#11784: Add more sanity checks to Galois Field constructor
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Reporter: lftabera | Owner: lftabera
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.8
Component: basic arithmetic | Keywords: begginer
Work_issues: | Upstream: N/A
Reviewer: | Author: Luis Felipe Tabera Alonso
Merged: | Dependencies:
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Old description:
> Galois fields admits a modulus argument and by default it checks if the
> modulus is irreducible mod the characteristic of the field.
>
> However, it does not check that the polynomial is of the right degree.
>
> An example:
>
> {{{
> sage: K=GF(3**2,name='a', modulus=QQ[x](x^3-x+1))
> sage: K
> Finite Field in a of size 3^2
> sage: K.list()
> [0, a + 1, 1, 2, 1, 2, 1, 2, 1]
> }}}
New description:
Galois fields admits a modulus argument and by default it checks if the
modulus is irreducible mod the characteristic of the field.
However, it does not check that the polynomial is of the right degree.
An example:
{{{
sage: K=GF(3**2,name='a', modulus=QQ[x](x^3-x+1))
sage: K
Finite Field in a of size 3^2
sage: K.list()
[0, a + 1, 1, 2, 1, 2, 1, 2, 1]
sage: K.modulus()
x^2
}}}
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Comment(by lftabera):
Rebase agains 4.7.2
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11784#comment:3>
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