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When defining a finite field of non-prime order, it is useful to give a name to the generator.
Likewise, when defining a polynomial ring, it is useful to give a name to the polynomial variable.
In the example, GF(2^8, 'a') returns the finite field with $2^8$
elements, with a as the display name of its generator.
And R.<x> = K[] simultaneously defines R as a polynomial ring
over the field K, and definds x as its generator, i.e., the
polynomial variable.
So x^254 is the monic monomial of degree 254 in this polynomial ring.
| | 2 | No.2 Revision |
When defining a finite field of non-prime order, it is useful to give a name to the generator.
Likewise, when defining a polynomial ring, it is useful to give a name to the polynomial variable.
In the example, GF(2^8, 'a') returns the finite field with $2^8$
elements, with a as the display name of its generator.
And R.<x> = K[] simultaneously defines R as a polynomial ring
over the field K, with a polynomial variable that displays as 'x',
and definds defines x as its generator, i.e., the
the polynomial variable.
So x^254 is the monic monomial of degree 254 in this polynomial ring.
For more, read the documentation or/and the source code for GF:
sage: GF?
sage: GF??
and for PolynomialRing:
sage: PolynomialRing?
sage: PolynomialRing??
Note that R.<x> = K[] is transformed by the Sage preparser into:
sage: preparse("R.<x> = K[]")
"R = K['x']; (x,) = R._first_ngens(1)"
