void embeddings_isomorphism(nmod_poly_t G, mp_srcptr F,
const embeddings_t FP, const embeddings_t FQ, const embeddings_t FR){
long m = nmod_poly_degree(FP->P);
long n = nmod_poly_degree(FQ->P);
long i;
nmod_poly_t tmpF, tmpG, S, X;
nmod_t mod = FP->P->mod;
nmod_poly_init(tmpF, mod.n);
nmod_poly_init(tmpG, mod.n);
nmod_poly_init(S, mod.n);
nmod_poly_init(X, mod.n);
nmod_poly_zero(G);
nmod_poly_zero(X);
nmod_poly_set_coeff_ui(X, 1, 1);
embeddings_embed(S, X, FP, FQ, FR);
for (i = m-1; i >= 0; i--){
nmod_poly_fit_length(tmpF, n);
long j;
long offset = i*n;
for (j = 0; j < n; j++)
tmpF->coeffs[j] = F[offset+j];
tmpF->length = n;
_nmod_poly_normalise(tmpF);
embeddings_embed(tmpG, tmpF, FQ, FP, FR);
nmod_poly_mulmod(G, G, S, FR->P);
nmod_poly_add(G, G, tmpG);
}
nmod_poly_clear(tmpF);
nmod_poly_clear(tmpG);
nmod_poly_clear(X);
nmod_poly_clear(S);
}
void pq_nmod_mul(pq_nmod_elt_t res, const pq_nmod_elt_t x,
const pq_nmod_elt_t y, const pq_nmod_t A) {
switch (nmod_poly_is_zero(y->mono) |
(nmod_poly_is_zero(y->dual) << 1) |
(nmod_poly_is_zero(x->mono) << 4) |
(nmod_poly_is_zero(x->dual) << 5)) {
const pq_nmod_elt_struct* tmp;
case 0x22:
// Both have only dual -> add mono to x
_pq_nmod_insure_mono(x, A);
case 0x12:
case 0x32:
// x has mono, y has dual -> swap them
tmp = x;
x = y;
y = tmp;
case 0x21:
case 0x23:
// y has mono, x has dual
nmod_poly_fit_length(res->dual, A->degree);
nmod_poly_tmulmod(res->dual->coeffs, x->dual->coeffs, y->mono, A->M, A->S);
nmod_poly_zero(res->mono);
break;
case 0x11:
case 0x13:
case 0x31:
case 0x33:
// both have mono
nmod_poly_mulmod(res->mono, x->mono, y->mono, A->M);
nmod_poly_zero(res->dual);
break;
default:
// in any other case, result is 0
nmod_poly_zero(res->mono);
nmod_poly_zero(res->dual);
break;
}
}
int
main(void)
{
int i, result;
flint_rand_t state;
flint_randinit(state);
printf("mulmod....");
fflush(stdout);
/* Aliasing res and a */
for (i = 0; i < 500; i++)
{
nmod_poly_t a, b, res, t, f;
mp_limb_t n = n_randtest_prime(state, 0);
nmod_poly_init(a, n);
nmod_poly_init(b, n);
nmod_poly_init(f, n);
nmod_poly_init(res, n);
nmod_poly_init(t, n);
nmod_poly_randtest(a, state, n_randint(state, 50));
nmod_poly_randtest(b, state, n_randint(state, 50));
do {
nmod_poly_randtest(f, state, n_randint(state, 50));
} while (nmod_poly_is_zero(f));
nmod_poly_mulmod(res, a, b, f);
nmod_poly_mulmod(a, a, b, f);
result = (nmod_poly_equal(res, a));
if (!result)
{
printf("FAIL:\n");
printf("a:\n"); nmod_poly_print(a), printf("\n\n");
printf("b:\n"); nmod_poly_print(b), printf("\n\n");
printf("f:\n"); nmod_poly_print(f), printf("\n\n");
printf("res1:\n"); nmod_poly_print(res), printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(f);
nmod_poly_clear(res);
nmod_poly_clear(t);
}
/* Aliasing res and b */
for (i = 0; i < 500; i++)
{
nmod_poly_t a, b, res, t, f;
mp_limb_t n = n_randtest_prime(state, 0);
nmod_poly_init(a, n);
nmod_poly_init(b, n);
nmod_poly_init(f, n);
nmod_poly_init(res, n);
nmod_poly_init(t, n);
nmod_poly_randtest(a, state, n_randint(state, 50));
nmod_poly_randtest(b, state, n_randint(state, 50));
do {
nmod_poly_randtest(f, state, n_randint(state, 50));
} while (nmod_poly_is_zero(f));
nmod_poly_mulmod(res, a, b, f);
nmod_poly_mulmod(b, a, b, f);
result = (nmod_poly_equal(res, b));
if (!result)
{
printf("FAIL:\n");
printf("a:\n"); nmod_poly_print(a), printf("\n\n");
printf("b:\n"); nmod_poly_print(b), printf("\n\n");
printf("f:\n"); nmod_poly_print(f), printf("\n\n");
printf("res1:\n"); nmod_poly_print(res), printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(f);
nmod_poly_clear(res);
nmod_poly_clear(t);
}
/* Aliasing res and f */
for (i = 0; i < 500; i++)
{
nmod_poly_t a, b, res, t, f;
mp_limb_t n = n_randtest_prime(state, 0);
nmod_poly_init(a, n);
nmod_poly_init(b, n);
nmod_poly_init(f, n);
nmod_poly_init(res, n);
nmod_poly_init(t, n);
nmod_poly_randtest(a, state, n_randint(state, 50));
nmod_poly_randtest(b, state, n_randint(state, 50));
do {
nmod_poly_randtest(f, state, n_randint(state, 50));
} while (nmod_poly_is_zero(f));
nmod_poly_mulmod(res, a, b, f);
nmod_poly_mulmod(f, a, b, f);
result = (nmod_poly_equal(res, f));
if (!result)
{
printf("FAIL:\n");
printf("a:\n"); nmod_poly_print(a), printf("\n\n");
printf("b:\n"); nmod_poly_print(b), printf("\n\n");
printf("f:\n"); nmod_poly_print(f), printf("\n\n");
printf("res1:\n"); nmod_poly_print(res), printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(f);
nmod_poly_clear(res);
nmod_poly_clear(t);
}
/* No aliasing */
for (i = 0; i < 1000; i++)
{
nmod_poly_t a, b, res1, res2, t, f;
mp_limb_t n = n_randtest_prime(state, 0);
nmod_poly_init(a, n);
nmod_poly_init(b, n);
nmod_poly_init(f, n);
nmod_poly_init(res1, n);
nmod_poly_init(res2, n);
nmod_poly_init(t, n);
nmod_poly_randtest(a, state, n_randint(state, 50));
nmod_poly_randtest(b, state, n_randint(state, 50));
do {
nmod_poly_randtest(f, state, n_randint(state, 50));
} while (nmod_poly_is_zero(f));
nmod_poly_mulmod(res1, a, b, f);
nmod_poly_mul(res2, a, b);
nmod_poly_divrem(t, res2, res2, f);
result = (nmod_poly_equal(res1, res2));
if (!result)
{
printf("FAIL:\n");
printf("a:\n"); nmod_poly_print(a), printf("\n\n");
printf("b:\n"); nmod_poly_print(b), printf("\n\n");
printf("f:\n"); nmod_poly_print(f), printf("\n\n");
printf("res1:\n"); nmod_poly_print(res1), printf("\n\n");
printf("res2:\n"); nmod_poly_print(res2), printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(f);
nmod_poly_clear(res1);
nmod_poly_clear(res2);
nmod_poly_clear(t);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
void embeddings_isomorphism_2(nmod_poly_t G, mp_srcptr F,
const embeddings_t FP, const embeddings_t FQ, const embeddings_t FR){
nmod_t mod = G->mod;
long m = nmod_poly_degree(FP->P);
long n = nmod_poly_degree(FQ->P);
long np = n + m - 1;
long p = ceil(sqrt(np));
long q = ceil((1.0*np)/p);
long i, j, k;
nmod_poly_t iT, iTm, T, X, tmp;
nmod_poly_struct *TT;
nmod_poly_init(iTm, mod.n);
nmod_poly_init(iT, mod.n);
nmod_poly_init(T, mod.n);
nmod_poly_init(X, mod.n);
nmod_poly_init(tmp, mod.n);
nmod_poly_mat_t MT, MH, MV;
nmod_poly_mat_init(MT, q, n, mod.n);
nmod_poly_mat_init(MH, p, q, mod.n);
nmod_poly_mat_init(MV, p, n, mod.n);
TT = flint_malloc(sizeof(nmod_poly_struct) * (q+1));
for (i = 0; i < q+1; i++)
nmod_poly_init(TT+i, mod.n);
nmod_poly_set_coeff_ui(X, 1, 1);
embeddings_embed(T, X, FQ, FP, FR);
nmod_poly_invmod(iT, T, FR->P);
nmod_poly_powmod_ui_binexp(iTm, iT, m-1, FR->P);
nmod_poly_zero(TT);
nmod_poly_set_coeff_ui(TT, 0, 1);
for (i = 1; i < q+1; i++)
nmod_poly_mulmod(TT+i, TT+(i-1), T, FR->P);
for (i = 0; i < q; i++)
for (j = 0; j < n; j++){
long jm = j*m;
for (k = 0; k < m; k++)
nmod_poly_set_coeff_ui(nmod_poly_mat_entry(MT, i, j), k, nmod_poly_get_coeff_ui(TT+i, k+jm));
}
for (i = 0; i < p; i++)
for (j = 0; j < q; j++){
long idx = i*q+j;
long lo = FLINT_MAX(0,m-1-idx);
long hi = FLINT_MIN(m,n+m-1-idx);
for (k = lo; k < hi; k++)
nmod_poly_set_coeff_ui(nmod_poly_mat_entry(MH, i, j), k, F[k*n+k+idx-m+1]);
}
nmod_poly_mat_mul(MV, MH, MT);
nmod_poly_zero(G);
for (i = p-1; i >= 0; i--){
nmod_poly_zero(tmp);
for (j = 0; j < n; j++){
long len = nmod_poly_mat_entry(MV, i, j)->length;
mp_ptr coefs = nmod_poly_mat_entry(MV, i, j)->coeffs;
long jm = j*m;
for (k = 0; k < len; k++)
nmod_poly_set_coeff_ui(tmp, k+jm, n_addmod(nmod_poly_get_coeff_ui(tmp, k+jm), coefs[k], mod.n));
}
nmod_poly_rem(tmp, tmp, FR->P);
nmod_poly_mulmod(G, G, TT+q, FR->P);
nmod_poly_add(G, G, tmp);
}
nmod_poly_mulmod(G, G, iTm, FR->P);
nmod_poly_clear(tmp);
nmod_poly_mat_clear(MT);
nmod_poly_mat_clear(MH);
nmod_poly_mat_clear(MV);
for (i = 0; i < q+1; i++)
nmod_poly_clear(TT+i);
flint_free(TT);
nmod_poly_clear(iTm);
nmod_poly_clear(iT);
nmod_poly_clear(T);
nmod_poly_clear(X);
}
