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: | |
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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: |

### 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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