Opened 14 years ago
Closed 14 years ago
#593 closed defect (fixed)
[with patch] MPolynomialIdeal.reduced_basis() doesn't behave as expected
Reported by: | malb | Owned by: | malb |
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Priority: | major | Milestone: | sage-2.8.6 |
Component: | commutative algebra | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
It is an important result in commutative algebra that reduced Gröbner bases are unique representations of ideals. Thus, one would believe that if two systems compute a Gröbner basis for the same initial basis which is reduced afterwards these reduced Gröbner bases are equal, however:
k.<a> = GF(2^4)
P.<k100,k101,k102,k103,x100,x101,x102,x103,w100,w101,w102,w103,s000,s001,s002,s003,k000,k001,k002,k003> = PolynomialRing(k,20)
F = [ w100 + k000 + (a^3 + 1), \ w101 + k001 + (a^3 + a^2 + 1), \ w102 + k002 + (a^3 + a^2 + a), \ w103 + k003 + (a^3 + a + 1), \ k000^2 + k001, \ k001^2 + k002, \ k002^2 + k003, \ k000 + k003^2, \ k100 + (a^2 + 1)*x100 + x101 + (a^3 + a^2)*x102 + (a^2 + 1)*x103 + (a^3 + a), \ k101 + (a)*x100 + (a)*x101 + x102 + (a^3 + a^2 + a + 1)*x103 + (a^3), \ k102 + (a^3 + a)*x100 + (a^2)*x101 + (a^2)*x102 + x103 + (a^3 + a^2), \ k103 + x100 + (a^3)*x101 + (a + 1)*x102 + (a + 1)*x103 + (a^3 + a^2 + a + 1), \ x100*w100 + 1, \ x101*w101 + 1, \ x102*w102 + 1, \ x103*w103 + 1, \ x100^2 + x101, \ x101^2 + x102, \ x102^2 + x103, \ x100 + x103^2, \ w100^2 + w101, \ w101^2 + w102, \ w102^2 + w103, \ w100 + w103^2, \ k100 + (a^2 + 1)*s000 + s001 + (a^3 + a^2)*s002 + (a^2 + 1)*s003 + (a^2 + a + 1), \ k101 + (a)*s000 + (a)*s001 + s002 + (a^3 + a^2 + a + 1)*s003 + (a^2 + a), \ k102 + (a^3 + a)*s000 + (a^2)*s001 + (a^2)*s002 + s003 + (a^2 + a + 1), \ k103 + s000 + (a^3)*s001 + (a + 1)*s002 + (a + 1)*s003 + (a^2 + a), \ k100^2 + k101, \ k101^2 + k102, \ k102^2 + k103, \ k100 + k103^2, \ s000^2 + s001, \ s001^2 + s002, \ s002^2 + s003, \ s000 + s003^2, \ s000*k000 + 1, \ s001*k001 + 1, \ s002*k002 + 1, \ s003*k003 + 1 ]
gb1 = sorted(Ideal(Ideal(F).groebner_basis('magma:GroebnerBasis')).reduced_basis()) print Ideal(gb1).basis_is_groebner() /// True
gb2 = sorted(Ideal(Ideal(F).groebner_basis('singular:std')).reduced_basis()) print Ideal(gb1).basis_is_groebner() /// True
set(gb1) == set(gb2) /// False
Attachments (1)
Change History (3)
Changed 14 years ago by
comment:1 Changed 14 years ago by
- Component changed from algebraic geometry to commutative algebra
- Milestone changed from sage-2.9 to sage-2.8.6
- Owner changed from was to malb
- Status changed from new to assigned
- Summary changed from MPolynomialIdeal.reduced_basis() doesn't behave as expected to [with patch] MPolynomialIdeal.reduced_basis() doesn't behave as expected
comment:2 Changed 14 years ago by
- Resolution set to fixed
- Status changed from assigned to closed
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The attached patch fixes this issue.