* Weierstrass $\wp$: `weierp`
* inverse Weierstrass $\wp$: `weierpinv`
* derivative of Weierstrass $\wp$: `weierpprime`
* Weierstrass zeta: `weierzeta`
* Weierstrass sigma: `weiersigma`
Also adds parameter conversion functions:
* Weierstrass invariants $g_2, g_3$: `weierinvariants`
* half-periods $\omega_1, \omega_2$: `weierhalfperiods`
The idea for this PR was inspired by the `pyweierstrass` package by @stla / Stéphane Laurent:
* https://pyweierstrass.readthedocs.io/en/latest/
* https://github.com/stla/pyweierstrass
The code implementation in this PR is different to that in `pyweierstrass` although both packages derive from similar well known mathematical formulas. Differences between `pyweierstrass` and this `mpmath` implementation include but are not limited to:
* function names adapted to `mpmath` conventions;
* tau normalization: `tau` specifies the normalized period lattice `(1, tau)`, corresponding to half-periods `(1/2, tau/2)`; this differs from `pyweierstrass`, where `tau` denotes half-periods `(1, tau)`;
* support for disambiguating inverse values of Weierstrass $\wp$ by optionally passing the corresponding derivative value;
* internal refactoring of helper functions for integration with `mpmath`.
Dedicated to Stéphane Laurent who opened the original PR to request this functionality in `mpmath` and whose `pyweierstrass` package provided great utility to the author of this PR in the years since.
Co-authored-by: Stéphane Laurent <stla@users.noreply.github.com>
Closes#612
Graham Hesketh
aa205a2821