Singular
http://www.singular.uni-kl.de/forum/

changed deg() behaviour in Singular
http://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2540
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Author:  jakobkroeker [ Wed Jun 15, 2016 1:01 am ]
Post subject:  changed deg() behaviour in Singular

In Singular the behaviour of deg() changed between v3.1.7 and v 4.0.3.
Question:
- Which answer is correct ?
- Which of the answers users really expected?

Code:
                     SINGULAR                                 /  Development
A Computer Algebra System for Polynomial Computations       /   version 3-1-7
                                                           0<
by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann     \   Aug 2013
FB Mathematik der Universitaet, D-67653 Kaiserslautern        \
// ** executing /run/media/jakob/TOEXT4/work/home_fc18/Projects/lipmanresolve/Singular-3-1-7/Singular/LIB/.singularrc
> ring rng = 0,(x,y,z),dp;
>
. intmat im[3][3] = 3,0,1,1,1,0,1,0,0;
> ring S = 0,(x,y,z),(M(im));
> S;
//   characteristic : 0
//   number of vars : 3
//        block   1 : ordering M
//                  : names    x y z
//                  : weights  3 0 1
//                  : weights  1 1 0
//                  : weights  1 0 0
//        block   2 : ordering C
> poly p = x^3*y+x*z^4;
>
. deg(p);
9
> quit;
Auf Wiedersehen.
[jakob@vogon lipmanresolve]$ ./singular-spielwiese
                     SINGULAR                                 /  Development
A Computer Algebra System for Polynomial Computations       /   version 4.0.3
                                                           0<
by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann     \   Jan 2016
FB Mathematik der Universitaet, D-67653 Kaiserslautern        \
// ** executing /run/media/jakob/TOEXT4/work/home_fc18/Projects/lipmanresolve/Singular-spielwiese/BUILD/Singular/LIB/.singularrc
> ring rng = 0,(x,y,z),dp;
>
. intmat im[3][3] = 3,0,1,1,1,0,1,0,0;
> ring S = 0,(x,y,z),(M(im));
> S;
//   characteristic : 0
//   number of vars : 3
//        block   1 : ordering M
//                  : names    x y z
//                  : weights  3 0 1
//                  : weights  1 1 0
//                  : weights  1 0 0
//        block   2 : ordering C
> poly p = x^3*y+x*z^4;
>
. deg(p);
5

Remark: the changes also affects software which depends on Singular

Author:  hannes [ Wed Jun 15, 2016 10:32 am ]
Post subject:  Re: changed deg() behaviour in Singular

deg(p) returns the maximal degree of all monomials in the polynomials
with respect to the weights of the variables.
The weights of the variables are derived from the ordering if
the ordering is not a block ordering and if all weights are positive.
Otherwise, the weights are 1.
This is a result of the requirement that there are only finitely many monomials
of the same degree (for non-blockorderings): it was not honored in 3-1.

If you do not like this choice of weights, use
Code:
deg(p,w);

where w is the weight vector of your choice.

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