Opened 9 years ago
Last modified 9 years ago
#491 new bug
Wrong constant factor in absFactorize
Reported by: | mlee | Owned by: | decker |
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Priority: | minor | Milestone: | 3-2-0 and higher |
Component: | singular-libs | Version: | 3-1-6 |
Keywords: | Cc: |
Description
SINGULAR / Development A Computer Algebra System for Polynomial Computations / version 3-1-6 0< by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Dec 2012 FB Mathematik der Universitaet, D-67653 Kaiserslautern \ // ** executing /home/q/Spielwiese/new/Singular/LIB/.singularrc > LIB "absfact.lib"; // ** loaded /home/q/Spielwiese/new/Singular/LIB/absfact.lib (14191,2011-05-04) > ring R = (0), (x,y), lp; > short= 0; > poly p = (5x2+y2); > def S = absFactorize(p) ; // 'absFactorize' created a ring, in which a list absolute_factors (the // absolute factors) is stored. // To access the list of absolute factors, type (if the name S was assigned // to the return value): setring(S); absolute_factors; > setring(S); > short= 0; > absolute_factors; [1]: _[1]=5 //should be 1 _[2]=(a)*x+y [2]: 1,1 [3]: _[1]=(a) _[2]=(a^2+5) [4]: 2 > kill R; > ring R = (0), (x,y), lp; > short= 0; > poly p = (5x4-5x2y2); > def S = absFactorize(p) ; // ** redefining S ** // 'absFactorize' created a ring, in which a list absolute_factors (the // absolute factors) is stored. // To access the list of absolute factors, type (if the name S was assigned // to the return value): setring(S); absolute_factors; > setring(S); > short= 0; > absolute_factors; [1]: _[1]=-5 //should be 5 _[2]=x-y _[3]=x+y _[4]=x [2]: 1,1,1,2 [3]: _[1]=(a) _[2]=(a) _[3]=(a) _[4]=(a) [4]: 4 >
Change History (3)
comment:1 Changed 9 years ago by
comment:2 Changed 9 years ago by
According to the description, the result says that over the ring ra, the polynomial x4-x2-1 should have four linear factors?
It actually says that over ra, at least one representative of the class of conjugated absolute factors is defined. Now a4-a2-1 has four roots which means, the class x+(-a) represents, has four members.
comment:3 Changed 9 years ago by
Owner: | changed from somebody to decker |
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http://www.singular.uni-kl.de/forum/viewtopic.php?t=2087
There it is said about the return value:
As Wienand said in the forum:http://www.singular.uni-kl.de/forum/viewtopic.php?t=1422
But does not lead the result of absolute_factors[4] to ambiguities ?
Consider the polynomial x4-x2-1, which is irreducible over Q and has Galois group D_4. This means that Q(a), a4-a2-1 is not the splitting field of x4-x2-1. A splitting field needs a further quadratic extension.
Now call absfactorize:
According to the description, the result says that over the ring ra, the polynomial x4-x2-1 should have four linear factors? This is not true; or should " (its degree is the number of conjugates in the class)." only refer to the splitting field? I did not read the whole article, so I don't know what they intend to say.