Fix division by zero in monomials_deflate.c.

[Jake-Moss]

The documentation for fmpz_mpoly_deflate (and similar) states

If any stride[v] is zero, the corresponding numerator e - shift[v] is assumed to
be zero, and the quotient is defined as zero. This allows the function to undo the
operation performed by fmpz_mpoly_inflate() when possible.

The previous comment and if-statement did not align, meaning that the denominator was not being checked leading to divisions by zero when stride[v] is 0.

Here is a MWE

#include "flint/fmpz_mpoly.h"

int main(void) {
    fmpz_mpoly_ctx_t ctx;
    fmpz_mpoly_t x, res;
    fmpz *stride, *shift;

    const char *vars = "x";

    fmpz_mpoly_ctx_init(ctx, 1, ORD_LEX);
    fmpz_mpoly_init(x, ctx);
    fmpz_mpoly_init(res, ctx);

    fmpz_mpoly_gen(x, 0, ctx);

    stride = flint_malloc(ctx->minfo->nvars * sizeof(fmpz));
    shift = flint_malloc(ctx->minfo->nvars * sizeof(fmpz));
    for (int i = 0; i < ctx->minfo->nvars; i++) {
      fmpz_init(stride + i);
      fmpz_init(shift + i);
    }

    fmpz_mpoly_print_pretty(x, &vars, ctx); flint_printf("\n");

    // Division by zero here
    fmpz_mpoly_deflate(res, x, shift, stride, ctx);

    fmpz_mpoly_print_pretty(res, &vars, ctx); flint_printf("\n");

    for (int i = 0; i < ctx->minfo->nvars; i++) {
      fmpz_clear(stride + i);
      fmpz_clear(shift + i);
    }
    flint_free(stride);
    flint_free(shift);

    fmpz_mpoly_clear(x, ctx);
    fmpz_mpoly_ctx_clear(ctx);
    return 0;
}

Without this patch:

~/ λ gcc scratch.c -lflint
~/ λ ./a.out
x
Exception (fmpz_divexact). Division by zero.
aborted (core dumped)

With:

~/ λ gcc scratch.c -lflint
~/ λ ./a.out
x
1

From python-flint here: flintlib/python-flint#216 (comment)

[Jake-Moss]

I believe I was miss-using the deflation functions that caused me to run into this, however it still does not look quite right to me in it's current form.

[albinahlback]

Could you add a test case for this?

[Jake-Moss]

Done, I've added the test to the fmpz_mpoly suite rather than the mpoly tests as it has existing inflation/deflation tests.

[fredrik-johansson]

Looks good, thanks!