Cannot compute Gröbner fan when ring variables contain each other as prefixes

[33faf789-25dd-432b-a36a-7506f5d99583]

Trying to compute a Gröbner fan over a ring in which one variable name contains the other as a prefix gives the following error:

sage: P = PolynomialRing(QQ,3*5,"x"); x = P.gens(); M = Matrix(3,x)
sage: M
[ x0  x1  x2  x3  x4]
[ x5  x6  x7  x8  x9]
[x10 x11 x12 x13 x14]
sage: I = P.ideal(M.minors(2))
sage: I.groebner_fan()
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
...
RuntimeError: Ring variables cannot contain each other as prefixes 

This was brought up in comments on ticket #20146 (now closed), but doesn't seem to have its own ticket.

Component: commutative algebra

Keywords: Gröbner basis, Gröbner fan, gfan, sd90

Author: Caitlin Lienkaemper

Issue created by migration from https://trac.sagemath.org/ticket/24093

[33faf789-25dd-432b-a36a-7506f5d99583]

Changed keywords from Gröbner basis, Gröbner fan, gfan to Gröbner basis, Gröbner fan, gfan, sd90

[fchapoton]

comment:2

Minimal case:

sage: R = PolynomialRing(QQ, 'x1,x11')
sage: I = R.ideal(R.gens())
sage: I.groebner_fan()