Opened 8 years ago
Closed 6 years ago
#687 closed bug (fixed)
standard bases over integers yield redundant basis elements
Reported by: | ren | Owned by: | popescu |
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Priority: | major | Milestone: | 4-1-0 and higher |
Component: | dontKnow | Version: | 4-0-1 |
Keywords: | Cc: |
Description
SINGULAR / Development A Computer Algebra System for Polynomial Computations / version 4.0.1 0< by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Sep 2014 FB Mathematik der Universitaet, D-67653 Kaiserslautern \ // ** executing /home/ren/Sources/Singular/LIB/.singularrc > ring r=integer,(t,x(1..3)),ws(1,-1,-1,-1); > ideal I = x(1)^2+2*x(1)*x(2)+3*x(2)*x(3), 3*x(1)*x(2)+4*x(2)*x(3)+5*x(3)^2, 2-t; > std(I); _[1]=x(2)^2*x(3)-15*x(1)*x(3)^2-14*x(2)*x(3)^2+20*x(3)^3+t*x(2)^2*x(3) _[2]=30*x(1)*x(3)^2+28*x(2)*x(3)^2-40*x(3)^3+t*x(1)^2*x(2)+2*t*x(1)*x(2)^2 _[3]=10*x(3)^3-t*x(1)*x(2)*x(3)+t*x(2)^2*x(3)-5*t*x(1)*x(3)^2-6*t*x(2)*x(3)^2 _[4]=x(1)^2+2*x(1)*x(2)+3*x(2)*x(3) _[5]=x(1)*x(2)+4*x(2)*x(3)+5*x(3)^2+t*x(1)*x(2) _[6]=2-t
The 2nd and 3rd standard basis elements are redundant, as their leading term is divisible by the leading term of the 6th basis element. This leads to problems parts of my code, as it assumes that standard basis is irredundant.
Change History (2)
comment:1 Changed 8 years ago by
Owner: | changed from somebody to popescu |
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comment:2 Changed 6 years ago by
Resolution: | → fixed |
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Status: | new → closed |
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fixed in 4.0.3p5