Changes between Version 8 and Version 9 of Ticket #23621
 Timestamp:
 12/07/21 16:03:20 (8 months ago)
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Ticket #23621
 Property Cc slelievre added
 Property Keywords ideal added

Property
Milestone
changed from
sage8.1
tosage9.5

Property
Summary
changed from
Quotients of univariate polynomial rings over ZZ return mathematical incorrect answers
toFix quotients of univariate polynomial rings over ZZ

Ticket #23621 – Description
v8 v9 1 The quotient of `ZZ[x]` by the ideal `(x, 2)` 2 works fine using a multivariate polynomial ring: 3 {{{ 4 sage: R.<x> = PolynomialRing(ZZ, 1) 5 sage: I = R.ideal([x, 2]) 6 sage: I 7 Ideal (x, 2) of Multivariate Polynomial Ring in x over Integer Ring 8 sage: S = R.quo(I) 9 sage: [[S(a) == S(b) for b in (0, 2, x)] for a in (0, 2, x)] 10 [[True, True, True], [True, True, True], [True, True, True]] 11 }}} 12 but it fails using a univariate polynomial ring, 13 returning mathematically wrong answers: 1 14 {{{ 2 15 sage: R.<x> = ZZ[] 3 sage: I = R.ideal([x,2]); I 16 sage: I = R.ideal([x, 2]) 17 sage: I 18 Ideal (x, 2) of Univariate Polynomial Ring in x over Integer Ring 4 19 sage: S = R.quo(I) 5 sage: S(x)==S(0) 6 False 7 sage: S(2)==S(2) 8 True 9 sage: S(2)==S(0) 10 False 20 sage: 21 sage: [[S(a) == S(b) for b in (0, 2, x)] for a in (0, 2, x)] 22 [[True, False, False], [False, True, False], [False, False, True]] 11 23 }}} 12 13 Note that if you create the quotient as a multivariate polynomial ring, then it works fine! 14 24 Expected: 15 25 {{{ 16 sage: R.<x> = PolynomialRing(ZZ,1) 17 sage: I = R.ideal([x,2]); I 18 Ideal (x, 2) of Multivariate Polynomial Ring in x over Integer Ring 19 sage: S = R.quo(I) 20 sage: S(x)==0 21 True 22 sage: S(2)==0 23 True 26 [[True, True, True], [True, True, True], [True, True, True]] 24 27 }}}