Changes between Version 8 and Version 9 of Ticket #23621


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Timestamp:
12/07/21 16:03:20 (8 months ago)
Author:
slelievre
Comment:

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  • Ticket #23621

    • Property Cc slelievre added
    • Property Keywords ideal added
    • Property Milestone changed from sage-8.1 to sage-9.5
    • Property Summary changed from Quotients of univariate polynomial rings over ZZ return mathematical incorrect answers to Fix quotients of univariate polynomial rings over ZZ
  • Ticket #23621 – Description

    v8 v9  
     1The quotient of `ZZ[x]` by the ideal `(x, 2)`
     2works fine using a multivariate polynomial ring:
     3{{{
     4sage: R.<x> = PolynomialRing(ZZ, 1)
     5sage: I = R.ideal([x, 2])
     6sage: I
     7Ideal (x, 2) of Multivariate Polynomial Ring in x over Integer Ring
     8sage: S = R.quo(I)
     9sage: [[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}}}
     12but it fails using a univariate polynomial ring,
     13returning mathematically wrong answers:
    114{{{
    215sage: R.<x> = ZZ[]
    3 sage: I = R.ideal([x,2]); I
     16sage: I = R.ideal([x, 2])
     17sage: I
     18Ideal (x, 2) of Univariate Polynomial Ring in x over Integer Ring
    419sage: 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
     20sage:
     21sage: [[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]]
    1123}}}
    12 
    13 Note that if you create the quotient as a multivariate polynomial ring, then it works fine!
    14 
     24Expected:
    1525{{{
    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]]
    2427}}}