Revision history [back]

I am having an error whenever I attempt to construct a homomorphism

• from a Laurent polynomial ring

• to a Laurent polynomial ring in more than one variable.

Ex (SageMath Cloud, 5/12/15):

R.<a>=LaurentPolynomialRing(ZZ)

S.<b,c>=LaurentPolynomialRing(ZZ)

phi=Hom(R,S)([b])

TypeError: images do not define a valid homomorphism

Additional data:

• An identical error occurs with the variant syntax R.hom([b]).

• There is no error if the domain is replaced by PolynomialRing(ZZ,'a').

• There is no error if the image of 'a' is 1.

• There is no error if the codomain is replaced by its own fraction field.

It appears that Sage is incorrectly determining that the reciprocal of the image of the generator(s) is not in the codomain.

I am having an error whenever I attempt to construct a homomorphism

• from a Laurent polynomial ring

• to a Laurent polynomial ring in more than one variable.

Ex (SageMath Cloud, 5/12/15):

R.<a>=LaurentPolynomialRing(ZZ)

S.<b,c>=LaurentPolynomialRing(ZZ)

phi=Hom(R,S)([b])

TypeError: images do not define a valid homomorphism

Additional data:

• An identical error occurs with the variant syntax R.hom([b]).

• An identical error occurs when trying to construct the identity homomorphism on LaurentPolynomialRing(ZZ,'x,y').

• There is no error if the domain is replaced by PolynomialRing(ZZ,'a').

• There is no error if the image of 'a' is 1.

• There is no error if the codomain is replaced by its own fraction field.

It appears that Sage is incorrectly determining that the reciprocal of the image of the generator(s) is not in the codomain.

I am having an error whenever I attempt to construct a homomorphism

• from a Laurent polynomial ring

• to a Laurent polynomial ring in more than one variable.

Ex (SageMath Cloud, 5/12/15):

R.<a>=LaurentPolynomialRing(ZZ)

S.<b,c>=LaurentPolynomialRing(ZZ)

phi=Hom(R,S)([b])

TypeError: images do not define a valid homomorphism

Additional data:

• An identical error occurs with the variant syntax R.hom([b]).

• An identical error occurs when trying to construct the identity homomorphism on LaurentPolynomialRing(ZZ,'x,y').

• There is no error if the domain is replaced by PolynomialRing(ZZ,'a').

• There is no error if the image of 'a' is 1.

• There is no error if the codomain is replaced by its own fraction field.

It appears that Sage is incorrectly determining that the reciprocal of the image of the generator(s) is not in the codomain.