[167] in mathematical software users group
grobner basis question
daemon@ATHENA.MIT.EDU (sywong@MIT.EDU)
Sun May 28 14:36:33 1995
From: sywong@MIT.EDU
To: msug@MIT.EDU
Reply-To: msug@MIT.EDU
Date: Sun, 28 May 1995 14:35:36 EDT
Dear MSUGers,
I've been trying to perform some grobner basis calculation with Maple V.3
and I got some strange error message. I have an ideal generated by two
polynomials G1, G2, with variables t,x,a,b. With I type
gbasis([G1,G2], [t,x,a,b], plex);
Maple keeps complaining that
Error, (in grobner/iplex/reduce) cannot evaluate boolean
On the other hand, if I compute just
gbasis([G1], [t,x,a,b], plex);
(or with [G2]) then I get no error message (and the expected answer).
What is going on?
I've enclosed the actual Maple session plus the input file "bup2". Any
comments/suggestions are appreciated!
By the way, if I use some other polynomials for G1, G2 than the
calculation seems to work out. What is going on????
Thanks!
Siman Wong
****** here is the Maple session ******
> maple
|\^/| Maple V Release 3 (Massachusetts Institute of Technology)
._|\| |/|_. Copyright (c) 1981-1994 by Waterloo Maple Software and the
\ MAPLE / University of Waterloo. All rights reserved. Maple and Maple V
<____ ____> are registered trademarks of Waterloo Maple Software.
| Type ? for help.
> read bup2;
> with(grobner):
> gbasis([G1], [t,x,a,b], plex);
2 2 2 2 3 2 3 2 4 2 4 2 3 2 2
[8 t x b - 4 t x a + 4 t x b + 2 t a + 4 t b + 8 t x - 4 t x
2 2 2 2 3 2 2 2
+ 6 t x + 8 x a + 16 a b + 4 I x - 8 I b - 4 t x a + 6 t x a
2 3 2 3 2 2 2 2 3 2 2
- 8 t x b - 8 t a b + 12 t a b - 8 t a b + 4 t x a - 12 t x b
2 2 2 4 2 2 2 2 2 2
- 4 t x a - 8 t x b + t x - 3 t - 4 x - 8 a - 8 b + 8 t x a b
2 2 2 3 3 3
- 12 t x a b + 16 t x a b - 8 t a b + 8 t b - 4 I t x + 8 I t a
3 2 2 2
- 8 I t b - 8 I x a + 16 I x b + 12 I t x a - 12 I t x b - 12 I t x a
2 2
+ 16 I t x a b - 24 I t a b + 24 I t a b ]
> maple
|\^/| Maple V Release 3 (Massachusetts Institute of Technology)
._|\| |/|_. Copyright (c) 1981-1994 by Waterloo Maple Software and the
\ MAPLE / University of Waterloo. All rights reserved. Maple and Maple V
<____ ____> are registered trademarks of Waterloo Maple Software.
| Type ? for help.
> read bup2;
> with(grobner):
> gbasis([G1], [t,x,a,b], plex);
2 2 2 2 3 2 3 2 4 2 4 2 3 2 2
[8 t x b - 4 t x a + 4 t x b + 2 t a + 4 t b + 8 t x - 4 t x
2 2 2 2 3 2 2 2
+ 6 t x + 8 x a + 16 a b + 4 I x - 8 I b - 4 t x a + 6 t x a
2 3 2 3 2 2 2 2 3 2 2
- 8 t x b - 8 t a b + 12 t a b - 8 t a b + 4 t x a - 12 t x b
2 2 2 4 2 2 2 2 2 2
- 4 t x a - 8 t x b + t x - 3 t - 4 x - 8 a - 8 b + 8 t x a b
2 2 2 3 3 3
- 12 t x a b + 16 t x a b - 8 t a b + 8 t b - 4 I t x + 8 I t a
3 2 2 2
- 8 I t b - 8 I x a + 16 I x b + 12 I t x a - 12 I t x b - 12 I t x a
2 2
+ 16 I t x a b - 24 I t a b + 24 I t a b ]
> gbasis([G2], [t,x,a,b], plex);
4 4 3 2 4 3 2 2
[2 t a + 4 t b + 8 t x - 4 t x + 6 t x + t x + 4 b - 3 t + 8 t x b
3 3 3 2 2 3 3
- 4 t x a + 4 t x b - 4 t x a + 6 t x a - 8 t x b - 8 t a b
2 2 3 2 2 2 2 2
+ 12 t a b - 8 t a b + 2 x a - 6 x b - 2 x a - 4 x b - 4 a b
3 3 3 2 2 2
- 2 I x + 4 I a - 4 I b + 8 t x a b - 12 t x a b + 8 x a b + 6 I x a
2 2 2 2
- 6 I x b - 6 I x a + 8 I x a b - 12 I a b + 12 I a b ]
> gbasis([G1,G2], [t,x,a,b], plex);
Error, (in grobner/iplex/reduce) cannot evaluate boolean
> infolevel[grobner] := 55;
> gbasis([G1,G2], [t,x,a,b], plex);
grobner/iplex/grob: pure lexicographic ordering in effect
grobner/iplex/hred: t^2*x^4 head-reduced to t*x^3 w.r.t..([t*x^4])
grobner/iplex/reduce: time 1.700 , elapsed .34e-1
Error, (in grobner/iplex/reduce) cannot evaluate boolean
> quit
bytes used=508172, alloc=393144, time=1.72
******* input file "bup2" ********
G1 := -t^2*x^4+4*t^2*x^3*a-4*t^2*x^3*b-6*t^2*x^2*a^2+12*t^2*x^2*a*b-8*t^2*x^2*b^2+4*t
^2*x*a^3-8*t^2*x*a^2*b+8*t^2*x*b^3-2*t^2*a^4+8*t^2*a^3*b-12*t^2*a^2*b^2+8*t^2*a
*b^3-4*t^2*b^4-8*t^2*x^3+4*t^2*x^2+4*I*t*x^3-4*t*x^2*a-12*I*t*x^2*a+12*t*x^2*b+
12*I*t*x^2*b+12*I*t*x*a^2+4*t*x*a^2-16*t*x*a*b-16*I*t*x*a*b+8*t*x*b^2-8*I*t*a^3
+24*I*t*a^2*b+8*t*a*b^2-24*I*t*a*b^2+8*I*t*b^3-8*t*b^3-6*t^2*x+3*t^2+4*x^2-4*I*
x^2-8*x*a+8*I*x*a-16*I*x*b+8*a^2-16*a*b+8*I*b^2+8*b^2:
G2 := diff(G1, t):
***** end ******
