#11878: Proper implementation of quotients of g-algebras
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Reporter: SimonKing | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.7.2
Component: algebra | Keywords: g-algebra Singular quotient
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies: #4539
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Comment(by SimonKing):
I have a question, and probably Oleksandr knows the answer:
Assume we are in a quotient ring Q (not sca) in Singular. As we know, the
normal form of a polynomial p with respect to the defining ideal of the
quotient ring is not automatically computed. But it can be obtained by
NF(p,std(0)).
I tried to create a Gröbner strategy object G for the zero ideal in Q.
However, G.normal_form(p) did ''not'' reduce p. G.normal_form relies on
the function `redNF`, I guess from Singular's `kstd2.cc`.
Is `redNF` the wrong thing to use in quotient rings? I see that `redNF`
accepts several arguments, that seem to be undocumented (like many
functions in Singular). Do I simply have to choose other arguments? Is it
possible to obtain reduction with respect to the defining ideal of a
quotient ring by using a Gröbner strategy object, or is that the wrong
approach?
I found another function `kNF2` in `kstd2.cc`, which seems to have an
argument for the defining ideal of a quotient ring; should I use this?
Would the result be tail reduced? I am afraid it would be less efficient
than using a fixed Gröbner strategy, but perhaps that's the only way.
Or, positively asked: What Singular function called from NF is responsible
for the reduction of quotient ring elements?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11878#comment:2>
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