REDUCE 3.4, 15-Jul-91 ...
1:
(WU)
% wu.tst
% Russell Bradford, 8 June 90.
% Some tests for the Wu algorithm
% The order directives are not necessary for general use: they just
% help tie things down for testing purposes.
% run after loading Wu code: in "wu.red"$
% test 1
order x,y,a,b;
wu({x^2+y^2-a,x*y-b}, {x,y});
4 2 2
{{{ - Y + Y *A - B , - X*Y + B},
Y}}
% test 2
order x,y,a,b;
wu({x^2+y^2-a,x*y-b},{x,y,a,b});
2
{{{B,Y, - X + A},1},
4 2 2
{{ - Y + Y *A - B , - X*Y + B},
Y}}
% test 3
order x,y,z,r;
wu({x^2+y^2+z^2-r^2, x*y+z^2-1, x*y*z-x^2-y^2-z+1}, {x,y,z});
3 2 2
{{{Z - Z + R - 1,
4 2 2 2 2 2 2 2
- Y - Y *Z + Y *R + Z + Z*R - Z + R - 2,
2
X*Y + Z - 1},
Y},
7 6 5 4 2 4 3 2 2 2 2
{{Z - Z - 2*Z + Z *R + Z + Z - 2*Z *R + Z + R - 1,
2 3 2 2
Y *(Z - Z + R - 1),
2
X*Y + Z - 1},
3 2 2
Y*(Z - Z + R - 1)}}
% test 4
order x,y,z,r;
wu({x^2+y^2+z^2-r^2, x*y+z^2-1, x*y*z-x^2-y^2-z+1}, {x,y,z,r});
3 2 2
{{{Z - Z + R - 1,
4 2 2 2 2 2 2 2
- Y - Y *Z + Y *R + Z + Z*R - Z + R - 2,
2
X*Y + Z - 1},
Y},
4 2
{{R - 4*R + 3,
2
Z + R - 2,
Y,
2 2
- X + R - 1},
1},
7 6 5 4 2 4 3 2 2 2 2
{{Z - Z - 2*Z + Z *R + Z + Z - 2*Z *R + Z + R - 1,
2 3 2 2
Y *(Z - Z + R - 1),
2
X*Y + Z - 1},
3 2 2
Y*(Z - Z + R - 1)}}
% test 5
order x,y,z;
wu({(x-1)*(y-1)*(z-1), (x-2)*(y-2)*(z-2), (x-3)*(y-3)*(z-3)}, {x,y,z});
2
{{{Z - 5*Z + 6,
2 2
2*(Y *Z - 3*Y - 4*Y*Z + 12*Y + 3*Z - 9),
X*Y*Z - 3*X*Y - 3*X*Z + 9*X - 3*Y*Z + 9*Y + 9*Z - 27},
2 2
2*(Y*Z - 6*Y*Z + 9*Y - 3*Z + 18*Z - 27)},
{{Z - 3,Y - 2,2*(X - 1)},2},
2
{{Z - 3,2*(Y - 3*Y + 2),X*Y - 2*X - 2*Y + 4},
2*(Y - 2)},
{{2*(Z - 3),2*(Y - 2),4*(X - 1)},16},
2
{{2*(Z - 3),4*(Y - 3*Y + 2),2*(X*Y - 2*X - 2*Y + 4)},
16*(Y - 2)},
2
{{Z - 5*Z + 6,
Y*Z - 3*Y - 3*Z + 9,
2*(X*Z - 3*X - Z + 3)},
2
2*(Z - 6*Z + 9)},
3 2
{{2*(Z - 6*Z + 11*Z - 6),
Y*Z - 3*Y - 3*Z + 9,
2 2
X*Z - 5*X*Z + 6*X - 2*Z + 10*Z - 12},
3 2
2*(Z - 8*Z + 21*Z - 18)},
3 2
{{4*(Z - 6*Z + 11*Z - 6),
2 2 2 2 2 2
Y *Z - 5*Y *Z + 6*Y - 5*Y*Z + 25*Y*Z - 30*Y + 6*Z - 30*Z + 36,
X*Y*Z - 3*X*Y - 3*X*Z + 9*X - 3*Y*Z + 9*Y + 9*Z - 27},
3 2 3 2
4*(Y*Z - 8*Y*Z + 21*Y*Z - 18*Y - 3*Z + 24*Z - 63*Z + 54)}}
% test 6
order x,y,z;
wu({(x-1)*(y-1)*(z-1), (x-2)*(y-2)*(z-2), (x-3)*(y-3)*(z-3)});
2
{{{Z - 5*Z + 6,
2 2
2*(Y *Z - 3*Y - 4*Y*Z + 12*Y + 3*Z - 9),
X*Y*Z - 3*X*Y - 3*X*Z + 9*X - 3*Y*Z + 9*Y + 9*Z - 27},
2 2
2*(Y*Z - 6*Y*Z + 9*Y - 3*Z + 18*Z - 27)},
{{Z - 3,Y - 2,2*(X - 1)},2},
2
{{Z - 3,2*(Y - 3*Y + 2),X*Y - 2*X - 2*Y + 4},
2*(Y - 2)},
{{2*(Z - 3),2*(Y - 2),4*(X - 1)},16},
2
{{2*(Z - 3),4*(Y - 3*Y + 2),2*(X*Y - 2*X - 2*Y + 4)},
16*(Y - 2)},
2
{{Z - 5*Z + 6,
Y*Z - 3*Y - 3*Z + 9,
2*(X*Z - 3*X - Z + 3)},
2
2*(Z - 6*Z + 9)},
3 2
{{2*(Z - 6*Z + 11*Z - 6),
Y*Z - 3*Y - 3*Z + 9,
2 2
X*Z - 5*X*Z + 6*X - 2*Z + 10*Z - 12},
3 2
2*(Z - 8*Z + 21*Z - 18)},
3 2
{{4*(Z - 6*Z + 11*Z - 6),
2 2 2 2 2 2
Y *Z - 5*Y *Z + 6*Y - 5*Y*Z + 25*Y*Z - 30*Y + 6*Z - 30*Z + 36,
X*Y*Z - 3*X*Y - 3*X*Z + 9*X - 3*Y*Z + 9*Y + 9*Z - 27},
3 2 3 2
4*(Y*Z - 8*Y*Z + 21*Y*Z - 18*Y - 3*Z + 24*Z - 63*Z + 54)}}
% test 7
order x1,x2,x3,x4;
p1 := x1+x2+x3+x4;
P1 := X1 + X2 + X3 + X4
p2 := x1*x2+x2*x3+x3*x4+x4*x1;
P2 := X1*X2 + X1*X4 + X2*X3 + X3*X4
p3 := x1*x2*x3+x2*x3*x4+x3*x4*x1+x4*x1*x2;
P3 := X1*X2*X3 + X1*X2*X4 + X1*X3*X4 + X2*X3*X4
p4 := x1*x2*x3*x4 - 1;
P4 := X1*X2*X3*X4 - 1
wu({p1,p2,p3,p4}, {x1,x2,x3,x4});
4
{{{X4*(X4 - 1),
2
X4 *(X3 - X4),
2 2 2
X4 *(X2 + 2*X2*X4 + X4 ),
2
X4 *(X1 + X2 + 2*X4)},
6
X4 },
4
{{X4 - 1,
2
X4 *(X3 - X4),
2 2
2*X4*(X2 + 2*X2*X4 + X4 ),
2
X4 *(X1 + X2 + 2*X4)},
5
2*X4 },
4
{{X4 - 1,
X3 - X4,
2 2
X2 + 2*X2*X4 + X4 ,
X1 + X2 + 2*X4},
1},
4
{{X4 - 1,
2 2
X3 - X4 ,
2 3 3
X2*X3*X4 - X2*X4 + X3*X4 - 1,
2
X1*X3 - X1*X4 - X3*X4 + X4 },
2 2 2
X4 *(X3 - 2*X3*X4 + X4 )},
8 4
{{X4 - 2*X4 + 1,
2 2
X3 - X4 ,
2 3 3
X2*X3*X4 - X2*X4 + X3*X4 - 1,
4 4
X1*X4 - X1 + X3*X4 - X3},
2 4 5
X4 *(X3*X4 - X3 - X4 + X4)},
2 4
{{X4 *(X4 - 1),
3
X4 *(X3 - X4),
3 2 2
X4 *(X2 + 2*X2*X4 + X4 ),
3
X4 *(X1 + X2 + 2*X4)},
9
X4 },
4
{{X4*(X4 - 1),
3
X4 *(X3 - X4),
2 2 2
2*X4 *(X2 + 2*X2*X4 + X4 ),
3
X4 *(X1 + X2 + 2*X4)},
8
2*X4 },
4
{{X4 - 1,
X4*(X3 - X4),
2 2
X4*(X2 + 2*X2*X4 + X4 ),
X4*(X1 + X2 + 2*X4)},
3
X4 },
4
{{X4*(X4 - 1),
2 2 2
X4 *(X3 - X4 ),
2 3 3
X4*(X2*X3*X4 - X2*X4 + X3*X4 - 1),
2
X4*(X1*X3 - X1*X4 - X3*X4 + X4 )},
6 2 2
X4 *(X3 - 2*X3*X4 + X4 )},
8 4
{{X4*(X4 - 2*X4 + 1),
2 2 2
X4 *(X3 - X4 ),
2 3 3
X4*(X2*X3*X4 - X2*X4 + X3*X4 - 1),
4 4
X4*(X1*X4 - X1 + X3*X4 - X3)},
6 4 5
X4 *(X3*X4 - X3 - X4 + X4)},
3 2 2 3
{{X3 *X4 + X3 *X4 - X3 - X4,
2 2 2 3
X2*X3 - X2*X4 + X3 *X4 - X4 ,
2 2 4 2 3 4
X1*X3 *X4 - X1*X4 - X3 *X4 - X3*X4 + X3 + X4},
4 4 2 2 4
X4 *(X3 - 2*X3 *X4 + X4 )}}
% test 8
order x,y,z;
wu({z*z,y*z-1,x*z-1}, {x,y,z});
{{{1},1}}
end;
Quitting