Opened 3 years ago

#26318 new defect

reduced form of polynomial modulo an ideal is broken for non default orderings

Reported by: mmarco Owned by:
Priority: major Milestone: sage-8.4
Component: interfaces Keywords:
Cc: SimonKing, tscrim, malb, john_perry, vbraun Merged in:
Authors: Miguel Marco Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

The expected behaviour of reducing a polynomial modulo an ideal is

sage: R.<x,y,z> = QQ[]
sage: I = R.ideal([y+z])
sage: I.reduce(x)
x
sage: I.reduce(y)
-z
sage: I.reduce(x+y)
x - z

But if we use an order which is not the default one, we get something that is not a normal form (even if the order is global):

sage: R.<x,y,z> = PolynomialRing(QQ,order='lex')
sage: I = R.ideal([y+z])
sage: I.reduce(x)
x
sage: I.reduce(y)
-z
sage: I.reduce(x+y)
x + y

This is a bug. In fact, Singular handles this correctly:

> ring r = 0,(x,y,z),lp;
> ideal i = y-z;
> reduce(x,i);
x
> reduce(y,i);
z
> reduce(x+y,i);
x+z

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