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TypeError for hom between multivariate Laurent polynomial rings?

asked 2015-05-12 11:47:39 -0600

Greg Muller gravatar image

updated 2015-10-16 12:19:59 -0600

FrédéricC gravatar image

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):




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.

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I note that R.hom([b], check=False) works ok.

Francis Clarke gravatar imageFrancis Clarke ( 2015-05-15 04:54:46 -0600 )edit

1 answer

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answered 2015-05-16 04:28:22 -0600

Francis Clarke gravatar image

It seems that the root of the problem is :

sage: R.<a> = LaurentPolynomialRing(ZZ)
sage: S.<b,c> = LaurentPolynomialRing(ZZ)
sage: a.is_unit()
sage: b.is_unit()
Traceback (most recent call last):
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Dang! I noticed even with your check=False workaround, I got a NotImplementedError when I tried to evaluate a map. How do I go about implementing it myself?

Greg Muller gravatar imageGreg Muller ( 2015-05-17 12:56:22 -0600 )edit

I just made a ticket about that :

FrédéricC gravatar imageFrédéricC ( 2015-05-21 05:05:24 -0600 )edit

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Asked: 2015-05-12 11:47:39 -0600

Seen: 63 times

Last updated: May 16 '15