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It would be very useful if for a congruence subgroup G and an integer d coprime to the level N of G, one could compute the action on cusps (modulo G) of `tau_d \in Gal(Q(zeta_N)/Q)`. This action i…
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```
sage: k = GF(7)
sage: k.gen()
1
```
Component: **number theory**
Keywords: **galois field**
_Issue created by migration from https://trac.sagemath.org/ticket/3045_
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When running -only_optional=magma without the database_gap.spkg installed we see two failures:
```
sage -t -only-optional=magma -long devel/sage/sage/rings/number_field/number_field.py
************…
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```
sage -t -long -optional devel/sage/sage/rings/number_field/number_field.py
**********************************************************************
File "/scratch/mabshoff/release-cycle/sage-3.2.…
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The attached patch adds support for pari's rnfidealdown. This is simple but exposes a weakness in Sage's number field relativize() function, which I address at the same time. Namely, relativize al…
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This attached patch makes several changes to
`sage/rings/number_field/number_field.py` and
`sage/rings/number_field/morphism.py` that are mainly concerned with
improving performance for cyclotomic f…
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```
File "tut.py", line 3390:
: G
Expected:
Group([ (1,2,3)(4,5), (3,4) ])
Got:
Group( [ (1,2,3)(4,5), (3,4) ] )
**********************************************************************
F…
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`.galois_closure` used to guess a variable name, which is not very Sage-like. This and a related issue with `.galois_conjugates` are fixed.
Component: **number theory**
Keywords: **number field g…
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I don't know about this code at all, but something is messed up:
```
[2.8 s]
sage -t devel/sage-main/sage/rings/number_field/totallyreal_rel.py********************************************…
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It would be useful, for multimodular algorithms (and more!) to be able to find degree one primes in a number field.
For posterity, the following IRC transcript, copied from #903, is relevant:
```
…