#5159: [with patches, with positive review but needs work] Add functionality to
Galois groups
---------------------------+------------------------------------------------
Reporter: davidloeffler | Owner: davidloeffler
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-3.4.2
Component: number theory | Keywords: galois groups, number theory
---------------------------+------------------------------------------------
Comment(by cremona):
Oops: on a 64-bit machine I get this:
{{{
j...@host-57-44:~/sage-3.4/devel/sage-5159$ sage -t
sage/rings/number_field/galois_group.py
sage -t "devel/sage-5159/sage/rings/number_field/galois_group.py"
**********************************************************************
File
"/home/jec/sage-3.4/devel/sage-5159/sage/rings/number_field/galois_group.py",
line 343:
sage: G.decomposition_group(P^2)
Expected:
Traceback (most recent call last):
...
ValueError: Fractional ideal (1/984*a^7 - 71/1968*a^5 + 29/984*a^3 +
527/328*a) is not prime
Got:
Traceback (most recent call last):
File "/home/jec/sage-3.4/local/bin/ncadoctest.py", line 1231, in
run_one_test
self.run_one_example(test, example, filename, compileflags)
File "/home/jec/sage-3.4/local/bin/sagedoctest.py", line 38, in
run_one_example
OrigDocTestRunner.run_one_example(self, test, example, filename,
compileflags)
File "/home/jec/sage-3.4/local/bin/ncadoctest.py", line 1172, in
run_one_example
compileflags, 1) in test.globs
File "<doctest __main__.example_18[6]>", line 1, in <module>
G.decomposition_group(P**Integer(2))###line 343:
sage: G.decomposition_group(P^2)
File "/home/jec/sage-3.4/local/lib/python2.5/site-
packages/sage/rings/number_field/galois_group.py", line 357, in
decomposition_group
raise ValueError, "%s is not prime" % P
ValueError: Fractional ideal (-1/492*a^7 + 101/1968*a^5 - 115/328*a^3
+ 1717/984*a) is not prime
**********************************************************************
File
"/home/jec/sage-3.4/devel/sage-5159/sage/rings/number_field/galois_group.py",
line 445:
sage: G.artin_symbol(K.primes_above(2)[0])
Expected:
Traceback (most recent call last):
...
ValueError: Fractional ideal (-1/8364*b^7 + 1/492*b^6 - 11/16728*b^5 -
101/1968*b^4 + 209/2788*b^3 + 115/328*b^2 - 3139/8364*b + 251/984) is
ramified
Got:
Traceback (most recent call last):
File "/home/jec/sage-3.4/local/bin/ncadoctest.py", line 1231, in
run_one_test
self.run_one_example(test, example, filename, compileflags)
File "/home/jec/sage-3.4/local/bin/sagedoctest.py", line 38, in
run_one_example
OrigDocTestRunner.run_one_example(self, test, example, filename,
compileflags)
File "/home/jec/sage-3.4/local/bin/ncadoctest.py", line 1172, in
run_one_example
compileflags, 1) in test.globs
File "<doctest __main__.example_22[7]>", line 1, in <module>
G.artin_symbol(K.primes_above(Integer(2))[Integer(0)])###line 445:
sage: G.artin_symbol(K.primes_above(2)[0])
File "/home/jec/sage-3.4/local/lib/python2.5/site-
packages/sage/rings/number_field/galois_group.py", line 463, in
artin_symbol
if len(t) > 1: raise ValueError, "%s is ramified" % P
ValueError: Fractional ideal (43/33456*b^7 + 7/1968*b^6 -
809/33456*b^5 - 35/656*b^4 + 367/2788*b^3 + 61/492*b^2 - 4651/16728*b +
757/984) is ramified
**********************************************************************
2 items had failures:
1 of 8 in __main__.example_18
1 of 8 in __main__.example_22
}}}
I think you cannot rely on pari giveing you the primes in a specific
order:
{{{
sage: P = K.primes_above(17)[0]
sage: P
Fractional ideal (1/492*a^7 - 101/1968*a^5 + 115/328*a^3 - 733/984*a)
sage: P^2
Fractional ideal (-1/492*a^7 + 101/1968*a^5 - 115/328*a^3 + 1717/984*a)
sage: Q = K.primes_above(17)[1]
sage: Q^2
Fractional ideal (-5/2788*a^7 + 587/11152*a^5 - 2791/5576*a^3 +
13915/5576*a)
}}}
so the doctest needs to be designed to allow for that. Perhaps define P
via
{{{
sage: P=K.ideal(17,a^2)
sage: P
Fractional ideal (1/492*a^7 - 101/1968*a^5 + 115/328*a^3 - 733/984*a)
sage: P.is_prime()
True
}}}
(which may or may not be the P i your doctest).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5159#comment:19>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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