Yes, b.list() works instead of list(b). There is also b.polynomial() which gives it as a polynomial over the prime field, so I could have done either Zy(b.list()) or Zy(b.polynomial()) as you can check.
I agree that b.coeffs() would make sense to have. Also, the parent field F125 = GF(5^3) has a dual_basis() method but no basis() method, which is strange. I think that finite fields should have a basis() method, giving their basis as a vector space over the prime field (or over its base field). On Wednesday, 27 November 2024 at 09:58:13 UTC Dima Pasechnik wrote: > I would have never guessed that list(b) works. Should there be b.list() or > b.coefs() ? > > > On 27 November 2024 02:48:05 GMT-06:00, John Cremona <john.c...@gmail.com> > wrote: > >> Use list() to get the coefficients: >> >> 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: Zy.<y> = ZZ[] >> sage: Zy(list(b)) >> 4*y^2 + 3*y + 1 >> >> On Wednesday, 27 November 2024 at 06:51:57 UTC Dima Pasechnik wrote: >> >>> A natural way would be to construct the quotient ring of GF(5)[x] >>> modulo (P), then b will be a polynomial in x, and you will have direct >>> access to its coefficients. >>> >>> >>> On 26 November 2024 16:46:50 GMT-06:00, "G. M.-S." <list...@gmail.com> >>> wrote: >>> >>>> >>>> Already asked on >>>> >>>> https://ask.sagemath.org/question/80389/conversion-from-finite-field-to-integer-polynomial >>>> >>>> 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. >>>> >>>> TIA, >>>> >>>> Guillermo >>>> >>>> -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sage-support/02b8aff6-c05b-4621-9d67-08678b139068n%40googlegroups.com.
