Division with remainder for Ore Polynomials

[vioneers]

The goal of this Pull Request is to implement division with remainder for Ore polynomials:

// Returns the unique pair (Q, R) such that U = QV + R and ord(R) < ord(V)
int _gr_ore_poly_divrem(gr_ptr Q, gr_ptr R, gr_srcptr U, slong lenU, gr_srcptr V, slong lenV, gr_ore_poly_ctx_t ctx)
int gr_ore_poly_divrem(gr_ore_poly_t Q, gr_ore_poly_t R, const gr_ore_poly_t U, gr_ore_poly_t V, gr_ore_poly_ctx_t ctx)

Tests and documnetation are also added.

If you have any feedback, please feel free to let me know. Thank you!

[rburing]

Besides adding these new methods, they will have to be registered in the table of GR methods for gr_ore_poly contexts, around here:

flint/src/gr_ore_poly/ctx.c

Lines 300 to 302 in 290bd1b

	{GR_METHOD_EUCLIDEAN_DIV, (gr_funcptr) gr_ore_poly_euclidean_div},
	{GR_METHOD_EUCLIDEAN_REM, (gr_funcptr) gr_ore_poly_euclidean_rem},
	{GR_METHOD_EUCLIDEAN_DIVREM, (gr_funcptr) gr_ore_poly_euclidean_divrem},

See e.g. gr_poly for how that's done:

flint/src/gr/polynomial.c

Lines 843 to 845 in 290bd1b

	{GR_METHOD_EUCLIDEAN_DIV, (gr_funcptr) polynomial_euclidean_div},
	{GR_METHOD_EUCLIDEAN_REM, (gr_funcptr) polynomial_euclidean_rem},
	{GR_METHOD_EUCLIDEAN_DIVREM, (gr_funcptr) polynomial_euclidean_divrem},

Those are some small wrapper functions.

After this, they will also be tested by the generic ring tests.

[mezzarobba]

Here I'm wondering if it wouldn't be better to call lmul_gen repeatedly instead, or introducing a function that multiplies by D^k.

[fredrik-johansson]

Besides adding these new methods, they will have to be registered in the table of GR methods for gr_ore_poly contexts, around here:

After this, they will also be tested by the generic ring tests.

Yes, though I have no idea if the tests do the right thing in the noncommutative case :-)

[rburing]

Yes, though I have no idea if the tests do the right thing in the noncommutative case :-)

Let's find out! :D