#11784: Add more sanity checks to FiniteField constructor
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Reporter: lftabera | Owner: lftabera
Type: defect | Status: positive_review
Priority: major | Milestone: sage-4.8
Component: basic arithmetic | Keywords: beginner GF
Work_issues: | Upstream: N/A
Reviewer: Johan Bosman | Author: Luis Felipe Tabera Alonso
Merged: | Dependencies:
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Changes (by jdemeyer):
* keywords: beginner => beginner GF
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]
> sage: K.modulus()
> x^2
> }}}
New description:
Galois (i.e. finite) 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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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11784#comment:7>
Sage <http://www.sagemath.org>
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