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Jun 27, 2016, 6:49:51 PM6/27/16

to libsingular-devel

Consider the following example:

when I use p_Deg() to compute the degree of x instead of pLDeg(), I get

`ring rng = 0,(x,y), lp;`

poly p = x;

deg(x);

when I use p_Deg() to compute the degree of x instead of pLDeg(), I get

65536 as an answer.

Is it not allowed to use p_Deg() for lexicographical orderings

or is it a bug?

Jun 28, 2016, 4:22:43 AM6/28/16

to libsingu...@googlegroups.com

On Mon, Jun 27, 2016 at 03:49:50PM -0700, Jakob Kroeker wrote:

> Consider the following example:

>

> ring rng = 0,(x,y), lp;

> poly p = x;

> deg(x);

> when I use p_Deg() to compute the degree of x instead of pLDeg(),A I get
> Consider the following example:

>

> ring rng = 0,(x,y), lp;

> poly p = x;

> deg(x);

>

> 65536 as an answer.

>

>

> Is it not allowed to use p_Deg() for lexicographical orderings

> or is it a bug?

A degree function is a map d: monomials -> integers>=0 which has the
> 65536 as an answer.

>

>

> Is it not allowed to use p_Deg() for lexicographical orderings

> or is it a bug?

properties:

- d(1) = 0

- d(f*g) = d(f) + d(g)

- if f > g then d(f) >= d(g)

Examples for degree functions are:

- p_Deg

- p_Totaldegree

- p_WTotaldegree (only for orderings with weights != 1)

To ease the choice for the different orderings there are function

pointers pointing to the most useful degree function for the ring given:

- p_FDeg for the degree of the leading monomial

- p_LDeg for the maximal degree of all monomials of the polynomials

The answers to your questions:

- no, it is allowed to use p_Deg, but it may return correct but

surprising results for block orderings

- no, it is not a bug

Suggestion: use p_FDeg or p_Totaldegree

Hannes

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