Rational result about sphericalharmonicexpansions.jl

[hofmannmartin]

The coefficients in the polynomial are inherently irrational (require sqrt for calculation) so simply using Rational would not do the trick. What are you trying to achieve?

[Lightup1]

Dear @hofmannmartin
Sorry for the ambiguous description.
What I mean is whether it is possible to give accurate symbolic return of spherical harmonics. In that way, one can get accurate ratianal result when dividing polyvar coeffients.

For example:

julia> p4
0.31735664074561293x⁴ + 0.6347132814912259x²y² - 2.5388531259649034x²z² + 0.31735664074561293y⁴ - 2.5388531259649034y²z² + 0.8462843753216343z⁴

julia> p4.terms[1].coefficient/p4.terms[end].coefficient
0.3750000000000001

If the coefficients are symbolic, one can get accurate $3//8$

[hofmannmartin]

In principle one could make different normalizations possible (#6), which would yield the polynomials you desire. However, this refactoring of the package would require some time, which I currently do not have.

Important is to use BigInt and Rational{BigInt}, respectively to avoid overflow. So the generation of the polynomials would be much slower.