Opened 17 months ago

#863 new bug

In groebner, don't use hilb if there are too many variables

Reported by: Ricardo Buring <ricardo.buring@…> Owned by: somebody
Priority: minor Milestone: 4-2-0 and higher
Component: dontKnow Version: 4-1-1
Keywords: groebner, stdhilb, hilb Cc:

Description

The function hilb doesn't work when there are (in some sense) too many variables. This causes the following:

> ring r=2, (x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34), lp;
> ideal i = x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34;
> groebner(i);
   ? int overflow in hilb 4
   ? error occurred in or before standard.lib::stdhilb line 299: `    intvec hi = hilb( Id(1),1,W );`
   ? expected intvec-expression. type 'help intvec;'
   ? leaving standard.lib::stdhilb
   skipping text from `)` error at token `)`
   ? leaving standard.lib::groebner

This seems avoidable. For example, "never use hilb when the ring has more than 33 variables" seems like it would be sufficient, though there may be a better criterion. It would also be good to document this limitation of hilb.

This was previously brought up in a forum post computing an ideal radical (with a silly workaround), and it is the source of a problem in SageMath which I would like to see fixed.

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