Are methods from calcium available in python-flint 0.5.x?

[kiryph]

I have used Calcium 0.4 and its python interface pycalcium/pyca.

Now it does not work anymore since macOS homebrew updated my Flint installation from 2.x to 3.x to which it was linked.

Since the documentation of Flint 3 says Arb and Calcium are merged into Flint, maybe the Python wrapper for Calcium has been merged into python-flint.

I have installed the current release of python-flint to pypi and try to see if I can access methods from Calcium

❯ pipenv install python-flint
Creating a virtualenv for this project...
...
❯ pipenv shell
Launching subshell in virtual environment...

❯ python
Python 3.9.4 (default, May  1 2021, 16:18:37)
[Clang 12.0.0 (clang-1200.0.32.29)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> import flint
>>> flint.__version__
'0.6.0'
>>> flint.
flint.Context(             flint.coerce_fmpz_mpolys(  flint.fmpz_mod(            flint.nmod(
flint.DomainError(         flint.ctx                  flint.fmpz_mod_ctx(        flint.nmod_mat(
flint.acb(                 flint.dirichlet_char(      flint.fmpz_mod_mat(        flint.nmod_poly(
flint.acb_mat(             flint.dirichlet_group(     flint.fmpz_mod_poly(       flint.nmod_series(
flint.acb_poly(            flint.flint_base           flint.fmpz_mod_poly_ctx(   flint.pyflint
flint.acb_series(          flint.fmpq(                flint.fmpz_mpoly(          flint.showgood(
flint.arb(                 flint.fmpq_mat(            flint.fmpz_mpoly_ctx(      flint.types
flint.arb_mat(             flint.fmpq_poly(           flint.fmpz_poly(           flint.utils
flint.arb_poly(            flint.fmpq_series(         flint.fmpz_series(
flint.arb_series(          flint.fmpz(                flint.functions
flint.arf(                 flint.fmpz_mat(            flint.good(

But I am struggling to check this.

The documentation of python-flint does not seem to be updated since the merge of Arb and Calcium into Flint:

https://fredrikj.net/python-flint/ (says version 0.3.0 from 2018)

[fredrik-johansson]

Instead of pycalcium it is currently possible to use flint_ctypes: https://github.com/flintlib/flint/blob/main/src/python/flint_ctypes.py

[oscarbenjamin]

It would definitely be good to add calcium wrappers in pytho-flint if anyone is interested in working on that.

[kiryph]

Instead of pycalcium it is currently possible to use flint_ctypes: https://github.com/flintlib/flint/blob/main/src/python/flint_ctypes.py

I am not sure if this helps me.

I had a simple method written for the GAP system which turns Cyclotomic numbers into LaTeX expressions with the help of Calcium:

PYTHONPATH := Filename(DirectoriesSystemPrograms(), "python3");
PYCALCIUM_DIRECTORY := Directory("~/Repositories/calcium/pycalcium"); # 0.4.0

InstallGlobalFunction(LaTeXStringCyclotomic, function (q)
  local input, str, output, pycode;
  input := InputTextString(String(q));
  str := "";
  output := OutputTextString(str, true);
  pycode := "import sys; from pyca import qqbar,Exp,Pi,I;";
  pycode := Concatenation(pycode, "E = lambda n: Exp(2*Pi*I/n);");
  pycode := Concatenation(pycode, "print(qqbar(eval(sys.stdin.read().replace('^', '**'))).fexpr().latex(), end='')");
  Process( PYCALCIUM_DIRECTORY, PYTHONPATH, input, output, [ "-c", pycode ] );
  return str;
end);

which can be used as following in GAP:

gap> mynumber := Sqrt(2);
E(8)-E(8)^3
gap> LaTeXStringCyclotomic(mynumber);
"\\sqrt{2}"

[fredrik-johansson]

This works:

>>> from flint_ctypes import *
>>> Exp = fexpr("Exp")
>>> Pi = fexpr("Pi")
>>> I = fexpr("NumberI")
>>> E = lambda n: Exp(2*Pi*I/n)
>>> qqbar(E(8) - E(8)**3).fexpr().latex()
'\\sqrt{2}'

More directly, you could do:

>>> E = lambda n: (qqbar(2) / n).exp_pi_i()
>>> qqbar(E(8) - E(8)**3).fexpr().latex()
'\\sqrt{2}'

[kiryph]

@fredrik-johansson Thanks for your help. Yes, this works as expected with Flint 3.1.0 without python-flint:

I have updated my GAP code accordingly:

PYTHONPATH := Filename(DirectoriesSystemPrograms(), "python3");
PYTHON_FLINT3_DIRECTORY := Directory("~/Repositories/flint-3.1.0/src/python");

InstallGlobalFunction(LaTeXStringCyclotomic, function (q)
  local input, str, output, pycode;
  input := InputTextString(String(q));
  str := "";
  output := OutputTextString(str, true);
  pycode := "import sys; from flint_ctypes import *;";
  pycode := Concatenation(pycode, "E = lambda n: (qqbar(2) / n).exp_pi_i();");
  pycode := Concatenation(pycode, "print(qqbar(eval(sys.stdin.read().replace('^', '**'))).fexpr().latex(), end='')");
  Process( PYTHON_FLINT3_DIRECTORY, PYTHONPATH, input, output, [ "-c", pycode ] );
  return str;
end);

Should I close this issue?

[fredrik-johansson]

Should I close this issue?

Looks like there is no other open issue about wrapping calcium in python-flint, so may as well leave it open if you don't mind!

[oscarbenjamin]

On the current main branch and also the 0.7.0a5 prerelease there is some very limited access to calcium via the newly added generic rings module:

In [10]: from flint.types import _gr

In [11]: CA = _gr.gr_complex_ca_ctx.new()

In [12]: CA(2).sqrt() + 1
Out[12]: 2.41421 {a+1 where a = 1.41421 [a^2-2=0]}

In [13]: pi = CA('pi')

In [14]: pi**2 - 1
Out[14]: 8.86960 {a^2-1 where a = 3.14159 [Pi]}

This is very incomplete and not well tested though. Also I would expect the interface to change in future.

Also the documentation for python-flint has been updated here:
https://python-flint.readthedocs.io/en/latest/