Opened 10 years ago
Closed 9 years ago
#636 closed bug (fixed)
std over integers in local ordering
Reported by: | ren | Owned by: | |
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Priority: | blocker | Milestone: | 4-1-0 and higher |
Component: | dontKnow | Version: | 4-0-0 |
Keywords: | Cc: |
Description
Here's a problem I encountered while doing tropical computations:
ring r=integer,(t,a,b,c,d,e,f,g,h,i,j),ws(1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1); ideal inI= 3, gh+2fi+ej, dh+2ci+bj, df+2cg+aj, de+2bg+ai, ce+2bf+ah; // std(inI); <- not sure if it terminates, but if it does, it takes a very long time
However, inI is already a standard basis:
ring s=3,(t,a,b,c,d,e,f,g,h,i,j),ws(1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1); ideal inI= 3, gh+2fi+ej, dh+2ci+bj, df+2cg+aj, de+2bg+ai, ce+2bf+ah; std(inI); // == I apart from the 3 vanishing and +2 changing to -1
Change History (8)
comment:1 Changed 10 years ago by
Priority: | critical → blocker |
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comment:2 Changed 10 years ago by
comment:3 Changed 10 years ago by
Owner: | changed from somebody to popescu |
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Adi, could you please take a look?
comment:4 Changed 10 years ago by
Owner: | changed from popescu to apopescu |
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comment:5 Changed 10 years ago by
Owner: | changed from apopescu to Popescu |
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comment:6 Changed 10 years ago by
Owner: | changed from Popescu to popescu@… |
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comment:7 Changed 10 years ago by
Another similar issue: This time, std(I) terminates, but std(std(I)) doesn't.
SINGULAR / Development A Computer Algebra System for Polynomial Computations / version 4.0.0 0< by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Dec 2013 FB Mathematik der Universitaet, D-67653 Kaiserslautern \ // ** executing /home/ren/Sources/Singular/LIB/.singularrc > ring r = integer,(t,x(1..4)),ws(1,-1,-11,-3,-19); > ideal I = 3-t, 8*t*x(3)*x(4)+t*x(1)*x(2)+2*x(1)^2, . t*x(1)*x(2)^2+2*x(1)^2*x(2)+2*t^3*x(1)*x(2)*x(3)-192*x(1)^3+4*t^2*x(1)^2*x(3); > I = std(I); // works fine > I = std(I); // doesn't finish
comment:8 Changed 9 years ago by
Resolution: | → fixed |
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Status: | new → closed |
fixed with 67e0dc31cecb425433f640594911fc9df2b15076 test in New/stdZtests.tst
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Here is a similar issue, which appeared in my work:
LM(I) should be generated by the leading monomials of the specified generating system and for J we should have LT(J) = <2> + LM(I).
So if you were to discard the generators of J whose leading term is divisible by 2 and make the remaining generatos have leading coefficient 1 with the help of 2-t, then that would already yield a standard basis.