fmpz_mpoly_pfrac_init: internal error

[F-Feng]

Dear flint developers,

I encountered an internal error when calling fmpz_mpoly_factor on a polynomial. Here is an example to reproduce it.

#include "flint/fmpz.h"
#include "flint/fmpz_mpoly_factor.h"

int main() {
    fmpz_mpoly_ctx_t ctx;
    fmpz_mpoly_t p;
    fmpz_mpoly_factor_t f;

    //const char * vars[] = {"x1", "x2", "x3", "x4", "x5"}; // no error
    const char * vars[] = {"x1", "x5", "x3", "x4", "x2"}; // fmpz_mpoly_pfrac_init: internal error

    fmpz_mpoly_ctx_init(ctx, 5, ORD_LEX);
    fmpz_mpoly_init(p, ctx);
    fmpz_mpoly_factor_init(f, ctx);

    int nok = fmpz_mpoly_set_str_pretty(p, "-2*x1*x5^2*x3*x4*x2^3+24*x1^4*x5^2*x3^3*x4*x2-4*x5^2*x4^3*x2^3-40*x1^2*x5^2*x3^4*x4^2*x2-6*x1^4*x5^2*x4^2*x2^2-4*x5^2*x3*x4^2*x2^2+14*x1*x5^2*x3^3*x2^2+36*x1*x5^2*x3^5*x4^2*x2^2+10*x5^2*x3^2*x4*x2^3-64*x5^2*x3^5*x4*x2^3+17*x1^2*x5^2*x4^4*x2^3-36*x1*x5^2*x3^2*x4^2*x2^2+29*x1^2*x5^2*x4^5*x2^2-36*x1^4*x5^2*x3^2*x4^2-6*x1^4*x5^2*x3*x4*x2^2-14*x1^3*x5^2*x3*x4^2-6*x1^3*x5^2*x3^4*x2^2-33*x1^3*x5^2*x3^2*x4*x2^2-4*x1^2*x5^2*x3*x4^5*x2-44*x1^4*x5^2*x3^2*x4^3*x2-132*x1^3*x5^2*x3*x4^3*x2-120*x5^2*x3^3*x4^3*x2^3+8*x1^3*x5^2*x3*x4^2*x2^3+4*x1*x5^2*x4^2*x2^2+6*x1^5*x5^2*x3*x4+50*x1*x5^2*x3^3*x4^4*x2^2-x5^2*x3^2*x2^3+16*x1^3*x5^2*x4^5*x2-24*x1^2*x5^2*x3^3*x4*x2-6*x1^6*x5^2*x3^2*x4^2-15*x1^2*x5^2*x3^4*x2-6*x1^4*x5^2*x4^2+55*x1*x5^2*x3^4*x4^3*x2^2+42*x1^2*x5^2*x3^2*x4^2*x2^3-6*x1^5*x5^2*x3^3*x4*x2-6*x1*x5^2*x3*x4^4*x2+4*x1^2*x5^2*x3^2*x4^3*x2-10*x1^2*x5^2*x3*x4*x2^2-12*x1^4*x5^2*x3^3*x4-18*x1^4*x5^2*x3^2*x4^2*x2^2-84*x1^3*x5^2*x3*x4^2*x2^2+6*x1^2*x5^2*x3^6*x2^2+120*x5^2*x3^3*x4^3*x2^2+4*x1^3*x5^2*x3^2*x4*x2^3+18*x1*x5^2*x3^3*x4*x2+24*x1^3*x5^2*x3*x4^3-6*x1^2*x5^2*x4^5*x2^3+18*x1^4*x5^2*x3^2*x4^3-5*x5^2*x3^2*x4*x2^2-19*x1^2*x5^2*x3*x4^4*x2-10*x1*x5^2*x3^3*x2^3+2*x1^3*x5^2*x3^5*x2^2+16*x1^3*x5^2*x3^3*x4^2*x2+13*x1*x5^2*x3^6*x4*x2^2-42*x1^4*x5^2*x4^3*x2-18*x1*x5^2*x3^2*x4^2*x2^3-60*x1^2*x5^2*x4^4*x2^2+44*x5^2*x3^5*x4*x2^2-3*x1^3*x5^2*x4^5+2*x1*x5^2*x3*x4*x2^2-24*x1*x5^2*x3^2*x4^3*x2-x5^2*x3*x4^2*x2^3+8*x1*x5^2*x3*x4^6*x2^2-x5^2*x4^3*x2^2+20*x1*x5^2*x3^4*x4^2*x2+4*x1^2*x5^2*x3*x4*x2^3-90*x1^2*x5^2*x3^2*x4^2*x2^2+13*x1^2*x5^2*x3^5*x2-48*x1^3*x5^2*x4^4*x2+15*x1^4*x5^2*x4^3+2*x1*x5^2*x3*x4^5*x2+8*x1^3*x5^2*x4^4-4*x1*x5^2*x4^2*x2^3+2*x1^3*x5^2*x3^6*x2-x1^4*x5^2*x3^2*x2+10*x1^3*x5^2*x3^2*x4^4*x2-31*x1^4*x5^2*x3*x4^4*x2+12*x1^4*x5^2*x3*x4^4-16*x1^3*x5^2*x3^4*x4*x2-3*x1^3*x5^2*x3^4*x4-2*x1^6*x5^2*x3^3*x4+84*x5^2*x3^4*x4*x2^3-55*x5^2*x3^2*x4^4*x2^3-32*x1^2*x5^2*x3^2*x4^3*x2^3-140*x1*x5^2*x3^4*x4^2*x2^2+50*x1*x5^2*x3*x4^4*x2^3-2*x1^6*x5^2*x4^4+42*x1^3*x5^2*x4^4*x2^2+18*x1^2*x5^2*x3^2*x4^2*x2-22*x1^2*x5^2*x3^5*x2^2-6*x1^2*x5^2*x3*x4^3+8*x1^2*x5^2*x3^3*x4*x2^3-3*x1^2*x5^2*x3^4*x2^3-18*x1^5*x5^2*x3^2*x4^2*x2-15*x1*x5^2*x4^3*x2^2-14*x1*x5^2*x3*x4^5*x2^2-5*x1^3*x5^2*x3^4*x4*x2^2+7*x5^2*x3^3*x2^3+24*x1^5*x5^2*x3*x4^3-27*x5^2*x3^2*x4^5*x2^2+88*x1^3*x5^2*x3*x4^2*x2-4*x1^2*x5^2*x3^6*x2+90*x1^4*x5^2*x3^2*x4^2*x2+x1^2*x5^2*x3^4*x4+12*x1^4*x5^2*x3^3*x4^2-x1^5*x5^2*x3^4*x4+116*x5^2*x3^3*x4^2*x2^3-6*x1^3*x5^2*x3*x4^3*x2^3-76*x1*x5^2*x3^3*x4*x2^2+21*x1^2*x5^2*x4^4*x2+x5^2*x4^2*x2^3-40*x1^3*x5^2*x3^3*x4^2*x2^2-8*x1^3*x5^2*x3^5*x2+20*x5^2*x3*x4^3*x2^2+12*x1^4*x5^2*x4^3*x2^2+94*x1^2*x5^2*x3*x4^4*x2^2+68*x1*x5^2*x3^2*x4^3*x2^2-6*x1^5*x5^2*x4^4*x2+6*x1^5*x5^2*x4^2-2*x1*x5^2*x3^2*x2^2-2*x5^2*x3^3*x2^2-6*x1^5*x5^2*x3*x4*x2+18*x5^2*x3^2*x4^5*x2^3-26*x1^5*x5^2*x3*x4^2+30*x1^2*x5^2*x3^3*x4*x2^2+4*x1^6*x5^2*x3^2*x4+30*x1^2*x5^2*x3^4*x2^2+2*x1^2*x5^2*x3*x4^2+3*x1^4*x5^2*x3^3*x2-13*x1^3*x5^2*x4^5*x2^2+16*x1*x5^2*x4^3*x2^3-16*x1*x5^2*x3*x4^5*x2^3-8*x1*x5^2*x3*x4^4*x2^2+x1^2*x5^2*x3^5*x2^3-2*x1^3*x5^2*x4^4*x2^3+80*x5^2*x3^2*x4^4*x2^2-4*x1^2*x5^2*x4^6*x2^2-54*x5^2*x3^4*x4*x2^2+4*x1^2*x5^2*x3*x4*x2+20*x1*x5^2*x3^4*x4^2*x2^3+86*x1^2*x5^2*x3^2*x4^3*x2^2+x1^2*x5^2*x4^3+40*x1*x5^2*x3^2*x4^3*x2^3+20*x1^3*x5^2*x3^3*x4^3*x2+17*x1^4*x5^2*x4^2*x2+40*x1^2*x5^2*x3^4*x4^2*x2^2-6*x1^4*x5^2*x3^3*x4*x2^2+2*x1*x5^2*x3^2*x2^3-13*x1^5*x5^2*x4^3+18*x1*x5^2*x3^2*x4^2*x2-2*x1*x5^2*x3^3*x2-23*x1^2*x5^2*x3*x4^4*x2^3+120*x1^3*x5^2*x3*x4^3*x2^2-96*x5^2*x3^3*x4^2*x2^2-14*x1^2*x5^2*x3*x4^5*x2^2+10*x1^3*x5^2*x3^5*x4*x2+12*x1^3*x5^2*x3^4*x2+32*x1^3*x5^2*x3^2*x4*x2-8*x1^2*x5^2*x4^5*x2+15*x1^4*x5^2*x3^2*x4+16*x1^4*x5^2*x3*x4*x2+2*x1^3*x5^2*x3*x4+30*x1*x5^2*x3^3*x4*x2^3-50*x1^3*x5^2*x3*x4^4*x2^2-2*x1^6*x5^2*x3*x4-16*x1^2*x5^2*x3^3*x4^2*x2^2+28*x5^2*x3*x4^5*x2^2-6*x1^2*x5^2*x3^2*x4^2-8*x1^3*x5^2*x3^3*x2+24*x1^5*x5^2*x3^2*x4^2+24*x1^5*x5^2*x3*x4^2*x2+27*x1*x5^2*x3^2*x4^5*x2^2+2*x1*x5^2*x3^7*x2^2-40*x1*x5^2*x3^4*x4*x2^3-20*x1*x5^2*x3^2*x4^4*x2^3-14*x1^2*x5^2*x4^2*x2^2-29*x1^2*x5^2*x3*x4^2*x2+100*x5^2*x3^4*x4^2*x2^2-2*x1^2*x5^2*x4^4+6*x5^2*x3*x4^4*x2^3+48*x1^2*x5^2*x3*x4^3*x2^3+6*x1*x5^2*x3^4*x2+8*x1^5*x5^2*x4^4+10*x1*x5^2*x3^5*x4*x2+28*x1*x5^2*x3*x4^3*x2^2-10*x1*x5^2*x4^5*x2^2+4*x5^2*x4^6*x2^2+4*x1^3*x5^2*x4^3*x2^3-2*x1^3*x5^2*x3^3*x4*x2^3-4*x1*x5^2*x3^2*x4*x2-84*x5^2*x3^2*x4^3*x2^2-10*x1^2*x5^2*x3^2*x4^4*x2^2+22*x5^2*x3^5*x2^3-16*x1^3*x5^2*x4^2*x2+4*x1*x5^2*x3^6*x2^3-2*x1^6*x5^2*x4^2-59*x1^2*x5^2*x3^4*x4*x2^2+20*x1*x5^2*x3^3*x4^3*x2+8*x5^2*x3^4*x2^2-108*x1^3*x5^2*x3^2*x4^2*x2-3*x1^4*x5^2*x3^4*x2-6*x1^4*x5^2*x3*x4+x1^2*x5^2*x4^5-18*x1^2*x5^2*x3^3*x2^2-20*x1*x5^2*x3^3*x4^2*x2^3-7*x1^3*x5^2*x3^2*x4-81*x1^4*x5^2*x3*x4^2*x2-x1^5*x5^2*x4^5+28*x5^2*x3^3*x4*x2^2-24*x1*x5^2*x4^4*x2^3-36*x5^2*x3*x4^4*x2^2-6*x1^4*x5^2*x4^4*x2^2-4*x1^2*x5^2*x3^2*x4*x2-18*x1^2*x5^2*x4^3*x2-20*x1^2*x5^2*x3^5*x4*x2-150*x1^2*x5^2*x3*x4^3*x2^2+5*x1^2*x5^2*x4^2*x2^3-70*x1*x5^2*x3^2*x4^4*x2^2+118*x1*x5^2*x3^4*x4*x2^2-125*x5^2*x3^4*x4^2*x2^3+12*x1^5*x5^2*x4^3*x2-6*x1^5*x5^2*x3^2*x4^3-40*x1^2*x5^2*x3^3*x4^3*x2-2*x1^2*x5^2*x3^3*x4-2*x1^3*x5^2*x3^2*x2^2-x5^2*x4^7*x2^2+12*x1^5*x5^2*x3^2*x4*x2+8*x1^5*x5^2*x3^3*x4-6*x1*x5^2*x3^5*x2+6*x1^2*x5^2*x3^2*x4^3-8*x5^2*x3*x4^5*x2^3-18*x1^2*x5^2*x3^3*x4^2*x2^3+152*x1*x5^2*x3^3*x4^2*x2^2+3*x1^2*x5^2*x3^3*x2^3+20*x1*x5^2*x4^4*x2^2-4*x1^5*x5^2*x3*x4^4-48*x5^2*x3^3*x4*x2^3+4*x1^2*x5^2*x3*x4^4-18*x5^2*x3^4*x2^3-70*x1^3*x5^2*x3^2*x4^3*x2^2-x1^2*x5^2*x3^2*x2-18*x1^4*x5^2*x3*x4^3*x2^2-12*x1^3*x5^2*x3^3*x4^2-14*x1^3*x5^2*x3*x4*x2-36*x1^4*x5^2*x3^2*x4*x2+64*x5^2*x3^2*x4^3*x2^3-2*x1*x5^2*x3*x4^2*x2-2*x1^2*x5^2*x3^4*x4*x2^3+4*x1^6*x5^2*x4^3-14*x1*x5^2*x3^6*x2^2-12*x5^2*x3^5*x2^2+x5^2*x4^6*x2^3-54*x1*x5^2*x3*x4^3*x2^3+16*x1*x5^2*x4^5*x2^3+24*x1^3*x5^2*x3^3*x4*x2^2-45*x1^3*x5^2*x4^3*x2^2+x1^4*x5^2*x3^5*x2-6*x1^3*x5^2*x3^2*x4^2*x2^3-18*x1^3*x5^2*x3^2*x4^3-36*x1*x5^2*x3^3*x4^2*x2-36*x1^4*x5^2*x3*x4^3+12*x1^4*x5^2*x3^2*x4*x2^2+14*x1^3*x5^2*x3*x4*x2^2+4*x1^2*x5^2*x3^2*x2^2+96*x1^4*x5^2*x3*x4^3*x2-7*x1^3*x5^2*x4^3+8*x1^3*x5^2*x3^3*x4+64*x1^3*x5^2*x3^2*x4^3*x2+x1*x5^2*x4^7*x2^2+2*x1*x5^2*x3^6*x2-12*x1^4*x5^2*x4^4-2*x1^3*x5^2*x4^2*x2^3-16*x1*x5^2*x3*x4^2*x2^2+3*x5^2*x3*x4^6*x2^3-12*x1^3*x5^2*x3^3*x4*x2+48*x1^3*x5^2*x4^3*x2-4*x1*x5^2*x3^2*x4*x2^3-36*x5^2*x3^5*x4^2*x2^2+3*x5^2*x3^7*x2^3+36*x5^2*x3^2*x4^2*x2^2+16*x1*x5^2*x3^5*x4*x2^3+18*x5^2*x3^6*x4*x2^3+18*x1*x5^2*x3^4*x2^3-55*x5^2*x3^4*x4^3*x2^2+48*x1^2*x5^2*x3*x4^3*x2+26*x1^2*x5^2*x3^5*x4*x2^2+2*x1^3*x5^2*x3*x4^5*x2+13*x1^2*x5^2*x3^2*x4*x2^2+49*x1^2*x5^2*x4^3*x2^2+33*x1^4*x5^2*x4^4*x2-29*x1^2*x5^2*x3*x4^2*x2^3-24*x1*x5^2*x3^4*x4*x2+4*x5^2*x4^4*x2^2+10*x1*x5^2*x3^2*x4^4*x2+4*x1^2*x5^2*x3^3*x4^2-4*x1*x5^2*x4^6*x2^3-4*x5^2*x4^5*x2^3+2*x1^3*x5^2*x3^2*x2+3*x1^4*x5^2*x4^5+20*x1^3*x5^2*x3^4*x4^2*x2+3*x1^4*x5^2*x3^4*x4+20*x1^2*x5^2*x3^3*x4^3*x2^2-12*x1^3*x5^2*x3*x4^4-50*x5^2*x3^3*x4^4*x2^2-6*x1^6*x5^2*x3*x4^3-18*x1^5*x5^2*x3*x4^3*x2+8*x5^2*x3^6*x2^2-4*x1^5*x5^2*x3^3*x4^2+32*x1*x5^2*x3^5*x2^2+45*x5^2*x3^5*x4^2*x2^3+13*x1*x5^2*x3^2*x4*x2^2+6*x1*x5^2*x3*x4^3*x2-13*x5^2*x3^6*x4*x2^2-2*x5^2*x3^7*x2^2-70*x1*x5^2*x3^5*x4*x2^2-36*x5^2*x3^2*x4^2*x2^3+16*x1^3*x5^2*x4^2*x2^2+44*x1^2*x5^2*x3^4*x4*x2-20*x1^2*x5^2*x3^2*x4^4*x2-26*x1^4*x5^2*x3^3*x4^2*x2-8*x5^2*x3*x4^6*x2^2+22*x1*x5^2*x3*x4^2*x2^3-2*x1^3*x5^2*x3*x4*x2^3-140*x1*x5^2*x3^3*x4^3*x2^2+2*x1^3*x5^2*x4^2-x1^2*x5^2*x3^2*x2^3+30*x1^4*x5^2*x3*x4^2+7*x1^2*x5^2*x3^3*x2+24*x1^3*x5^2*x3^2*x4^2+24*x1^4*x5^2*x3*x4^2*x2^2+108*x1^3*x5^2*x3^2*x4^2*x2^2-8*x1^4*x5^2*x4^5*x2+x1^2*x5^2*x3^2*x4+6*x1^3*x5^2*x3^3*x2^2+8*x1^6*x5^2*x3*x4^2+46*x1^2*x5^2*x3^3*x4^2*x2-4*x1^4*x5^2*x3^4*x4*x2+56*x1^3*x5^2*x3*x4^4*x2-14*x1*x5^2*x3^5*x2^3-13*x5^2*x3^6*x2^3-6*x5^2*x4^5*x2^2-13*x1^5*x5^2*x3^2*x4+45*x5^2*x3^3*x4^4*x2^3+80*x1^2*x5^2*x3*x4^2*x2^2+5*x1^2*x5^2*x4^2*x2+6*x5^2*x4^4*x2^3-6*x1^5*x5^2*x4^2*x2+60*x5^2*x3^4*x4^3*x2^3-32*x1*x5^2*x3^4*x2^2-16*x1^2*x5^2*x4^3*x2^3-10*x1^2*x5^2*x3^2*x4*x2^3", vars, ctx);
    if(nok) {
        flint_printf("fmpz_mpoly_set_str_pretty failed.\n");
        fflush(stdout);
        flint_abort();
    }

    if (!fmpz_mpoly_factor(f, p, ctx)) {
        flint_printf("fmpz_mpoly_factor failed.\n");
        fflush(stdout);
        flint_abort();
    }

    fmpz_mpoly_clear(p, ctx);
    fmpz_mpoly_factor_clear(f, ctx);
    fmpz_mpoly_ctx_clear(ctx);

    flint_cleanup_master();

    return 0;
}

PS: If I change the order of elements in the vars, no error occurs.

Best regards, Feng

[albinahlback]

That's a long polynomial! Can you print the exact error message you get? What version of FLINT are you using?

It shouldn't error inside fmpz_mpoly_pfrac_init. I suspect fmpz_mpoly_set_str_pretty is wrong in that case.

[F-Feng]

Apologies for the lengthy polynomial. I encountered this issue during my research, which is why I have included the entire polynomial here.

I am using flint-3.1.3, and the complete error message from the terminal appears as follows:

Flint exception (General error):
    fmpz_mpoly_pfrac_init: internal errorAborted (core dumped)

PS: The function fmpz_mpoly_set_str_pretty returns 0, indicating that fmpz_mpoly_set_str_pretty may work in this case.

[albinahlback]

Not sure if we will be able to solve this quickly. If you are able to answer these questions, it could be helpful in investigating this:

• Where does this polynomial arise?
• Do you know of any characteristics of this polynomial? (For instance, I think I see that it is not a homogeneous polynomial)
• Have you checked if fmpz_mpoly_set_str_pretty yields the correct output? (The initialization should always work, but just to make sure that this indeed is the problematic representation of this polynomial for fmpz_mpoly_pfrac_init)

[F-Feng]

Thank you for your response. Please take your time. I hope the following information may be helpful.

• The polynomial arises from my calculations of certain Feynman diagrams in Particle Physics, which often result in lengthy polynomials.
• I suspect that these polynomials do not exhibit any specific characteristics and are generally non-homogeneous.
• After using fmpz_mpoly_set_str_pretty, I verified the output with fmpz_mpoly_get_str_pretty and obtained the correct result.

[F-Feng]

By the way, here is the factorized output for the polynomial:

[tthsqe12]

This one doesn't look too bad to fix. While I am installing 3.1.3, could you, @F-Feng, change the string in fmpz_mpoly_set_str_pretty to the more wieldy factored form you just displayed? It is highly unlikely the set_str function has a bug.

[F-Feng]

@tthsqe12 Thanks a lot, and here is the string in the factored form,

"-((-1+x3+x4)^2*(x3+x4)*(-x1+x1^2-x2+x1*x2+x2*x3+x2*x4)*(-(x1*x2*x3)+x1^2*x2*x3-x2^2*x3+x1*x2^2*x3-2*x2*x3^2+3*x1*x2*x3^2-x1^2*x2*x3^2+4*x2^2*x3^2-x1*x2^2*x3^2+2*x2*x3^3-2*x1*x2*x3^3-3*x2^2*x3^3+2*x1^2*x4-4*x1^3*x4+2*x1^4*x4+3*x1*x2*x4-7*x1^2*x2*x4+4*x1^3*x2*x4+x2^2*x4-3*x1*x2^2*x4+2*x1^2*x2^2*x4+x1*x3*x4-2*x1^2*x3*x4+x1^3*x3*x4-3*x2*x3*x4-x1*x2*x3*x4+4*x1^2*x2*x3*x4+3*x2^2*x3*x4+3*x1*x2^2*x3*x4+5*x2*x3^2*x4-5*x1*x2*x3^2*x4-6*x2^2*x3^2*x4+x1*x4^2-2*x1^2*x4^2+x1^3*x4^2-x2*x4^2-4*x1*x2*x4^2+5*x1^2*x2*x4^2-x2^2*x4^2+4*x1*x2^2*x4^2+4*x2*x3*x4^2-4*x1*x2*x3*x4^2-3*x2^2*x3*x4^2+x2*x4^3-x1*x2*x4^3)*x5^2)"