From 0d9b5cc5b2a13e89349b1505c31c2329f6c65ce7 Mon Sep 17 00:00:00 2001 From: Jeroen Demeyer Date: Tue, 28 Oct 2014 14:51:27 +0100 Subject: [PATCH] Clarify docs for polynomial() --- .../rings/finite_rings/finite_field_base.pyx | 23 ++++++++++++++++--- 1 file changed, 20 insertions(+), 3 deletions(-) diff --git a/src/sage/rings/finite_rings/finite_field_base.pyx b/src/sage/rings/finite_rings/finite_field_base.pyx index d3c9d35f878..3f23e7c8c92 100644 --- a/src/sage/rings/finite_rings/finite_field_base.pyx +++ b/src/sage/rings/finite_rings/finite_field_base.pyx @@ -741,6 +741,10 @@ cdef class FiniteField(Field): coefficients in the base field that has `a` as a root. In finite field extensions, `\GF{p^n}`, the base field is `\GF{p}`. + OUTPUT: + + - a monic polynomial over `\GF{p}` in the variable `x`. + EXAMPLES:: sage: F. = GF(7^2); F @@ -829,9 +833,22 @@ cdef class FiniteField(Field): def polynomial(self, name=None): """ - Return the irreducible characteristic polynomial of the - generator of this finite field, i.e., the polynomial `f(x)` so - elements of the finite field as elements modulo `f`. + Return the minimal polynomial of the generator of ``self`` over + the prime finite field. + + INPUT: + + - ``name`` -- a variable name to use for the polynomial. By + default, use the name given when constructing this field. + + OUTPUT: + + - a monic polynomial over `\GF{p}` in the variable ``name``. + + .. SEEALSO:: + + Except for the ``name`` argument, this is identical to the + :meth:`modulus` method. EXAMPLES::