# Revision history [back]

First define k to be the field GF(2^5):

sage: k.<a> = FiniteField(2^5); k
Finite Field in a of size 2^5


Alternatively :

sage: k = GF(2^5, 'a')


Then define the polynomial ring k[x]:

sage: R.<x> = PolynomialRing(k)


Alternatively:

sage: S = k[x]


Then, do your computation in R:

sage: P = R(x^6)
sage: P.mod(x^5+x^2+1)
x^3 + x


First define k to be the field GF(2^5):

sage: k.<a> = FiniteField(2^5); k
Finite Field in a of size 2^5


Alternatively :

sage: k = GF(2^5, 'a')


Then define the polynomial ring k[x]:

sage: R.<x> = PolynomialRing(k)


Alternatively:

sage: S R = k[x]


Then, do your computation in R:

sage: P = R(x^6)
sage: P.mod(x^5+x^2+1)
x^3 + x


First define k to be the field GF(2^5):GF(2^5), whose generator is named a:

sage: k.<a> = FiniteField(2^5); k
Finite Field in a of size 2^5


Alternatively :

sage: k = GF(2^5, 'a')


Then define the polynomial ring k[x]:

sage: R.<x> = PolynomialRing(k)


Alternatively:

sage: R = k[x]


Then, do your computation in R:

sage: P = R(x^6)
sage: P.mod(x^5+x^2+1)
x^3 + x


First define k to be the field GF(2^5), whose generator is named a:

sage: k.<a> = FiniteField(2^5); k
Finite Field in a of size 2^5


Alternatively :

sage: k = GF(2^5, 'a')


Then define the polynomial ring k[x]:

sage: R.<x> = PolynomialRing(k)


Alternatively:

sage: R = k[x]
k['x']


Then, do your computation in R:

sage: P = R(x^6)
sage: P.mod(x^5+x^2+1)
x^3 + x


First First, define k to be the field GF(2^5), whose generator is named a:

sage: k.<a> = FiniteField(2^5); k
Finite Field in a of size 2^5


Alternatively :

sage: k = GF(2^5, 'a')
'a'); k
Finite Field in a of size 2^5


Then Then, define the polynomial ring k[x]:

sage: R.<x> = PolynomialRing(k)
PolynomialRing(k); R
Univariate Polynomial Ring in x over Finite Field in a of size 2^5


Alternatively:

sage: R = k['x']
k['x'] ; R
Univariate Polynomial Ring in x over Finite Field in a of size 2^5


Then, do your computation in R:

sage: P = R(x^6)
sage: P.mod(x^5+x^2+1)
x^3 + x


First, define k to be the field GF(2^5), whose generator is named a:

sage: k.<a> = FiniteField(2^5); k
Finite Field in a of size 2^5


Alternatively :

sage: k = GF(2^5, 'a'); k
Finite Field in a of size 2^5


Then, define the polynomial ring k[x]:

sage: R.<x> = PolynomialRing(k); R
Univariate Polynomial Ring in x over Finite Field in a of size 2^5


Alternatively:

sage: R = k['x'] ; k['x']; R
Univariate Polynomial Ring in x over Finite Field in a of size 2^5


Then, do your computation in R:

sage: P = R(x^6)
sage: P.mod(x^5+x^2+1)
x^3 + x