share/to_poly_solve/rtest_to_poly.mac

   1 (load(to_poly),0);
   2 0$
   3
   4 /* constants and symbols */
   5
   6 to_poly(42);
   7 [[42],[],[]]$
   8
   9 to_poly(42.01);
  10 [[4201],[],[]]$
  11
  12 to_poly(42.01b0);
  13 [[4201],[],[]]$
  14
  15 to_poly(8/3);
  16 [[8],[],[]]$
  17
  18 to_poly(%pi);
  19 [[%pi],[],[]]$
  20
  21 map('first, map('to_poly, [false, true, %i, %phi, minf, inf]));
  22 [[false],[true],[%i],[%phi],[minf],[inf]]$
  23
  24 to_poly(x);
  25 [[x],[],[]]$
  26
  27 to_poly(x,[x]);
  28 [[x],[],[]]$
  29
  30 to_poly(x,[x,y,z]);
  31 [[x],[],[]]$
  32
  33 to_poly(x,[a,b,c]);
  34 [[x],[],[]]$
  35
  36 to_poly(sqrt(5),[]);
  37 [[sqrt(5)],[],[]]$
  38
  39 /* powers */
  40 first(elim_allbut(first(to_poly(sqrt(a)= b)),[a,b]));
  41 [b^2-a]$
  42
  43 first(elim_allbut(first(to_poly(sqrt(a)= sqrt(b))),[a,b]));
  44 [b-a]$
  45
  46 first(elim_allbut(first(to_poly(a^(1/3)= b)),[a,b]));
  47 [b^3-a]$
  48
  49 first(elim_allbut(first(to_poly(a^(1/42)=b)),[a,b]));
  50 [b^42-a]$
  51
  52 first(elim_allbut(first(to_poly(a^(1/4)=b^(1/3))),[a,b]));
  53 [b^4-a^3]$
  54
  55 /* abs */
  56
  57 first(elim_allbut(first(to_poly(abs(a) = b)),[a,b]));
  58 [b^2 - a^2]$
  59
  60 first(elim_allbut(first(to_poly(abs(a) = abs(b))),[a,b]));
  61 [b^2 - a^2]$
  62
  63 first(elim_allbut(first(to_poly(abs(1-abs(1-abs(a))))),[a]));
  64 [a*(a^2-4)]$
  65
  66 /* polynomials */
  67
  68 to_poly(-x);
  69 [[-x],[],[]]$
  70
  71 to_poly(4.3-x);
  72 [[43-10*x],[],[]]$
  73
  74 to_poly((x-1)*(x-2)*(x-3));
  75 [[x^3-6*x^2+11*x-6],[],[]]$
  76
  77 expand(to_poly((x-1)*(x-sqrt(2))*(x-sqrt(3)),[x]));
  78 [[x^3-sqrt(3)*x^2-sqrt(2)*x^2-x^2+sqrt(2)*sqrt(3)*x+sqrt(3)*x+sqrt(2)*x-sqrt(2)*sqrt(3)],[],[]]$
  79
  80 first(first(elim_allbut(first(to_poly((x-1)*(x-sqrt(2))*(x-sqrt(3)),[x,1])),[x])));
  81 (x^2-3)*(x^3-x^2-2*x+2)$
  82
  83 /* regression tests for #4043 bug in to_poly */
  84 first(nicedummies(to_poly((3^(3/2)+5)^(1/3)-(3^(3/2)-5)^(1/3),[1])));
  85 [%g2-%g1,%g0^3+5=%g2^3,%g0^3-5=%g1^3,3=%g0^2]$
  86
  87 factor(first(elim_allbut(first(to_poly(z-(3^(3/2)+5)^(1/3)+(3^(3/2)-5)^(1/3),[1,z])),[z])));
  88 [(z^3-4)*(z^6-80*z^3-128)*(z^6-26*z^3+250)*(z^6+10*z^3-2)]$
  89
  90 /* more tests*/
  91 nicedummies(to_poly(z-2^(1/2),[z,1]));
  92 [[z-%g0,2=%g0^2],[parg(%g0)<=%pi/2,-%pi/2<parg(%g0)],[]]$
  93
  94 nicedummies(to_poly(z-107*2^(1/2),[z,1]));
  95 [[z-107*%g0,2=%g0^2],[parg(%g0)<=%pi/2,-%pi/2<parg(%g0)],[]]$
  96
  97 nicedummies(to_poly(z - sqrt(2) - sqrt(3),[z,1]));
  98 [[z-%g1-%g0,3=%g1^2,2=%g0^2],[parg(%g1)<=%pi/2,-%pi/2<parg(%g1),parg(%g0)<=%pi/2,-%pi/2<parg(%g0)],[]]$
  99
 100 first(nicedummies(to_poly(z - sqrt(2) - sqrt(3),[z,1])));
 101 [z-%g1-%g0,3=%g1^2,2=%g0^2]$
 102
 103 /* make sure we didn't make assignments or assumptions */
 104 [values,facts()];
 105 [[],[]]$