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  1.                         SYMBOLIC MATHEMATICS
  2.  
  3. Prolog can be used for solving symbolic and mathematical problems.
  4. Expressions can be modeled by composite objects. (In the program this
  5. is demonstrated by EXPR)
  6.  
  7. In the example, the differentiation is followed by a reduction.
  8.  
  9. The formulas of differentiation are:
  10.  
  11. d(K)/dx      = 0.
  12. d(x)/dx      = 1.
  13. d(y)/dx      = 0.
  14. d(F+G)/dx    = d(F)/dx+d(G)/dx.
  15. d(F-G)/dx    = d(F)/dx-d(G)/dx.
  16. d(F*G)/dx    = G*d(F)/dx+F*d(G)/dx.
  17. d(F/G)/dx    = (F*d(G)/dx-G*d(F)/dx)/G^2
  18. d(F^n)/dx    = n*F^(n-1)*d(F)/dx.
  19. d(ln(F))/dx  = 1/F*d(F)/dx.
  20. d(sin(F))/dx = cos(F)*d(F)/dx.
  21. d(cos(F))/dx = -sin(F)*d(F)/dx.
  22. d(tan(F))/dx = sec(F)^2*d(F)/dx.
  23.  
  24. Differentiation is realized by the predicate DIFF. Two parameters are 
  25. used:
  26.     1) The original expression
  27.     2) The differentiated result
  28.  
  29. Each differentiation-rule has a corresponding rule in the predicate
  30. diff.
  31.