API for crt_cartesion

[Chris Smith]

There are several APIs for crt-like functions as described in the `crt` docstring:

• crt(mod, rem)
• gf_crt(rem, mod)
• solve_congruence(*rem_mod_pairs)

There is a new function, `crt_cartesian` being introduced by this PR. e.g.

    >>> from sympy.ntheory.modular import crt_cartesian
    >>> from sympy.utilities.iterables import cartes
    >>> rem = [[3, 5], [3, 7]]
    >>> crt_cartesian(rem, [7, 11])
     [3, 73, 47, 40]
    >>> [(p%7, p%11) for p in _]
    [(3, 3), (3, 7), (5, 3), (5, 7)]
    >>> assert _ == list(cartes(*rem))

 

Does anyone use such a calculation? Should the API of the new function be the same as `crt`? reversed? a dictionary of `{modulus m: list of residuals wrt modulus m}`? Should the output include the product of `mod` like crt does?

[Aaron Meurer]

I don't use crt very often and I can't speak to the usefulness of this
function, but it does seem odd to me that crt() has mod as the first
argument. I would expect it to be the second argument.

Aaron Meurer

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