composition of two polynomials for sage program

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A specific example could be helpful...

Did you mean

P.<x>=QQ[]
p=x^3+1
q=x^2+3
p(x=q)

x^6 + 9*x^4 + 27*x^2 + 28

Composition of two polynomials in finite field using sage program

Sorry, my misinterpretation

Some ugly workaround (subs works in GF(2)[])

P.<x>=GF(2)[]
p=x^3+1
q=x^2+1
p1=p(x=q); p1

x^6 + x^4 + x^2

Now the result in GF(2^4)

k.<y>=GF(2^4)
k(p1.change_variable_name(y))

y^3 + y + 1

Check:

(y^2+1)^3+1

y^3 + y + 1