Conversion from finite field to integer polynomial

GMS103
11 ●1

I am looking for a function myf doing the following:

sage: var('x')
x
sage: P=x^3-2*x^2-x-2
sage: F125.<a>=GF(5^3,name='a',modulus=P)
sage: b=a^37;b
4*a^2 + 3*a + 1
sage: c=myf(b,y)
1 + 3*y + 4*y^2
sage: c.parent()
Power Series Ring in y over Integer Ring

or better still (symmetric representation):

sage: c=myf(b,y)
1 - 2*y - y^2
sage: c.parent()
Power Series Ring in y over Integer Ring

I can manage with str, replace, preparse, eval but there is surely a natural way.

Comments

b.polynomial() might be close to what you're looking for. You can also get the coefficients from b.list().

John Palmieri ( 0 years ago )

add a comment

sage: R.<y> = PowerSeriesRing(ZZ) sage: R(b.polynomial().map_coefficients(lambda c: c.lift(), new_base_ring=ZZ)) 1 + 3*y + 4*y^2 sage: R(b.polynomial().map_coefficients(lambda c: c.lift_centered(), new_base_ring=ZZ)) 1 - 2*y - y^2

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Conversion from finite field to integer polynomial

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Conversion from finite field to integer polynomial