
  112.