Hey, You need to make sure the order of the variables agrees: sage: A = QQ['t'] sage: B = A['x','y'] sage: C = QQ['t', 'x','y'] sage: C.coerce(B.0) x
The reason the order is important is say you have QQ['x,y'] and QQ['y,x'], should the coercion be index to index or name to name? (Although I'd advocate for multivariate polynomial rings to sort their generators upon creation so that QQ['x,y'] is QQ['y,x'] in the sense of python.) Best, Travis On Thursday, October 1, 2015 at 1:05:20 PM UTC-5, len...@ackermans.info wrote: > > Thanks for your answer! I was able to create the required homomorphism > with your suggested method. Out of curiosity: how would you explicitly > define what is mapped to the variable of the inner polynomial ring? (When > for example, they have different names.) The homomorphism in your example > clearly sends x in B to x in C, so why doesn't hom() tell this? Is there a > way to find out what a homomorphism actually does, apart from by giving it > some input? > > My original problem was actually coercing from a multivariate polynomial > ring over a polynomial ring to a single multivariate polynomial ring. In > this case there is no coercion: > sage: A = QQ['t'] > sage: B = A['x','y'] > sage: C = QQ['x','y', 't'] > sage: C.coerce(B(1)) > (...) > TypeError: no canonical coercion from Multivariate Polynomial Ring in x, y > over Univariate Polynomial Ring in t over Rational Field to Multivariate > Polynomial Ring in x, y, t over Rational Field > > > On Thursday, October 1, 2015 at 6:47:36 PM UTC+2, Nils Bruin wrote: >> >> On Thursday, October 1, 2015 at 8:15:39 AM UTC-7, len...@ackermans.info >> wrote: >>> >>> In my code I often encounter elements of polynomial rings of polynomial >>> rings. Since some functions only work on multivariate polynomial rings I >>> need to create a homomorphism, but I'm unable to do this. What is the >>> recommended way? >>> >> >> This is actually one of the things where sage's coercion framework is >> pretty advanced. You do have to make sure that the names of the variables >> agree, tough. Sage uses those names to figure out how to coerce. To define >> the homomorphism: >> >> sage: A=QQ['x'] >> sage: B=A['y'] >> sage: C=QQ['x','y'] >> sage: B.hom([C.1]) >> Ring morphism: >> From: Univariate Polynomial Ring in y over Univariate Polynomial Ring >> in x over Rational Field >> To: Multivariate Polynomial Ring in x, y over Rational Field >> Defn: y |--> y >> >> The homomorphism is described by "send the generator of B (over A) to the >> second generator of C, and figure out yourself how to coerce A into C". It >> can do the latter because both A and C are generated over a common subring >> (QQ) and the generator of A has a name that is equal to the name of a >> generator of C: an obvious target. >> >> Indeed, these rules allow sage to even coerce B into C: you can just mix >> them in expressions: >> >> sage: A.0+B.0+C.0 >> 2*x + y >> >> It chooses the multivariate ring as the common parent: >> >> sage: parent(A.0+B.0+C.0) is C >> True >> >> You can also obtain the coercion map sage uses itself and use it as the >> homomorphism you asked for at the top: >> >> sage: C.coerce_map_from(B) >> Conversion map: >> From: Univariate Polynomial Ring in y over Univariate Polynomial Ring >> in x over Rational Field >> To: Multivariate Polynomial Ring in x, y over Rational Field >> >> >> >>> Further questions: >>> Why is there no standard coercion between nested polynomial rings and >>> multivariate polynomial rings? >>> >> >> There is such a coercion >> >> Should we change functions on polynomials like factor() to work in the >>> case of nested polynomial rings, by using a coercion to multivariate >>> polynomial rings? >>> >> >> In individual cases: possibly. In general: no. There could be merit in >> "nested" arithmetic. >> >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
