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So I was reading the source code of the solve_poly_system function. This is a function that finds the
solutions of a system of multivariate polynomial equations. As far as I understand it, the soluti…
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While trying to find a Groebner basis, a message like this is output:
```
Info: Possible overflow of exponent vector detected.
Restarting with at least 32 bits per exponent.
```
Does this mea…
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```
groebner does not give the groebner basis in monic form.
sdp_groebner does, but then polytools.groebner changes the normalizazion
when domain.has_Field is False.
see e.g. the cyclic5 lex example:…
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### Problem Description
I frequently use polynomial rings over other polynomial rings for easy extraction of terms. For example:
```
sage: R. = QQ[]
sage: S. = R[]
sage: p = (x+y+z)^2*sum(a^k fo…
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An exception can be raised by testing membership of an element contained in a ring ideal, perhaps due to a bug in the Groebner basis algorithms.
The following minimal working example exercises the …
mcncm updated
4 months ago
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See http://ask.sagemath.org/question/55/implementing-different-groebner_basis-algorithms
Component: **commutative algebra**
_Issue created by migration from https://trac.sagemath.org/ticket/9789_
…
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Define
```
sage: P.=QQ[]
sage: J = P*[P.random_element() for _ in range(100)]
```
**__Hash is broken__**
`J.__hash__` is:
```
def __hash__(self):
return hash(str(self))
```
However, …
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I've seen a lot of cases where in each step of an iterative algorithm, an ideal is updated and the new ideal is used for some membership test. I think this is somewhat slow because:
- a new ideal is …
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Looks a bit like #17143.
```
sage: def foo():
....: sr = mq.SR(2,1,1,4,gf2=True, polybori=True)
....: F, s = sr.polynomial_system()
....: I = F.ideal()
....: r…
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I'm using generic polynomial rings `S = A[x,y,...]` over other base rings `A`. Now I have the following problem:
The arithmetic is rather slow, for instance when multiplying polynomials. The reason…