Hello, I want to do some calculations over an extension of the polynomial ring Z[q] which many quantum integers have square roots.
Initially I thought that I was going to be easy and that I could do the following: sage: R.<q>=PolynomialRing(QQ) sage: s3=(1+q+q^2).sqrt(name='s3') sage: s4=(1+q+q^2+q^3).sqrt(name='s4') sage: s3*s4 # this blows up:( Unfortunately, the last line blows up as s3 and s4 do not belong to a common ring as far as sage is concerned, which is fair enough. So then I tried: sage: R=PolynomialRing(ZZ,'q') sage: R2.<s2>=R.extension(x^2-1-q,'s2') sage: R3.<s3>=R2.extension(x^2-1-q-q^2,'s3') sage: R4.<s4>=R3.extension(x^2-1-q-q^2-q^3,'s4') sage: (s2*s3)^2 (q + 1)*s2 + q^2 + 3*q + 2 This seems to work but it is quite cumbersome especially as I want to be able to adjoin the square roots s2, s3, ..., s<n> for an integer n. Two questions: 1. Is there a better way to do this? Ultimately I want to work with modules defined over this (awful) ring. So, by "better" I do not necessarily mean less cumbersome: I need arithmetic to be efficient. 2. Second, I really need to work of the fraction of this ring -- or rather, I need s2, s3, ... to be invertible. Unfortunately, sage: FractionField(R4) returns a not implemented error.I can probably get around this by adjoining inverses, but I am hoping that there is a better to do this. Any suggestions? Cheers, Andrew -- 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 post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
