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Here are a couple proposals for searching for Galois fields.
First, an easy one. We should add a dropdown to the number field search for `is_galois`. This can go to the right of the `Galois group…
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The knowl for geometry of a Belyi map says that it corresponds to a triangle group Delta(a,b,c).
- the values of a, b, and c for the page we are on are not given
- "triangle group" should probab…
jwj61 updated
2 weeks ago
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GAP can compute Galois groups of number fields of degree up to 15. This will allow avoiding Kash (not available for all platforms, binary only, etc) usage for degrees between 11 and 15.
It will need…
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As a first step toward Galois groups of general p-adic extensions, we should add Galois groups of tame extensions, which are easy to compute.
Depends on #31469
CC: @alexjbest
Component: **padics…
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Magma is really good at computing Galois groups. We should improve our interface so that we can take advantage of it when available.
Depends on #31489
Component: **number fields**
_Issue created…
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This is essentially #4105 but for Galois group elements.
```
sage: K. = NumberField(x^6 + 40*x^3 + 1372)
sage: G = K.galois_group()
sage: L = [G.artin_symbol(Q) for Q in K.primes_above(5)]
sage: L[…
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What about skipping the Galois group and introducing the Galois groupoid, instead? Is there any reason to artificially single out a particular splitting field?
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Let `K. = NumberField(f)`. The method `K.is_galois()` does the following:
```
if self.degree() < 12:
return self.galois_group(type='pari').order() == self.degree()
else:
return len(self.aut…
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Given a polynomial from ℚ[X], we need a better way to express its roots using radical expressions if such an expression is possible.
The current approach, as used by e.g. `NumberFieldElement._symbo…
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Would be nice if something like this could be made to work out of the box, unsure as to difficulty
```
sage: D = DirichletGroup(13)
....: c = D.Element(D,vector([2]))
....: N = Newforms(c,2,names="…