gr_poly_integral fails for polynomial over matrix ring

[rburing]

Example code:

#include <stdio.h>
#include "flint/gr_poly.h"

int main() {
    int status = GR_SUCCESS;

    gr_ctx_t ctx;
    gr_ctx_init_fmpq(ctx);

    gr_ctx_t mat_ctx;
    gr_ctx_init_matrix_ring(mat_ctx, ctx, 2);

    gr_poly_t f;
    gr_poly_init(f, mat_ctx);
    status |= gr_poly_gen(f, mat_ctx);

    printf("f = ");
    gr_poly_print(f, mat_ctx);
    printf("\n");

    status |= gr_poly_integral(f, f, mat_ctx);

    if (status == GR_SUCCESS) {
        printf("integral(f) = ");
        gr_poly_print(f, mat_ctx);
        printf("\n");
    } else {
        printf("failed to calculate integral(f)\n");
    }

    gr_poly_clear(f, mat_ctx);

    gr_ctx_clear(mat_ctx);
    gr_ctx_clear(ctx);

    flint_cleanup_master();

    return 0;
}

Output:

f = [[1, 0],
[0, 1]]*x
failed to calculate integral(f)

The reason is that gr_div_ui fails for elements of a matrix ring. For example:

    gr_ptr res;
    GR_TMP_INIT(res, mat_ctx);
    int my_status = gr_one(res, mat_ctx);
    my_status |= gr_div_ui(res, res, 12, mat_ctx);
    printf("success = %d\n", (my_status == GR_SUCCESS));
    GR_TMP_CLEAR(res, mat_ctx);

outputs success = 0, even though there would be a well-defined result.

[fredrik-johansson]

gr_mat is missing most scalar methods. Will fix.