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(int argc, char *argv[])
{
int ans;
char *str, *strout;
fmpz_poly_t zpoly;
fmpz_poly_q_t qpoly1;
mpz_t mpzzero, mpzone, mpztwo;
mpq_t mpqzero, mpqone, mpqtwo, mpqtwoinv;
FLINT_TEST_INIT(state);
flint_printf("all... ");
fflush(stdout);
/* Accessing numerator and denominator ***********************************/
fmpz_poly_q_init(qpoly1);
fmpz_poly_q_set_str(qpoly1, "2 -1 1/2 0 1");
str = "2 -1 1";
strout = fmpz_poly_get_str(fmpz_poly_q_numref(qpoly1));
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_numref: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
flint_printf(" qpoly1 = \""), fmpz_poly_q_print(qpoly1), flint_printf("\"\n");
abort();
}
fmpz_poly_q_clear(qpoly1);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_q_set_str(qpoly1, "2 -1 1/2 0 1");
str = "2 0 1";
strout = fmpz_poly_get_str(fmpz_poly_q_denref(qpoly1));
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_denref: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_init(zpoly);
fmpz_poly_q_set_str(qpoly1, "2 -1 1/2 0 1");
fmpz_poly_set(zpoly, fmpz_poly_q_numref(qpoly1));
str = "2 -1 1";
strout = fmpz_poly_get_str(zpoly);
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_get_num: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_clear(zpoly);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_init(zpoly);
fmpz_poly_q_set_str(qpoly1, "2 -1 1/2 0 1");
fmpz_poly_set(zpoly, fmpz_poly_q_denref(qpoly1));
str = "2 0 1";
strout = fmpz_poly_get_str(zpoly);
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_get_den: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_clear(zpoly);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_init(zpoly);
fmpz_poly_q_set_str(qpoly1, "1 1/1 1");
fmpz_poly_set_str(zpoly, "2 0 1");
fmpz_poly_set(fmpz_poly_q_numref(qpoly1), zpoly);
str = "2 0 1";
strout = fmpz_poly_get_str(fmpz_poly_q_numref(qpoly1));
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_set_num: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_clear(zpoly);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_init(zpoly);
fmpz_poly_q_set_str(qpoly1, "1 1/1 1");
fmpz_poly_set_str(zpoly, "2 0 1");
fmpz_poly_set(fmpz_poly_q_denref(qpoly1), zpoly);
str = "2 0 1";
strout = fmpz_poly_get_str(fmpz_poly_q_denref(qpoly1));
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_set_den: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_clear(zpoly);
flint_free(strout);
/* Canonicalise **********************************************************/
fmpz_poly_q_init(qpoly1);
str = "2 -1 1/2 0 1";
fmpz_poly_q_set_str(qpoly1, str);
strout = fmpz_poly_q_get_str(qpoly1);
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_canonicalize: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
str = "2 -1 -1/2 0 1";
fmpz_poly_q_set_str(qpoly1, "2 1 1/2 0 -1");
strout = fmpz_poly_q_get_str(qpoly1);
ans = !strcmp("2 -1 -1/2 0 1", strout);
if (!ans)
{
flint_printf("test_canonicalize: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
flint_free(strout);
fmpz_poly_q_clear(qpoly1);
/* Initialization, memory management and basic operations ****************/
test_set("0", "0");
test_set("0/1 1", "0");
test_set("3 -1 0 1/2 0 1", "3 -1 0 1/2 0 1");
test_set("3 -1 0 1/2 1 1", "2 -1 1");
test_set_si(-1, "1 -1");
test_set_si(13, "1 13");
test_set_si(0, "0");
test_swap("3 -1 0 1/2 0 1", "1 2/1 3", "1 2/1 3", "3 -1 0 1/2 0 1");
test_zero("0", "0");
test_zero("0/1 1", "0");
test_zero("3 -1 0 1/2 0 1", "0");
test_neg("0", "0");
test_neg("1 1/1 2", "1 -1/1 2");
test_neg("3 -1 0 1/2 0 1", "3 1 0 -1/2 0 1");
test_inv("1 1/1 2", "1 2");
test_inv("3 -1 0 1/2 0 1", "2 0 1/3 -1 0 1");
test_inv("3 -1 0 -1/2 0 1", "2 0 -1/3 1 0 1");
test_inv_inplace("1 1/1 2", "1 2");
test_inv_inplace("3 -1 0 1/2 0 1", "2 0 1/3 -1 0 1");
test_inv_inplace("3 -1 0 -1/2 0 1", "2 0 -1/3 1 0 1");
test_is_zero("0", 1);
test_is_zero("0/1 1", 1);
test_is_zero("3 -1 0 1/2 0 1", 0);
test_is_zero("3 -1 0 1/2 1 1", 0);
test_is_one("0", 0);
test_is_one("0/1 1", 0);
test_is_one("1 1/1 1", 1);
test_is_one("2 1 1/2 1 1", 1);
test_is_one("3 -1 0 1/2 0 1", 0);
test_equal("1 1/1 2", "1 1/1 2", 1);
test_equal("1 1/1 2", "1 1/1 2", 1);
test_equal("3 -1 0 1/2 1 1", "2 -1 1", 1);
test_equal("3 -1 0 1/2 -1 1", "2 -1 1", 0);
/* Addition and subtraction **********************************************/
test_add("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 1 0 1/4 0 1 0 1");
test_add("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 3 -2 1/2 -1 1");
test_add("0/2 1 1", "1 2/1 1", "1 2");
test_add("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_add("2 1 1/1 1", "2 -1 1/1 1", "2 0 2");
test_add("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 -1 2 2/3 0 -1 1");
test_add("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 7 12 7 1/3 2 3 1");
test_add("2 1 1/2 -1 1", "2 1 1", "3 0 1 1/2 -1 1");
test_add("1 1/2 1 1", "2 0 1/2 1 1", "1 1");
test_add("2 1 1/3 4 -4 1", "1 1/2 -2 1", "2 -1 2/3 4 -4 1");
test_add("3 0 1 1/3 1 2 1", "2 0 -1/2 1 1", "0");
test_add("2 1 1/2 0 1", "2 -1 1/2 0 1", "1 2");
test_add("1 1/3 3 5 2", "1 1/3 6 7 2", "1 1/3 2 3 1");
test_add_in_place1("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 1 0 1/4 0 1 0 1");
test_add_in_place1("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 3 -2 1/2 -1 1");
test_add_in_place1("0/2 1 1", "1 2/1 1", "1 2");
test_add_in_place1("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_add_in_place1("2 1 1/1 1", "2 -1 1/1 1", "2 0 2");
test_add_in_place1("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 -1 2 2/3 0 -1 1");
test_add_in_place1("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 7 12 7 1/3 2 3 1");
test_add_in_place1("2 1 1/2 -1 1", "2 1 1", "3 0 1 1/2 -1 1");
test_add_in_place1("1 1/2 1 1", "2 0 1/2 1 1", "1 1");
test_add_in_place1("2 1 1/3 4 -4 1", "1 1/2 -2 1", "2 -1 2/3 4 -4 1");
test_add_in_place1("3 0 1 1/3 1 2 1", "2 0 -1/2 1 1", "0");
test_add_in_place1("2 1 1/2 0 1", "2 -1 1/2 0 1", "1 2");
test_add_in_place2("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 1 0 1/4 0 1 0 1");
test_add_in_place2("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 3 -2 1/2 -1 1");
test_add_in_place2("0/2 1 1", "1 2/1 1", "1 2");
test_add_in_place2("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_add_in_place2("2 1 1/1 1", "2 -1 1/1 1", "2 0 2");
test_add_in_place2("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 -1 2 2/3 0 -1 1");
test_add_in_place2("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 7 12 7 1/3 2 3 1");
test_add_in_place2("2 1 1/2 -1 1", "2 1 1", "3 0 1 1/2 -1 1");
test_add_in_place2("1 1/2 1 1", "2 0 1/2 1 1", "1 1");
test_add_in_place2("2 1 1/3 4 -4 1", "1 1/2 -2 1", "2 -1 2/3 4 -4 1");
test_add_in_place2("3 0 1 1/3 1 2 1", "2 0 -1/2 1 1", "0");
test_add_in_place2("2 1 1/2 0 1", "2 -1 1/2 0 1", "1 2");
test_add_in_place3("2 1 1", "2 2 2");
test_add_in_place3("2 1 1/1 2", "2 1 1");
test_sub("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 3 0 1/4 0 1 0 1");
test_sub("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 -1 -2 1/2 -1 1");
test_sub("0/2 1 1", "1 2/1 1", "1 -2");
test_sub("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_sub("2 1 1/1 1", "2 -1 1/1 1", "1 2");
test_sub("2 1 1/2 0 1", "2 2 1/2 -1 1", "2 -1 -2/3 0 -1 1");
test_sub("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 -9 -12 -5 -1/3 2 3 1");
test_sub("2 -1 1/2 0 1", "1 1", "1 -1/2 0 1");
test_sub("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 3 0 1/4 0 1 0 1");
test_sub("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 -1 -2 1/2 -1 1");
test_sub("0/2 1 1", "1 2/1 1", "1 -2");
test_sub("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_sub("2 1 1/1 1", "2 -1 1/1 1", "1 2");
test_sub("2 1 1/2 0 1", "2 2 1/2 -1 1", "2 -1 -2/3 0 -1 1");
test_sub("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 -9 -12 -5 -1/3 2 3 1");
test_sub("2 1 1/2 -1 1", "2 1 1", "3 2 1 -1/2 -1 1");
test_sub("1 1/2 1 1", "2 0 1/2 1 1", "2 1 -1/2 1 1");
test_sub("2 1 1/3 4 -4 1", "1 1/2 -2 1", "1 3/3 4 -4 1");
test_sub("3 0 1 1/3 1 2 1", "2 0 -1/2 1 1", "2 0 2/2 1 1");
test_sub("2 1 1/2 0 1", "2 -1 1/2 0 1", "1 2/2 0 1");
test_sub("1 1/3 3 5 2", "1 1/3 6 7 2", "1 1/4 6 13 9 2");
test_sub("2 1 1/2 0 2", "2 1 1/2 0 2", "0");
test_sub("2 -1 2/2 0 1", "2 -1 1/2 0 1", "1 1");
test_sub_in_place1("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 3 0 1/4 0 1 0 1");
test_sub_in_place1("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 -1 -2 1/2 -1 1");
test_sub_in_place1("0/2 1 1", "1 2/1 1", "1 -2");
test_sub_in_place1("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_sub_in_place1("2 1 1/1 1", "2 -1 1/1 1", "1 2");
test_sub_in_place1("2 1 1/2 0 1", "2 2 1/2 -1 1", "2 -1 -2/3 0 -1 1");
test_sub_in_place1("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 -9 -12 -5 -1/3 2 3 1");
test_sub_in_place2("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 3 0 1/4 0 1 0 1");
test_sub_in_place2("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 -1 -2 1/2 -1 1");
test_sub_in_place2("0/2 1 1", "1 2/1 1", "1 -2");
test_sub_in_place2("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_sub_in_place2("2 1 1/1 1", "2 -1 1/1 1", "1 2");
test_sub_in_place2("2 1 1/2 0 1", "2 2 1/2 -1 1", "2 -1 -2/3 0 -1 1");
test_sub_in_place2("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 -9 -12 -5 -1/3 2 3 1");
test_sub_in_place3("2 -1 1/2 2 1", "0");
test_addmul("1 1/2 0 2", "2 3 1/1 4", "3 1 0 1/4 -2 0 0 1", "5 -4 3 1 5 1/5 0 -8 0 0 4");
test_submul("1 1/2 0 2", "2 3 1/1 4", "3 1 0 1/4 -2 0 0 1", "5 -4 -3 -1 -1 -1/5 0 -8 0 0 4");
/* Scalar multiplication and devision ************************************/
flint_mpz_init_set_si(mpzzero, 0);
flint_mpz_init_set_si(mpzone, 1);
flint_mpz_init_set_si(mpztwo, 2);
mpq_init(mpqzero); flint_mpq_set_si(mpqzero, 0, 1);
mpq_init(mpqone); flint_mpq_set_si(mpqone, 1, 1);
mpq_init(mpqtwo); flint_mpq_set_si(mpqtwo, 2, 1);
mpq_init(mpqtwoinv); flint_mpq_set_si(mpqtwoinv, 1, 2);
test_scalar_mul_si("0", 1, "0");
test_scalar_mul_si("0", 0, "0");
test_scalar_mul_si("1 2", 0, "0");
test_scalar_mul_si("1 1/1 2", -2, "1 -1");
test_scalar_mul_si("2 1 1/2 -2 3", 5, "2 5 5/2 -2 3");
test_scalar_mul_si("2 1 1/2 -2 2", 3, "2 3 3/2 -2 2");
test_scalar_mul_mpz("0", mpzone, "0");
test_scalar_mul_mpz("0", mpzzero, "0");
test_scalar_mul_mpz("1 2", mpzzero, "0");
test_scalar_mul_mpz("1 1/1 2", mpztwo, "1 1");
test_scalar_mul_mpq("0", mpqone, "0");
test_scalar_mul_mpq("0", mpqzero, "0");
test_scalar_mul_mpq("1 2", mpqzero, "0");
test_scalar_mul_mpq("1 1/1 2", mpqtwo, "1 1");
test_scalar_mul_mpq("1 -2/1 1", mpqtwoinv, "1 -1");
test_scalar_div_si("0", 1, "0");
test_scalar_div_si("1 2", 2, "1 1");
test_scalar_div_si("1 1/1 2", -2, "1 -1/1 4");
test_scalar_div_si("3 -5 0 3/2 1 1", 2, "3 -5 0 3/2 2 2");
test_scalar_div_si("3 2 8 4/2 0 1", 3, "3 2 8 4/2 0 3");
test_scalar_div_si("3 2 8 4/2 0 1", -3, "3 -2 -8 -4/2 0 3");
test_scalar_div_si("3 -27 0 9/2 0 1", -3, "3 9 0 -3/2 0 1");
test_scalar_div_mpz("0", mpzone, "0");
test_scalar_div_mpz("1 2", mpztwo, "1 1");
test_scalar_div_mpz("1 1/1 2", mpztwo, "1 1/1 4");
test_scalar_div_mpq("0", mpqone, "0");
test_scalar_div_mpq("1 2", mpqone, "1 2");
test_scalar_div_mpq("1 1/1 2", mpqtwo, "1 1/1 4");
test_scalar_div_mpq("1 -2/1 1", mpqtwoinv, "1 -4");
mpz_clear(mpzzero);
mpz_clear(mpzone);
mpz_clear(mpztwo);
mpq_clear(mpqzero);
mpq_clear(mpqone);
mpq_clear(mpqtwo);
mpq_clear(mpqtwoinv);
/* Multiplication, division and powing *********************************/
test_mul("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "1 -1");
test_mul("3 -1 0 1/2 1 1", "1 2/2 -1 1", "1 2");
test_mul("0/2 1 1", "1 2/1 1", "0");
test_mul("1 -3/1 4", "0/3 1 0 1", "0");
test_mul("2 1 1/1 1", "2 -1 1/1 1", "3 -1 0 1");
test_mul("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 2 3 1/3 0 -1 1");
test_mul("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "3 -2 1 1/2 1 1");
test_mul_in_place1("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "1 -1");
test_mul_in_place1("3 -1 0 1/2 1 1", "1 2/2 -1 1", "1 2");
test_mul_in_place1("0/2 1 1", "1 2/1 1", "0");
test_mul_in_place1("1 -3/1 4", "0/3 1 0 1", "0");
test_mul_in_place1("2 1 1/1 1", "2 -1 1/1 1", "3 -1 0 1");
test_mul_in_place1("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 2 3 1/3 0 -1 1");
test_mul_in_place1("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "3 -2 1 1/2 1 1");
test_mul_in_place2("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "1 -1");
test_mul_in_place2("3 -1 0 1/2 1 1", "1 2/2 -1 1", "1 2");
test_mul_in_place2("0/2 1 1", "1 2/1 1", "0");
test_mul_in_place2("1 -3/1 4", "0/3 1 0 1", "0");
test_mul_in_place2("2 1 1/1 1", "2 -1 1/1 1", "3 -1 0 1");
test_mul_in_place2("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 2 3 1/3 0 -1 1");
test_mul_in_place2("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "3 -2 1 1/2 1 1");
test_mul_in_place3("2 0 1/2 1 1", "3 0 0 1/3 1 2 1");
test_div("3 -1 0 1/1 2", "2 1 1/1 1", "2 -1 1/1 2");
test_div("0/2 1 1", "2 1 1/1 1", "0");
test_div("3 -1 0 1/1 4", "2 -1 -1/1 2", "2 1 -1/1 2");
test_div("2 1 1", "2 1 -1/2 1 -1", "2 1 1");
test_div("2 1 1/3 4 4 1", "2 -1 1/3 6 5 1", "3 3 4 1/3 -2 1 1");
test_div_in_place1("3 -1 0 1/1 2", "2 1 1/1 1", "2 -1 1/1 2");
test_div_in_place1("0/2 1 1", "2 1 1/1 1", "0");
test_div_in_place1("3 -1 0 1/1 4", "2 -1 -1/1 2", "2 1 -1/1 2");
test_div_in_place1("2 1 1", "2 1 -1/2 1 -1", "2 1 1");
test_div_in_place1("2 1 1/3 4 4 1", "2 -1 1/3 6 5 1", "3 3 4 1/3 -2 1 1");
test_div_in_place1("0", "1 2/2 3 5", "0");
test_div_in_place2("3 -1 0 1/1 2", "2 1 1/1 1", "2 -1 1/1 2");
test_div_in_place2("0/2 1 1", "2 1 1/1 1", "0");
test_div_in_place2("3 -1 0 1/1 4", "2 -1 -1/1 2", "2 1 -1/1 2");
test_div_in_place2("2 1 1", "2 1 -1/2 1 -1", "2 1 1");
test_div_in_place2("2 1 1/3 4 4 1", "2 -1 1/3 6 5 1", "3 3 4 1/3 -2 1 1");
test_div_in_place3("3 -1 0 1/1 2", "1 1");
test_pow("2 0 -1/1 2", 3, "4 0 0 0 -1/1 8");
test_pow("0", 0, "1 1");
test_pow("2 1 -1", 0, "1 1");
test_pow("2 1 1/2 0 1", 0, "1 1");
/* Derivative ************************************************************/
test_derivative("0", "0");
test_derivative("1 2", "0");
test_derivative("1 -1/1 2", "0");
test_derivative("2 0 1", "1 1");
test_derivative("3 1 0 1", "2 0 2");
test_derivative("1 1/2 0 1", "1 -1/3 0 0 1");
test_derivative("2 2 1/2 -1 1", "1 -3/3 1 -2 1");
test_derivative("2 0 1/3 1 2 1", "2 1 -1/4 1 3 3 1");
/* Bug which allowed constant factors */
test_derivative("3 5 1 -2/2 10 2", "3 0 -10 -1/3 25 10 1");
/* Evaluation ************************************************************/
test_evaluate("1 1/1 2", -2, 3, "1/2");
test_evaluate("3 1 0 1/2 0 1", -1, 2, "-5/2");
test_evaluate("2 3 1/2 -1 1", 1, 1, "P");
test_evaluate("2 3 1/2 -1 1", 2, 3, "-11");
test_evaluate("2 3 1/2 -1 2", 1, 2, "P");
test_evaluate("2 1 1/2 -1 1", 2, 1, "3");
/* String methods ********************************************************/
fmpz_poly_q_init(qpoly1);
ans = fmpz_poly_q_set_str(qpoly1, "1 3/xyz");
if ((ans == 0) || !fmpz_poly_q_is_zero(qpoly1))
{
flint_printf("test_set_str: failed\n");
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_q_init(qpoly1);
ans = fmpz_poly_q_set_str(qpoly1, "abc/1 3");
if ((ans == 0) || !fmpz_poly_q_is_zero(qpoly1))
{
flint_printf("test_set_str: failed\n");
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_q_init(qpoly1);
ans = fmpz_poly_q_set_str(qpoly1, "abc/xyz");
if ((ans == 0) || !fmpz_poly_q_is_zero(qpoly1))
{
flint_printf("test_set_str: failed\n");
abort();
}
fmpz_poly_q_clear(qpoly1);
test_get_str_pretty("1 -3", "-3");
test_get_str_pretty("3 1 2 1", "t^2+2*t+1");
test_get_str_pretty("1 -2/2 1 1", "-2/(t+1)");
test_get_str_pretty("2 1 1/2 -1 1", "(t+1)/(t-1)");
test_get_str_pretty("2 1 1/1 2", "(t+1)/2");
test_get_str_pretty("1 1/1 2", "1/2");
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
