#13849: deprecate degrevlex when using PolyBoRi
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Reporter: malb | Owner: malb
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.6
Component: commutative algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Martin Albrecht | Merged in:
Dependencies: #13848 | Stopgaps:
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Comment (by PolyBoRi):
Martin, what you say is correct (unless you define degnexlex otherwise in
some context I do not know).
Degrevlex as in Singular corresponds to
{{{
1 1 1
0 0 -1
0 -1 0
}}}
or equivalenty, but redundant.
{{{
1 1 1
0 0 -1
0 -1 0
-1 0 0
}}}
So you see, it has to aspects (one negative and one from behind),
the name might be considered as broken and irritating.
Negative lexicographical as in Singular (not a well ordering).
{{{
-1 0 0
0 -1 0
0 0 -1
}}}
As you can see degrevlex as in Singular is composed of the
degree vector and
negative lexicographical ordering (ls), but in reversed variable ordering.
deglex as in PolyBoRi and in Singular (Dp with a big D)
{{{
1 1 1
1 0 0
0 1 0
}}}
dp_asc as in PolyBoRi (degree reverse lexicographical ordering ascending)
{{{
1 1 1
-1 0 0
0 -1 0
}}}
So, the notion, degneglex can have it's benefits from systematic
perspective
as it's composed of the degree vector and the (non well ordering) negative
lexicographical and indeed itself again a well ordering.
From an unsystematical perspective, I just always added the ascending to
the "degree reverse lexicographical" as it made sure it's the same order
but twised
It's a simple ordering, but it is not equivalenty to degrevlex as in
Singular
and does not feature the nice theoretical properties for a certain class
of systems (I've never come to the observation that that they apply in
Boolean context).
While most people agree on these notions, here is no proper
standardization on notions in computational algebra.
I have indeed already seen some people define degree reverse
lexicographical ordering to be the ordering PolyBoRi calls dp_asc.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13849#comment:12>
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