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How to sum or product of two elements of two different fields?

asked 2019-06-02 00:47:14 -0600

I would like to sum of product two elements from different fields and the resultant operation should be in the bigger field. I have used the following codes, but it gives errors.

R.<x> = PolynomialRing(GF(2))
F = GF(2^3, name='x', modulus=x^3 + x^2 + 1)
G = GF(2^8, name='x', modulus=x^8 + x^5 + x^3 + x + 1)
print F.fetch_int(3)
print  G.fetch_int(5)
#F.fetch_int(3) => x + 1
#G.fetch_int(5) => x^2 + 1
#print F.fetch_int(3)*G.fetch_int(5) 
print (x^2 + 1)*(x + 1)
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Is it homework ?

tmonteil gravatar imagetmonteil ( 2019-06-02 15:55:35 -0600 )edit

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answered 2019-06-02 15:52:13 -0600

tmonteil gravatar image

updated 2019-06-02 15:55:30 -0600

Regarding mathematics, how could F be embedded in G ? How could the generator "x" of F be the same that the generator "x" of G ?

Regarding Sage code, you can have a look at https://doc.sagemath.org/html/en/refe...

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Asked: 2019-06-02 00:47:14 -0600

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Last updated: Jun 02