-
```
A. = QQ[]
Gauss. = A.quotient(x^2+1)
R. = Gauss[]
S = R.quotient([(X1^2+Y1^2)*Z1^2-c^2*(Z1^4+d*X1^2*Y1^2),
(X2^2+Y2^2)*Z2^2-c^2*(Z2^4+d*X2^2*Y2^2)])
S(1)
```
Produces the tr…
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This error occurs in several places; e.g.
```
sage -t src/sage/rings/polynomial/multi_polynomial_sequence.py
**********************************************************************
File "src/sage/ri…
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It would be nice if this would work:
```python
sage: P. = GF(32003)[]
sage: I = sage.rings.ideal.Katsura(P)
sage: _ = I.groebner_basis('magma', prot=True)
Homogeneous weights search
Number of varia…
-
Define the following polynomial ring, polynomial, and ideal:
```
sage: term_order = TermOrder('degrevlex', 2) + TermOrder('degrevlex', 2)
sage: K = PolynomialRing(QQ, 'x,y,a0,a1', order=term_order)…
-
Reported by Mate Soos:
As of Sage 5.5, `Sequence`s of polynomials offers special methods:
```python
sage: B. = GF(2)[]
sage: F0 = Sequence(map(lambda f: f.lm(),[a,b,c,d]))
sage: F0.groebner_basis(…
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`MPolynomialIdeal.interreduced_basis()` should return the same sorted list as `MPolynomialIdeal.groebner_basis()` when called on an ideal which has a (not reduced) Groebner basis as set of generator…
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I was observing that `is_zero` is rather slow for quotient rings. For instance, try the following code:
```julia
R, (x,y,z) = QQ["x", "y", "z"]
I = ideal(R, [x^4 + y*z^7 - 35*x^3*z, x^29 - 15 + z…
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Split from #12426. Doctest involving `polybori` segfault when everything is built with clang
```
sage -t --long --warn-long 62.3 src/sage/rings/polynomial/multi_polynomial_sequence.py
*************…
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this shouldn't happen:
```
P. = PolynomialRing(ZZ,3)
I = sage.rings.ideal.Katsura(P,3) # regenerate to prevent caching
I.groebner_basis('macaulay2:gb') # optional - macaulay2
TypeError: _groebner_b…
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The `forward_map` and `reverse_map` in `sage/rings/qqbar_decorators.py` do not currently handle polynomial sequences. Because of that, the call to `groebner_basis` in a polynomial ring over `QQbar` …