What is the best way to implement polynomials with fractional exponents with SageMath?

Question

I want to perform manipulations in a polynomial ring where the terms can have fractional exponents. However just trying to use the fractions returns a value error. Obviously I could just set the indeterminate to be some power of itself to eliminate the fractional exponents, but this would involve altering all the formulas, is there a better way?

Answer 1

Puiseux series and Puiseux polynomials in SageMath

There are two Sage tickets on the topic, one about Puiseux series and a later one about Puiseux polynomials.

• Sage Trac ticket 9289: Implement Puiseux polynomials
• Sage Trac ticket 4618: Puiseux series

There have also been numerous discussions on sage-devel and sage-support.

• sage-devel discussions mentioning Puiseux
• sage-support discussions mentioning Puiseux

There is a package where this functionality is implemented.

• abelfunctions: Abelian functions, Riemann surfaces, and algebraic curves

  A library for computing with Abelian functions, Riemann surfaces, and algebraic curves.

  Documentation: https://github.com/abelfunctions/abelfunctions/blob/master/doc/README.md

Puiseux series and Puiseux polynomials in Oscar

If using Sage is not a strong requirement, you could have a look at the implementation in Oscar. See the recent post on the Oscar blog:

• Puiseux series: a challenging computation