ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 02 Aug 2020 00:12:42 +0200change_ring for DirichletGroup: some initialisation is required for ComplexIntervalField?https://ask.sagemath.org/question/52801/change_ring-for-dirichletgroup-some-initialisation-is-required-for-complexintervalfield/Dear all,
A code will better explain my predicament:
myCIF = ComplexIntervalField( 200 )
myD = DirichletGroup(5)
myDCIF = myD.change_ring(myCIF)
[e.values() for e in myDCIF]
--> NotImplementedError followed by lots of shouting involving in particular 'cachefunc.pyx'
Then do it a second time:
[e.values() for e in myDCIF]
--> Good result!
The mystery gets more mysterious if one tries it with 'ComplexField' rather than with 'ComplexIntervalField': everything goes smoothly. Here is thus my way out:
myCF = ComplexField( 200 + 1)
myCIF = ComplexIntervalField( 200 )
myD = DirichletGroup(5)
myDCF = myD.change_ring(myCF)
[[myCIF(v) for v in e.values()] for e in myDCF]
Maybe there is something simple I didn't get that would avoid the above manipulation?
Many thanks in advance! OlivierOlivier R.Sun, 02 Aug 2020 00:12:42 +0200https://ask.sagemath.org/question/52801/Understanding Output in SageMath Regarding Dirichlet Charactershttps://ask.sagemath.org/question/44593/understanding-output-in-sagemath-regarding-dirichlet-characters/ p=7
G = DirichletGroup(p); G
m=3; n=ZZ((p-1)/m); print m,n
c=G[1]
c1=c^n;c1
The output is:
Dirichlet character modulo 7 of conductor 7 mapping 3 |--> zeta6 - 1
Can anyone explain what zeta6 is? Is this the Riemann-Zeta function? Is this the whole group of units? Is there a relation to the Eisenstein primes? I'm still a bit weak in this material and am having trouble grasping some of these sage outputs. Thank you in advance!NicklovnWed, 05 Dec 2018 18:17:59 +0100https://ask.sagemath.org/question/44593/Characters and number fieldshttps://ask.sagemath.org/question/7734/characters-and-number-fields/Hello!
I have again a question. Could you help me? I defined the Q(6th primitive unity) by
A=DirichletGroup(7)
K.<a>=NumberField(cyclotomic_polynomial(6))
R=K.maximal_order()
Then I take a character, namely
character=A[1]
print character(3)
This character(3) is zeta6, so I would think that the following should be true:
character(3) in R.fractional_ideal(a)
But it is false, I think because we defined Q(6th primitive unity) without using zeta6.
Mathemathically this is true, so could you help me to persuade the computer to recognize
such a relation? Thank you! :-)KatikaTue, 19 Oct 2010 11:22:52 +0200https://ask.sagemath.org/question/7734/