int main()
{
fmpq_poly_t Pn, Pn1, Pn2, R;
long n;
printf("legendre_polynomial....");
fflush(stdout);
fmpq_poly_init(Pn);
fmpq_poly_init(Pn1);
fmpq_poly_init(Pn2);
fmpq_poly_init(R);
fmpq_poly_set_ui(Pn, 1UL);
fmpq_poly_set_coeff_ui(Pn1, 1, 1UL);
for (n = 0; n <= 500; n++)
{
legendre_polynomial(R, n);
if (!fmpq_poly_equal(Pn, R))
{
printf("FAIL: n = %ld\n", n);
printf("Direct: "); fmpq_poly_print_pretty(R, "x"); printf("\n");
printf("Recur.: "); fmpq_poly_print_pretty(Pn, "x"); printf("\n");
abort();
}
fmpq_poly_shift_left(Pn2, Pn1, 1);
fmpq_poly_scalar_mul_ui(Pn2, Pn2, 2*n + 3);
fmpq_poly_scalar_mul_si(Pn, Pn, -(n+1));
fmpq_poly_add(Pn2, Pn2, Pn);
fmpq_poly_scalar_div_ui(Pn2, Pn2, n+2);
fmpq_poly_swap(Pn, Pn1);
fmpq_poly_swap(Pn1, Pn2);
}
fmpq_poly_clear(Pn);
fmpq_poly_clear(Pn1);
fmpq_poly_clear(Pn2);
fmpq_poly_clear(R);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
void fmpq_poly_exp_series(fmpq_poly_t res, const fmpq_poly_t poly, long n)
{
fmpz *copy;
int alloc;
if (poly->length == 0)
{
fmpq_poly_set_ui(res, 1UL);
return;
}
if (!fmpz_is_zero(poly->coeffs))
{
printf("Exception: fmpq_poly_exp_series: constant term != 0");
abort();
}
if (n < 2)
{
if (n == 0) fmpq_poly_zero(res);
if (n == 1) fmpq_poly_set_ui(res, 1UL);
return;
}
if (poly->length >= n)
{
copy = poly->coeffs;
alloc = 0;
}
else
{
long i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < poly->length; i++)
copy[i] = poly->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (res != poly)
{
fmpq_poly_fit_length(res, n);
_fmpq_poly_exp_series(res->coeffs, res->den, copy, poly->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_exp_series(t->coeffs, t->den, copy, poly->den, n);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(res, n);
_fmpq_poly_normalise(res);
if (alloc)
flint_free(copy);
}
void
fmpq_poly_revert_series(fmpq_poly_t res,
const fmpq_poly_t poly, long n)
{
fmpz *copy;
int alloc;
if (poly->length < 2 || !fmpz_is_zero(poly->coeffs)
|| fmpz_is_zero(poly->coeffs + 1))
{
printf("exception: fmpq_poly_revert_series: input must have "
"zero constant term and nonzero coefficient of x^1");
abort();
}
if (n < 2)
{
fmpq_poly_zero(res);
return;
}
if (poly->length >= n)
{
copy = poly->coeffs;
alloc = 0;
}
else
{
long i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < poly->length; i++)
copy[i] = poly->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (res != poly)
{
fmpq_poly_fit_length(res, n);
_fmpq_poly_revert_series(res->coeffs,
res->den, copy, poly->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_revert_series(t->coeffs,
t->den, copy, poly->den, n);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(res, n);
_fmpq_poly_normalise(res);
if (alloc)
flint_free(copy);
}
void
fmpq_poly_compose(fmpq_poly_t res,
const fmpq_poly_t poly1, const fmpq_poly_t poly2)
{
const long len1 = poly1->length;
const long len2 = poly2->length;
long lenr;
if (len1 == 0L)
{
fmpq_poly_zero(res);
return;
}
if (len1 == 1L || len2 == 0L)
{
fmpq_poly_fit_length(res, 1);
fmpz_set(res->coeffs, poly1->coeffs);
fmpz_set(res->den, poly1->den);
{
fmpz_t d;
fmpz_init(d);
fmpz_gcd(d, res->coeffs, res->den);
if (*d != 1L)
{
fmpz_divexact(res->coeffs, res->coeffs, d);
fmpz_divexact(res->den, res->den, d);
}
fmpz_clear(d);
}
_fmpq_poly_set_length(res, 1);
_fmpq_poly_normalise(res);
return;
}
lenr = (len1 - 1L) * (len2 - 1L) + 1L;
if ((res != poly1) && (res != poly2))
{
fmpq_poly_fit_length(res, lenr);
_fmpq_poly_compose(res->coeffs, res->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2);
_fmpq_poly_set_length(res, lenr);
_fmpq_poly_normalise(res);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, lenr);
_fmpq_poly_compose(t->coeffs, t->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2);
_fmpq_poly_set_length(t, lenr);
_fmpq_poly_normalise(t);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
}
void fmpq_poly_sqrt_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n)
{
fmpz *copy;
int alloc;
if (poly->length < 1 || !fmpz_equal(poly->coeffs, poly->den))
{
flint_printf("Exception (fmpq_poly_sqrt_series). Constant term != 1.\n");
abort();
}
if (n < 1)
{
fmpq_poly_zero(res);
return;
}
if (poly->length >= n)
{
copy = poly->coeffs;
alloc = 0;
}
else
{
slong i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < poly->length; i++)
copy[i] = poly->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (res != poly)
{
fmpq_poly_fit_length(res, n);
_fmpq_poly_sqrt_series(res->coeffs, res->den, copy, poly->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_sqrt_series(t->coeffs, t->den, copy, poly->den, n);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(res, n);
fmpq_poly_canonicalise(res);
if (alloc)
flint_free(copy);
}
void fmpq_poly_div(fmpq_poly_t Q,
const fmpq_poly_t poly1, const fmpq_poly_t poly2)
{
long lenA, lenB, lenQ;
if (fmpq_poly_is_zero(poly2))
{
printf("Exception: division by zero in fmpq_poly_div\n");
abort();
}
if (poly1->length < poly2->length)
{
fmpq_poly_zero(Q);
return;
}
/* Deal with aliasing */
if (Q == poly1 || Q == poly2)
{
fmpq_poly_t tempQ;
fmpq_poly_init(tempQ);
fmpq_poly_div(tempQ, poly1, poly2);
fmpq_poly_swap(Q, tempQ);
fmpq_poly_clear(tempQ);
return;
}
lenA = poly1->length;
lenB = poly2->length;
lenQ = lenA - lenB + 1;
fmpq_poly_fit_length(Q, lenQ);
_fmpq_poly_div(Q->coeffs, Q->den,
poly1->coeffs, poly1->den, poly1->length,
poly2->coeffs, poly2->den, poly2->length);
_fmpq_poly_set_length(Q, lenQ);
}
void fmpq_poly_inv_series_newton(fmpq_poly_t Qinv, const fmpq_poly_t Q, long n)
{
fmpz *copy;
int alloc;
if (Q->length >= n)
{
copy = Q->coeffs;
alloc = 0;
}
else
{
long i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < Q->length; i++)
copy[i] = Q->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (Qinv != Q)
{
fmpq_poly_fit_length(Qinv, n);
_fmpq_poly_inv_series_newton(Qinv->coeffs, Qinv->den, copy, Q->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_inv_series_newton(t->coeffs, t->den, copy, Q->den, n);
fmpq_poly_swap(Qinv, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(Qinv, n);
fmpq_poly_canonicalise(Qinv);
if (alloc)
flint_free(copy);
}
void
fmpq_poly_compose_series_horner(fmpq_poly_t res,
const fmpq_poly_t poly1, const fmpq_poly_t poly2, long n)
{
long len1 = poly1->length;
long len2 = poly2->length;
long lenr;
if (len2 != 0 && !fmpz_is_zero(poly2->coeffs))
{
printf("exception: fmpq_poly_compose_series_horner: inner polynomial "
"must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
fmpq_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
fmpq_poly_fit_length(res, 1);
fmpz_set(res->coeffs, poly1->coeffs);
fmpz_set(res->den, poly1->den);
{
fmpz_t d;
fmpz_init(d);
fmpz_gcd(d, res->coeffs, res->den);
if (!fmpz_is_one(d))
{
fmpz_divexact(res->coeffs, res->coeffs, d);
fmpz_divexact(res->den, res->den, d);
}
fmpz_clear(d);
}
_fmpq_poly_set_length(res, 1);
_fmpq_poly_normalise(res);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
fmpq_poly_fit_length(res, lenr);
_fmpq_poly_compose_series_horner(res->coeffs, res->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2, lenr);
_fmpq_poly_set_length(res, lenr);
_fmpq_poly_normalise(res);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, lenr);
_fmpq_poly_compose_series_horner(t->coeffs, t->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2, lenr);
_fmpq_poly_set_length(t, lenr);
_fmpq_poly_normalise(t);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
}
void fmpq_poly_divrem(fmpq_poly_t Q, fmpq_poly_t R,
const fmpq_poly_t poly1, const fmpq_poly_t poly2)
{
slong lenA, lenB, lenQ, lenR;
if (fmpq_poly_is_zero(poly2))
{
flint_printf("Exception (fmpq_poly_divrem). Division by zero.\n");
abort();
}
if (Q == R)
{
flint_printf("Exception (fmpq_poly_divrem). Output arguments aliased.\n");
abort();
}
/* Deal with the various other cases of aliasing. */
if (R == poly1 || R == poly2)
{
if (Q == poly1 || Q == poly2)
{
fmpq_poly_t tempQ, tempR;
fmpq_poly_init(tempQ);
fmpq_poly_init(tempR);
fmpq_poly_divrem(tempQ, tempR, poly1, poly2);
fmpq_poly_swap(Q, tempQ);
fmpq_poly_swap(R, tempR);
fmpq_poly_clear(tempQ);
fmpq_poly_clear(tempR);
return;
}
else
{
fmpq_poly_t tempR;
fmpq_poly_init(tempR);
fmpq_poly_divrem(Q, tempR, poly1, poly2);
fmpq_poly_swap(R, tempR);
fmpq_poly_clear(tempR);
return;
}
}
else
{
if (Q == poly1 || Q == poly2)
{
fmpq_poly_t tempQ;
fmpq_poly_init(tempQ);
fmpq_poly_divrem(tempQ, R, poly1, poly2);
fmpq_poly_swap(Q, tempQ);
fmpq_poly_clear(tempQ);
return;
}
}
if (poly1->length < poly2->length)
{
fmpq_poly_set(R, poly1);
fmpq_poly_zero(Q);
return;
}
lenA = poly1->length;
lenB = poly2->length;
lenQ = lenA - lenB + 1;
lenR = lenB - 1;
fmpq_poly_fit_length(Q, lenQ);
fmpq_poly_fit_length(R, lenA); /* XXX: Need at least that much space */
_fmpq_poly_divrem(Q->coeffs, Q->den, R->coeffs, R->den,
poly1->coeffs, poly1->den, poly1->length,
poly2->coeffs, poly2->den, poly2->length, NULL);
_fmpq_poly_set_length(Q, lenQ);
_fmpq_poly_set_length(R, lenR);
_fmpq_poly_normalise(R);
}
