share/contrib/format/coeflist.demo

   1 /* -*- Mode: Macsyma -*- */
   2
   3 /*************************************************************************************
   4   Demo of Coeflist package.
   5   This package defines tools for extracting coefficients of polynomials,
   6   trigonometric sums and power and Taylor series
   7 *************************************************************************************/
   8
   9 /* COEFFS: Coefficients of Polynomials */
  10
  11 coeffs(a+b*x^2*y+c*x^3*y^2+d*x^4,x);
  12
  13 ptest : (a+b*x^2*y+c*x^3*y^2+d*x^4)^2 + (d*y+c*x^2+a*x^4)^2$
  14 ctest:coeffs(ptest,x);
  15 coeffs(ptest,x,y);
  16
  17 /* GET_COEF finds a particular coefficient.  UNCOEF rebuilds the result. */
  18 get_coef(ctest,3);
  19 ratsimp(ptest-uncoef(ctest));
  20
  21 /* Stretching the definition of Polynomials: */
  22 coeffs(x^m*(x+x^2+x^m)+x^(2*m),x);
  23
  24 nptest:(a+b*sin(x)*x^2)^3$
  25 coeffs(nptest,x);
  26
  27 /* Partitioning a polynomial: */
  28 partition_poly(ptest,'evenp,x);
  29
  30 /* TRIG_COEFFS: Trigonometric series */
  31 trig_coeffs(a*cos(x+y)+b*sin(x+2*y),x);
  32
  33 ftest : (a*cos(x+y)+b*sin(x+2*y))^2+(a*cos(x-y)+b*cos(2*x+3*y))^2$
  34 trig_coeffs(ftest,x);
  35 trig_coeffs(ftest,x,y);
  36
  37 /* SERIES_COEFFS & TAYLOR_COEFFS: Power Series & Taylor series*/
  38 series_coeffs(ptest,x,4);
  39 Taylor_coeffs(ptest,x,4);
  40 /* Notice Series only expands over arithmetic: */
  41 series_coeffs(nptest,x,4);
  42 Taylor_coeffs(nptest,x,4);
  43
  44 /* Alternative specification of variables */
  45 sqrtp(s) := not(atom(s)) and op(s)='sqrt$
  46 coeffs(a+sqrt(1+b)+c,match('sqrtp));
  47 coeffs(a*log(x)+log(y)*log(x),operator(log));
  48
  49 /* Additional Utilities: */
  50 matching_parts(a+sqrt(1+b)+c,'sqrtp);
  51 function_calls(a*log(x)+log(y)*log(x),log);
  52 function_arguments(a*log(x)+log(y)*log(x),log);
  53
  54 /* Clean up*/
  55 (remvalue(ptest,ctest,nptest,ftest),remfunction(sqrtp))$