static void
binary_splitting(fmpz_poly_mat_t P, fmpz_poly_mat_t * const factors,
long n1, long n2)
{
if (n2 - n1 <= 0)
{
fmpz_poly_mat_one(P);
}
else if (n2 - n1 == 1)
{
fmpz_poly_mat_set(P, factors[n1]);
}
else if (n2 - n1 == 2)
{
fmpz_poly_mat_mul(P, factors[n1], factors[n1 + 1]);
}
else
{
fmpz_poly_mat_t P1, P2;
long m = (n1 + n2) / 2;
fmpz_poly_mat_init(P1, P->r, P->c);
fmpz_poly_mat_init(P2, P->r, P->c);
binary_splitting(P1, factors, n1, m);
binary_splitting(P2, factors, m, n2);
fmpz_poly_mat_mul(P, P1, P2);
fmpz_poly_mat_clear(P1);
fmpz_poly_mat_clear(P2);
}
}
void
fmpz_poly_mat_pow(fmpz_poly_mat_t B, const fmpz_poly_mat_t A, ulong exp)
{
long d = fmpz_poly_mat_nrows(A);
if (exp == 0 || d == 0)
{
fmpz_poly_mat_one(B);
}
else if (exp == 1)
{
fmpz_poly_mat_set(B, A);
}
else if (exp == 2)
{
fmpz_poly_mat_sqr(B, A);
}
else if (d == 1)
{
fmpz_poly_pow(fmpz_poly_mat_entry(B, 0, 0),
fmpz_poly_mat_entry(A, 0, 0), exp);
}
else
{
fmpz_poly_mat_t T, U;
long i;
fmpz_poly_mat_init_set(T, A);
fmpz_poly_mat_init(U, d, d);
for (i = ((long) FLINT_BIT_COUNT(exp)) - 2; i >= 0; i--)
{
fmpz_poly_mat_sqr(U, T);
if (exp & (1L << i))
fmpz_poly_mat_mul(T, U, A);
else
fmpz_poly_mat_swap(T, U);
}
fmpz_poly_mat_swap(B, T);
fmpz_poly_mat_clear(T);
fmpz_poly_mat_clear(U);
}
}
void
fmpz_poly_mat_mullow(fmpz_poly_mat_t C, const fmpz_poly_mat_t A,
const fmpz_poly_mat_t B, long len)
{
long ar, bc, br;
long i, j, k;
fmpz_poly_t t;
ar = A->r;
br = B->r;
bc = B->c;
if (br == 0 || len < 1)
{
fmpz_poly_mat_zero(C);
return;
}
if (C == A || C == B)
{
fmpz_poly_mat_t T;
fmpz_poly_mat_init(T, ar, bc);
fmpz_poly_mat_mullow(T, A, B, len);
fmpz_poly_mat_swap(C, T);
fmpz_poly_mat_clear(T);
return;
}
fmpz_poly_init(t);
for (i = 0; i < ar; i++)
{
for (j = 0; j < bc; j++)
{
fmpz_poly_mullow(fmpz_poly_mat_entry(C, i, j),
fmpz_poly_mat_entry(A, i, 0),
fmpz_poly_mat_entry(B, 0, j), len);
for (k = 1; k < br; k++)
{
fmpz_poly_mullow(t, fmpz_poly_mat_entry(A, i, k),
fmpz_poly_mat_entry(B, k, j), len);
fmpz_poly_add(fmpz_poly_mat_entry(C, i, j),
fmpz_poly_mat_entry(C, i, j), t);
}
}
}
fmpz_poly_clear(t);
}
void frob(const mpoly_t P, const ctx_t ctxFracQt,
const qadic_t t1, const qadic_ctx_t Qq,
prec_t *prec, const prec_t *prec_in,
int verbose)
{
const padic_ctx_struct *Qp = &Qq->pctx;
const fmpz *p = Qp->p;
const long a = qadic_ctx_degree(Qq);
const long n = P->n - 1;
const long d = mpoly_degree(P, -1, ctxFracQt);
const long b = gmc_basis_size(n, d);
long i, j, k;
/* Diagonal fibre */
padic_mat_t F0;
/* Gauss--Manin Connection */
mat_t M;
mon_t *bR, *bC;
fmpz_poly_t r;
/* Local solution */
fmpz_poly_mat_t C, Cinv;
long vC, vCinv;
/* Frobenius */
fmpz_poly_mat_t F;
long vF;
fmpz_poly_mat_t F1;
long vF1;
fmpz_poly_t cp;
clock_t c0, c1;
double c;
if (verbose)
{
printf("Input:\n");
printf(" P = "), mpoly_print(P, ctxFracQt), printf("\n");
printf(" p = "), fmpz_print(p), printf("\n");
printf(" t1 = "), qadic_print_pretty(t1, Qq), printf("\n");
printf("\n");
fflush(stdout);
}
/* Step 1 {M, r} *********************************************************/
c0 = clock();
mat_init(M, b, b, ctxFracQt);
fmpz_poly_init(r);
gmc_compute(M, &bR, &bC, P, ctxFracQt);
{
fmpz_poly_t t;
fmpz_poly_init(t);
fmpz_poly_set_ui(r, 1);
for (i = 0; i < M->m; i++)
for (j = 0; j < M->n; j++)
{
fmpz_poly_lcm(t, r, fmpz_poly_q_denref(
(fmpz_poly_q_struct *) mat_entry(M, i, j, ctxFracQt)));
fmpz_poly_swap(r, t);
}
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Gauss-Manin connection:\n");
printf(" r(t) = "), fmpz_poly_print_pretty(r, "t"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
{
qadic_t t;
qadic_init2(t, 1);
fmpz_poly_evaluate_qadic(t, r, t1, Qq);
if (qadic_is_zero(t))
{
printf("Exception (deformation_frob).\n");
printf("The resultant r evaluates to zero (mod p) at t1.\n");
abort();
}
qadic_clear(t);
}
/* Precisions ************************************************************/
if (prec_in != NULL)
{
*prec = *prec_in;
}
else
{
deformation_precisions(prec, p, a, n, d, fmpz_poly_degree(r));
}
if (verbose)
{
printf("Precisions:\n");
printf(" N0 = %ld\n", prec->N0);
printf(" N1 = %ld\n", prec->N1);
printf(" N2 = %ld\n", prec->N2);
printf(" N3 = %ld\n", prec->N3);
printf(" N3i = %ld\n", prec->N3i);
printf(" N3w = %ld\n", prec->N3w);
printf(" N3iw = %ld\n", prec->N3iw);
printf(" N4 = %ld\n", prec->N4);
printf(" m = %ld\n", prec->m);
printf(" K = %ld\n", prec->K);
printf(" r = %ld\n", prec->r);
printf(" s = %ld\n", prec->s);
printf("\n");
fflush(stdout);
}
/* Initialisation ********************************************************/
padic_mat_init2(F0, b, b, prec->N4);
fmpz_poly_mat_init(C, b, b);
fmpz_poly_mat_init(Cinv, b, b);
fmpz_poly_mat_init(F, b, b);
vF = 0;
fmpz_poly_mat_init(F1, b, b);
vF1 = 0;
fmpz_poly_init(cp);
/* Step 2 {F0} ***********************************************************/
{
padic_ctx_t pctx_F0;
fmpz *t;
padic_ctx_init(pctx_F0, p, FLINT_MIN(prec->N4 - 10, 0), prec->N4, PADIC_VAL_UNIT);
t = _fmpz_vec_init(n + 1);
c0 = clock();
mpoly_diagonal_fibre(t, P, ctxFracQt);
diagfrob(F0, t, n, d, prec->N4, pctx_F0, 0);
padic_mat_transpose(F0, F0);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Diagonal fibre:\n");
printf(" P(0) = {"), _fmpz_vec_print(t, n + 1), printf("}\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
_fmpz_vec_clear(t, n + 1);
padic_ctx_clear(pctx_F0);
}
/* Step 3 {C, Cinv} ******************************************************/
/*
Compute C as a matrix over Z_p[[t]]. A is the same but as a series
of matrices over Z_p. Mt is the matrix -M^t, and Cinv is C^{-1}^t,
the local solution of the differential equation replacing M by Mt.
*/
c0 = clock();
{
const long K = prec->K;
padic_mat_struct *A;
gmde_solve(&A, K, p, prec->N3, prec->N3w, M, ctxFracQt);
gmde_convert_soln(C, &vC, A, K, p);
for(i = 0; i < K; i++)
padic_mat_clear(A + i);
free(A);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Local solution:\n");
printf(" Time for C = %f\n", c);
fflush(stdout);
}
c0 = clock();
{
const long K = (prec->K + (*p) - 1) / (*p);
mat_t Mt;
padic_mat_struct *Ainv;
mat_init(Mt, b, b, ctxFracQt);
mat_transpose(Mt, M, ctxFracQt);
mat_neg(Mt, Mt, ctxFracQt);
gmde_solve(&Ainv, K, p, prec->N3i, prec->N3iw, Mt, ctxFracQt);
gmde_convert_soln(Cinv, &vCinv, Ainv, K, p);
fmpz_poly_mat_transpose(Cinv, Cinv);
fmpz_poly_mat_compose_pow(Cinv, Cinv, *p);
for(i = 0; i < K; i++)
padic_mat_clear(Ainv + i);
free(Ainv);
mat_clear(Mt, ctxFracQt);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf(" Time for C^{-1} = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 4 {F(t) := C(t) F(0) C(t^p)^{-1}} ********************************/
/*
Computes the product C(t) F(0) C(t^p)^{-1} modulo (p^{N_2}, t^K).
This is done by first computing the unit part of the product
exactly over the integers modulo t^K.
*/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
for (i = 0; i < b; i++)
{
/* Find the unique k s.t. F0(i,k) is non-zero */
for (k = 0; k < b; k++)
if (!fmpz_is_zero(padic_mat_entry(F0, i, k)))
break;
if (k == b)
{
printf("Exception (frob). F0 is singular.\n\n");
abort();
}
for (j = 0; j < b; j++)
{
fmpz_poly_scalar_mul_fmpz(fmpz_poly_mat_entry(T, i, j),
fmpz_poly_mat_entry(Cinv, k, j),
padic_mat_entry(F0, i, k));
}
}
fmpz_poly_mat_mul(F, C, T);
fmpz_poly_mat_truncate(F, prec->K);
vF = vC + padic_mat_val(F0) + vCinv;
/* Canonicalise (F, vF) */
{
long v = fmpz_poly_mat_ord_p(F, p);
if (v == LONG_MAX)
{
printf("ERROR (deformation_frob). F(t) == 0.\n");
abort();
}
else if (v > 0)
{
fmpz_pow_ui(pN, p, v);
fmpz_poly_mat_scalar_divexact_fmpz(F, F, pN);
vF = vF + v;
}
}
/* Reduce (F, vF) modulo p^{N2} */
fmpz_pow_ui(pN, p, prec->N2 - vF);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Matrix for F(t):\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 5 {G = r(t)^m F(t)} **********************************************/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_t t;
fmpz_init(pN);
fmpz_poly_init(t);
fmpz_pow_ui(pN, p, prec->N2 - vF);
/* Compute r(t)^m mod p^{N2-vF} */
if (prec->denR == NULL)
{
fmpz_mod_poly_t _t;
fmpz_mod_poly_init(_t, pN);
fmpz_mod_poly_set_fmpz_poly(_t, r);
fmpz_mod_poly_pow(_t, _t, prec->m);
fmpz_mod_poly_get_fmpz_poly(t, _t);
fmpz_mod_poly_clear(_t);
}
else
{
/* TODO: We don't really need a copy */
fmpz_poly_set(t, prec->denR);
}
fmpz_poly_mat_scalar_mul_fmpz_poly(F, F, t);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
/* TODO: This should not be necessary? */
fmpz_poly_mat_truncate(F, prec->K);
fmpz_clear(pN);
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Analytic continuation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Steps 6 and 7 *********************************************************/
if (a == 1)
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t f, g, t, pN;
fmpz_init(f);
fmpz_init(g);
fmpz_init(t);
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_padic_teichmuller(f, t1->coeffs + 0, p, N);
if (prec->denR == NULL)
{
_fmpz_mod_poly_evaluate_fmpz(g, r->coeffs, r->length, f, pN);
fmpz_powm_ui(t, g, prec->m, pN);
}
else
{
_fmpz_mod_poly_evaluate_fmpz(t, prec->denR->coeffs, prec->denR->length, f, pN);
}
_padic_inv(g, t, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
if (len == 0)
{
fmpz_poly_zero(fmpz_poly_mat_entry(F1, i, j));
}
else
{
fmpz_poly_fit_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_mod_poly_evaluate_fmpz(t, poly->coeffs, len, f, pN);
fmpz_mul(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, g, t);
fmpz_mod(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0,
fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, pN);
_fmpz_poly_set_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_poly_normalise(fmpz_poly_mat_entry(F1, i, j));
}
}
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(t);
fmpz_clear(pN);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
else
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t pN;
fmpz *f, *g, *t;
fmpz_init(pN);
f = _fmpz_vec_init(a);
g = _fmpz_vec_init(2 * a - 1);
t = _fmpz_vec_init(2 * a - 1);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_qadic_teichmuller(f, t1->coeffs, t1->length, Qq->a, Qq->j, Qq->len, p, N);
if (prec->denR == NULL)
{
fmpz_t e;
fmpz_init_set_ui(e, prec->m);
_fmpz_mod_poly_compose_smod(g, r->coeffs, r->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
_qadic_pow(t, g, a, e, Qq->a, Qq->j, Qq->len, pN);
fmpz_clear(e);
}
else
{
_fmpz_mod_poly_reduce(prec->denR->coeffs, prec->denR->length, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_normalise(prec->denR);
_fmpz_mod_poly_compose_smod(t, prec->denR->coeffs, prec->denR->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
}
_qadic_inv(g, t, a, Qq->a, Qq->j, Qq->len, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
fmpz_poly_struct *poly2 = fmpz_poly_mat_entry(F1, i, j);
if (len == 0)
{
fmpz_poly_zero(poly2);
}
else
{
_fmpz_mod_poly_compose_smod(t, poly->coeffs, len, f, a,
Qq->a, Qq->j, Qq->len, pN);
fmpz_poly_fit_length(poly2, 2 * a - 1);
_fmpz_poly_mul(poly2->coeffs, g, a, t, a);
_fmpz_mod_poly_reduce(poly2->coeffs, 2 * a - 1, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_set_length(poly2, a);
_fmpz_poly_normalise(poly2);
}
}
/* Now the matrix for p^{-1} F_p at t=t_1 is (F1, vF1). */
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
_fmpz_vec_clear(f, a);
_fmpz_vec_clear(g, 2 * a - 1);
_fmpz_vec_clear(t, 2 * a - 1);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 7 {Norm} *****************************************************/
/*
Computes the matrix for $q^{-1} F_q$ at $t = t_1$ as the
product $F \sigma(F) \dotsm \sigma^{a-1}(F)$ up appropriate
transpositions because our convention of columns vs rows is
the opposite of that used by Gerkmann.
Note that, in any case, transpositions do not affect
the characteristic polynomial.
*/
c0 = clock();
{
const long N = prec->N1 - a * vF1;
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
fmpz_pow_ui(pN, p, N);
fmpz_poly_mat_frobenius(T, F1, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
for (i = 2; i < a; i++)
{
fmpz_poly_mat_frobenius(T, T, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
}
vF1 = a * vF1;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Norm:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
/* Step 8 {Reverse characteristic polynomial} ****************************/
c0 = clock();
deformation_revcharpoly(cp, F1, vF1, n, d, prec->N0, prec->r, prec->s, Qq);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Reverse characteristic polynomial:\n");
printf(" p(T) = "), fmpz_poly_print_pretty(cp, "T"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Clean up **************************************************************/
padic_mat_clear(F0);
mat_clear(M, ctxFracQt);
free(bR);
free(bC);
fmpz_poly_clear(r);
fmpz_poly_mat_clear(C);
fmpz_poly_mat_clear(Cinv);
fmpz_poly_mat_clear(F);
fmpz_poly_mat_clear(F1);
fmpz_poly_clear(cp);
}
int main(void)
{
char *str; /* String for the input polynomial P */
mpoly_t P; /* Input polynomial P */
int n; /* Number of variables minus one */
long K; /* Required t-adic precision */
long N, Nw;
long b; /* Matrix dimensions */
long i, j, k;
mat_t M;
ctx_t ctxM;
mon_t *rows, *cols;
padic_mat_struct *C;
fmpz_t p;
fmpz_poly_mat_t B;
long vB;
printf("solve... \n");
fflush(stdout);
/* Example 3-1-1 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[1 1 1]"; */
/* Example 3-3-2 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[2 1 0] (2 0 1)[0 2 1] (2 0 1)[1 0 2]"; */
/* Example 4-4-2 */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[3 1 0 0] (2 0 1)[1 0 1 2] (2 0 1)[0 1 0 3]"; */
/* Example ... */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[1 1 1 1]"; */
/* Example from AKR */
str = "4 (1 3)[0 3 0 0] (2 0 3)[0 1 2 0] "
"(2 0 -1)[1 1 1 0] (2 0 3)[1 1 0 1] "
"(2 0 -1)[2 1 0 0] [0 0 3 0] (2 0 -1)[1 0 2 0] "
"(1 2)[0 0 0 3] [3 0 0 0]";
n = atoi(str) - 1;
K = 616;
N = 10;
Nw = 22;
fmpz_init(p);
fmpz_set_ui(p, 5);
ctx_init_fmpz_poly_q(ctxM);
ctxM->print = &__fmpz_poly_q_print_pretty;
mpoly_init(P, n + 1, ctxM);
mpoly_set_str(P, str, ctxM);
printf("P = "), mpoly_print(P, ctxM), printf("\n");
b = gmc_basis_size(n, mpoly_degree(P, -1, ctxM));
mat_init(M, b, b, ctxM);
fmpz_poly_mat_init(B, b, b);
vB = 0;
gmc_compute(M, &rows, &cols, P, ctxM);
mat_print(M, ctxM);
printf("\n");
gmde_solve(&C, K, p, N, Nw, M, ctxM);
gmde_convert_soln(B, &vB, C, K, p);
printf("Solution to (d/dt + M) C = 0:\n");
fmpz_poly_mat_print(B, "t");
printf("vB = %ld\n", vB);
gmde_check_soln(B, vB, p, N, K, M, ctxM);
mpoly_clear(P, ctxM);
mat_clear(M, ctxM);
free(rows);
free(cols);
fmpz_poly_mat_clear(B);
ctx_clear(ctxM);
fmpz_clear(p);
for (i = 0; i < K; i++)
padic_mat_clear(C + i);
free(C);
_fmpz_cleanup();
return EXIT_SUCCESS;
}
int
fmpz_poly_mat_inv(fmpz_poly_mat_t Ainv, fmpz_poly_t den,
const fmpz_poly_mat_t A)
{
long n = fmpz_poly_mat_nrows(A);
if (n == 0)
{
fmpz_poly_one(den);
return 1;
}
else if (n == 1)
{
fmpz_poly_set(den, E(A, 0, 0));
fmpz_poly_one(E(Ainv, 0, 0));
return !fmpz_poly_is_zero(den);
}
else if (n == 2)
{
fmpz_poly_mat_det(den, A);
if (fmpz_poly_is_zero(den))
{
return 0;
}
else if (Ainv == A)
{
fmpz_poly_swap(E(A, 0, 0), E(A, 1, 1));
fmpz_poly_neg(E(A, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(A, 1, 0), E(A, 1, 0));
return 1;
}
else
{
fmpz_poly_set(E(Ainv, 0, 0), E(A, 1, 1));
fmpz_poly_set(E(Ainv, 1, 1), E(A, 0, 0));
fmpz_poly_neg(E(Ainv, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(Ainv, 1, 0), E(A, 1, 0));
return 1;
}
}
else
{
fmpz_poly_mat_t LU, I;
long * perm;
int result;
perm = _perm_init(n);
fmpz_poly_mat_init_set(LU, A);
result = (fmpz_poly_mat_fflu(LU, den, perm, LU, 1) == n);
if (result)
{
fmpz_poly_mat_init(I, n, n);
fmpz_poly_mat_one(I);
fmpz_poly_mat_solve_fflu_precomp(Ainv, perm, LU, I);
fmpz_poly_mat_clear(I);
}
else
fmpz_poly_zero(den);
if (_perm_parity(perm, n))
{
fmpz_poly_mat_neg(Ainv, Ainv);
fmpz_poly_neg(den, den);
}
_perm_clear(perm);
fmpz_poly_mat_clear(LU);
return result;
}
}
int
main(void)
{
flint_rand_t state;
long i;
printf("inv....");
fflush(stdout);
flint_randinit(state);
/* Test aliasing */
for (i = 0; i < 400; i++)
{
fmpz_poly_mat_t A, Ainv;
fmpz_poly_t den1, den2;
long n, bits, deg;
float density;
int ns1, ns2;
int result;
n = n_randint(state, 8);
deg = 1 + n_randint(state, 5);
bits = 1 + n_randint(state, 100);
density = n_randint(state, 100) * 0.01;
fmpz_poly_mat_init(A, n, n);
fmpz_poly_mat_init(Ainv, n, n);
fmpz_poly_init(den1);
fmpz_poly_init(den2);
fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density);
ns1 = fmpz_poly_mat_inv(Ainv, den1, A);
ns2 = fmpz_poly_mat_inv(A, den2, A);
result = ns1 == ns2;
if (result && ns1 != 0)
{
result = fmpz_poly_equal(den1, den2) &&
fmpz_poly_mat_equal(A, Ainv);
}
if (!result)
{
printf("FAIL (aliasing)!\n");
fmpz_poly_mat_print(A, "x"); printf("\n");
fmpz_poly_mat_print(Ainv, "x"); printf("\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(Ainv);
fmpz_poly_clear(den1);
fmpz_poly_clear(den2);
}
/* Check A^(-1) = A = 1 */
for (i = 0; i < 1000; i++)
{
fmpz_poly_mat_t A, Ainv, B, Iden;
fmpz_poly_t den, det;
long n, bits, deg;
float density;
int nonsingular;
n = n_randint(state, 10);
deg = 1 + n_randint(state, 5);
bits = 1 + n_randint(state, 100);
density = n_randint(state, 100) * 0.01;
fmpz_poly_mat_init(A, n, n);
fmpz_poly_mat_init(Ainv, n, n);
fmpz_poly_mat_init(B, n, n);
fmpz_poly_mat_init(Iden, n, n);
fmpz_poly_init(den);
fmpz_poly_init(det);
fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density);
nonsingular = fmpz_poly_mat_inv(Ainv, den, A);
fmpz_poly_mat_det_interpolate(det, A);
if (n == 0)
{
if (nonsingular == 0 || !fmpz_poly_is_one(den))
{
printf("FAIL: expected empty matrix to pass\n");
abort();
}
}
else
{
if (!fmpz_poly_equal(den, det))
{
fmpz_poly_neg(det, det);
printf("FAIL: den != det(A)\n");
abort();
}
fmpz_poly_mat_mul(B, Ainv, A);
fmpz_poly_mat_one(Iden);
fmpz_poly_mat_scalar_mul_fmpz_poly(Iden, Iden, den);
if (!fmpz_poly_mat_equal(B, Iden))
{
printf("FAIL:\n");
printf("A:\n");
fmpz_poly_mat_print(A, "x");
printf("Ainv:\n");
fmpz_poly_mat_print(Ainv, "x");
printf("B:\n");
fmpz_poly_mat_print(B, "x");
printf("den:\n");
fmpz_poly_print_pretty(den, "x");
abort();
}
}
fmpz_poly_clear(den);
fmpz_poly_clear(det);
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(Ainv);
fmpz_poly_mat_clear(B);
fmpz_poly_mat_clear(Iden);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
slong i;
FLINT_TEST_INIT(state);
flint_printf("add....");
fflush(stdout);
/* Check evaluation homomorphism */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpz_poly_mat_t A, B, C;
fmpz_mat_t a, b, c, d;
fmpz_t x;
slong m, n, bits, deg;
m = n_randint(state, 20);
n = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
bits = 1 + n_randint(state, 100);
fmpz_poly_mat_init(A, m, n);
fmpz_poly_mat_init(B, m, n);
fmpz_poly_mat_init(C, m, n);
fmpz_mat_init(a, m, n);
fmpz_mat_init(b, m, n);
fmpz_mat_init(c, m, n);
fmpz_mat_init(d, m, n);
fmpz_init(x);
fmpz_poly_mat_randtest(A, state, deg, bits);
fmpz_poly_mat_randtest(B, state, deg, bits);
fmpz_poly_mat_add(C, A, B);
fmpz_randtest(x, state, 1 + n_randint(state, 100));
fmpz_poly_mat_evaluate_fmpz(a, A, x);
fmpz_poly_mat_evaluate_fmpz(b, B, x);
fmpz_poly_mat_evaluate_fmpz(d, C, x);
fmpz_mat_add(c, a, b);
if (!fmpz_mat_equal(c, d))
{
flint_printf("FAIL:\n");
flint_printf("A:\n");
fmpz_poly_mat_print(A, "x");
flint_printf("B:\n");
fmpz_poly_mat_print(B, "x");
flint_printf("C:\n");
fmpz_poly_mat_print(C, "x");
flint_printf("\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(B);
fmpz_poly_mat_clear(C);
fmpz_mat_clear(a);
fmpz_mat_clear(b);
fmpz_mat_clear(c);
fmpz_mat_clear(d);
fmpz_clear(x);
}
/* Check aliasing C and A */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpz_poly_mat_t A, B, C;
slong m, n, bits, deg;
m = n_randint(state, 20);
n = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
bits = 1 + n_randint(state, 100);
fmpz_poly_mat_init(A, m, n);
fmpz_poly_mat_init(B, m, n);
fmpz_poly_mat_init(C, m, n);
fmpz_poly_mat_randtest(A, state, deg, bits);
fmpz_poly_mat_randtest(B, state, deg, bits);
fmpz_poly_mat_add(C, A, B);
fmpz_poly_mat_add(A, A, B);
if (!fmpz_poly_mat_equal(C, A))
{
flint_printf("FAIL:\n");
flint_printf("A:\n");
fmpz_poly_mat_print(A, "x");
flint_printf("B:\n");
fmpz_poly_mat_print(B, "x");
flint_printf("C:\n");
fmpz_poly_mat_print(C, "x");
flint_printf("\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(B);
fmpz_poly_mat_clear(C);
}
/* Check aliasing C and B */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpz_poly_mat_t A, B, C;
slong m, n, bits, deg;
m = n_randint(state, 20);
n = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
bits = 1 + n_randint(state, 100);
fmpz_poly_mat_init(A, m, n);
fmpz_poly_mat_init(B, m, n);
fmpz_poly_mat_init(C, m, n);
fmpz_poly_mat_randtest(A, state, deg, bits);
fmpz_poly_mat_randtest(B, state, deg, bits);
fmpz_poly_mat_add(C, A, B);
fmpz_poly_mat_add(B, A, B);
if (!fmpz_poly_mat_equal(C, B))
{
flint_printf("FAIL:\n");
flint_printf("A:\n");
fmpz_poly_mat_print(A, "x");
flint_printf("B:\n");
fmpz_poly_mat_print(B, "x");
flint_printf("C:\n");
fmpz_poly_mat_print(C, "x");
flint_printf("\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(B);
fmpz_poly_mat_clear(C);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
slong i;
FLINT_TEST_INIT(state);
flint_printf("nullspace....");
fflush(stdout);
for (i = 0; i < 200 * flint_test_multiplier(); i++)
{
fmpz_poly_mat_t A, N, AN;
slong n, m, bits, deg, rank, nullity;
float density;
m = n_randint(state, 13);
n = n_randint(state, 13);
deg = 1 + n_randint(state, 5);
bits = 1 + n_randint(state, 100);
density = n_randint(state, 100) * 0.01;
fmpz_poly_mat_init(A, m, n);
fmpz_poly_mat_init(N, n, n);
fmpz_poly_mat_init(AN, m, n);
fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density);
rank = fmpz_poly_mat_rank(A);
nullity = fmpz_poly_mat_nullspace(N, A);
if (nullity + rank != n)
{
flint_printf("FAIL: wrong nullity!\n");
flint_printf("rank = %wd\n", rank);
flint_printf("nullity = %wd\n", nullity);
fmpz_poly_mat_print(A, "x");
flint_printf("\n");
fmpz_poly_mat_print(N, "x");
flint_printf("\n");
abort();
}
if (fmpz_poly_mat_rank(N) != nullity)
{
flint_printf("FAIL: wrong rank(N) != nullity!\n");
abort();
}
fmpz_poly_mat_mul(AN, A, N);
if (!fmpz_poly_mat_is_zero(AN))
{
flint_printf("FAIL: A * N != 0\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(N);
fmpz_poly_mat_clear(AN);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
flint_rand_t state;
long i;
printf("pow....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 1000; i++)
{
fmpz_poly_mat_t A, B, C;
long m, j, exp, bits, deg;
m = n_randint(state, 6);
deg = 1 + n_randint(state, 6);
bits = 1 + n_randint(state, 100);
exp = n_randint(state, 20);
fmpz_poly_mat_init(A, m, m);
fmpz_poly_mat_init(B, m, m);
fmpz_poly_mat_init(C, m, m);
fmpz_poly_mat_randtest(A, state, deg, bits);
fmpz_poly_mat_pow(B, A, exp);
fmpz_poly_mat_one(C);
for (j = 0; j < exp; j++)
fmpz_poly_mat_mul(C, C, A);
if (!fmpz_poly_mat_equal(C, B))
{
printf("FAIL:\n");
printf("exp = %ld\n", exp);
printf("A:\n");
fmpz_poly_mat_print(A, "x");
printf("B:\n");
fmpz_poly_mat_print(B, "x");
printf("C:\n");
fmpz_poly_mat_print(C, "x");
printf("\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(B);
fmpz_poly_mat_clear(C);
}
/* Check aliasing B and A */
for (i = 0; i < 1000; i++)
{
fmpz_poly_mat_t A, B;
long m, exp, bits, deg;
m = n_randint(state, 6);
deg = 1 + n_randint(state, 6);
bits = 1 + n_randint(state, 100);
exp = n_randint(state, 20);
fmpz_poly_mat_init(A, m, m);
fmpz_poly_mat_init(B, m, m);
fmpz_poly_mat_randtest(A, state, deg, bits);
fmpz_poly_mat_pow(B, A, exp);
fmpz_poly_mat_pow(A, A, exp);
if (!fmpz_poly_mat_equal(A, B))
{
printf("FAIL (aliasing)\n");
printf("exp = %ld\n", exp);
printf("A:\n");
fmpz_poly_mat_print(A, "x");
printf("B:\n");
fmpz_poly_mat_print(B, "x");
printf("\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(B);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
long i;
flint_rand_t state;
printf("trace....");
fflush(stdout);
flint_randinit(state);
/* Test trace(AB) = trace(BA) */
for (i = 0; i < 1000; i++)
{
fmpz_poly_mat_t A, B, AB, BA;
fmpz_poly_t trab, trba;
long m, n;
m = n_randint(state, 10);
n = n_randint(state, 10);
fmpz_poly_mat_init(A, m, n);
fmpz_poly_mat_init(B, n, m);
fmpz_poly_mat_init(AB, m, m);
fmpz_poly_mat_init(BA, n, n);
fmpz_poly_init(trab);
fmpz_poly_init(trba);
fmpz_poly_mat_randtest(A, state, 1 + n_randint(state, 10),
1 + n_randint(state, 100));
fmpz_poly_mat_randtest(B, state, 1 + n_randint(state, 10),
1 + n_randint(state, 100));
fmpz_poly_mat_mul(AB, A, B);
fmpz_poly_mat_mul(BA, B, A);
fmpz_poly_mat_trace(trab, AB);
fmpz_poly_mat_trace(trba, BA);
if (!fmpz_poly_equal(trab, trba))
{
printf("FAIL:\n");
fmpz_poly_mat_print(A, "x"), printf("\n");
fmpz_poly_mat_print(B, "x"), printf("\n");
fmpz_poly_mat_print(AB, "x"), printf("\n");
fmpz_poly_mat_print(BA, "x"), printf("\n");
printf("tr(AB): "), fmpz_poly_print(trab), printf("\n");
printf("tr(BA): "), fmpz_poly_print(trba), printf("\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(B);
fmpz_poly_mat_clear(AB);
fmpz_poly_mat_clear(BA);
fmpz_poly_clear(trab);
fmpz_poly_clear(trba);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
