Status: New
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 2456 by [email protected]: bug in polytools.groebner
http://code.google.com/p/sympy/issues/detail?id=2456
groebner does not give the groebner basis in monic form.
sdp_groebner does, but then polytools.groebner changes the normalizazion
when domain.has_Field is False.
see e.g. the cyclic5 lex example:
from sympy import *
x0,x1,x2,x3,x4 = X = symbols('x0,x1,x2,x3,x4')
I = [x0 + x1 + x2 + x3 + x4, x0*x1 + x0*x4 + x1*x2 + x2*x3 + x3*x4,
x0*x1*x2 + x0*x1*x4 + x0*x3*x4 + x1*x2*x3 + x2*x3*x4, x0*x1*x2*x3 +
x0*x1*x2*x4 + x0*x1*x3*x4 + x0*x2*x3*x4 + x1*x2*x3*x4, x0*x1*x2*x3*x4 -
1]
G = groebner(I, X, order='lex')
G[1]
275*x1**2 + 825*x1*x4 + 550*x3**6*x4 + 1650*x3**5*x4**2 + 275*x3**4*x4**3 -
550*x3**3*x4**4 + 275*x3**2 - 566*x3*x4**11 - 69003*x3*x4**6 + 69019*x3*x4
- 1467*x4**12 - 178981*x4**7 + 179073*x4**2
instead x1**2 should be normalized to 1
Setting by hand domain.has_Field = True one gets the correct normalization;
this function should find that for this example domain.has_Field = True.
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