Thank you very much, Dima and John. As they say in Spanish: "No te acostarás sin saber una cosa más."
Guillermo On Wed, 27 Nov 2024 at 12:26, John Cremona <john.crem...@gmail.com> wrote: > 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/CANnG18_z%3Dzpm%2BUTRsx07m_XAVsRVH3KX_zUC%3DdnCOEAB%2BO3F1A%40mail.gmail.com.
