Hi!
On 19 Apr., 03:33, vdelecroix <20100.delecr...@gmail.com> wrote:
> My two attempts were the followings
> {{{
> sage: K.<t> = PolynomialRing(QQ,'t')
> sage: A2 = QuotientRing(K, Ideal(t^2))
> sage: A3 = QuotientRing(K, Ideal(t^3))
> sage: P = A2(t^4 + 3*t + 1)
>
> }}}
>
> First method: try to coerce
> {{{
> sage: A3(P)
> Traceback (click to the left of this block for traceback)
> ...
> TypeError: Unable to coerce 3*tbar + 1 (<class
> 'sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotie
> \
> ntRingElement'>) to Rational
This works:
sage: A3(P.lift())
3*tbar + 1
P.lift() returns the unique polynomial (in K!) mapping to P of degree
less then the modulus of the quotient.
Alternatively (although this is probably just a very nasty work-
around) you could use multi-variate polynomial rings. Here, the
conversion works (it is not coercion, since there is no ring map from
A2 to A3 mapping A2(t) to A3(t)).
sage: K.<t,foobar> = QQ[]
sage: A2 = QuotientRing(K, Ideal(t^2))
sage: A3 = QuotientRing(K, Ideal(t^3))
sage: P = A2(t^4 + 3*t + 1)
sage: A3(P)
3*tbar + 1
I often found that multivariate polynomial rings are much better
implemented in Sage than univariate rings. And I find it annoying that
both provide different methods.
Cheers,
Simon
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