Mon Jan 4 00:16:16 MET 1999
REDUCE 3.7, 15-Jan-99 ...
1: 1:
2: 2: 2: 2: 2: 2: 2: 2: 2:
3: 3: % 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;
4: 4: 4: 4: 4: 4: 4: 4: 4:
Time for test: 420 ms
5: 5:
Quitting
Mon Jan 4 00:16:17 MET 1999