void padic_poly_sub(padic_poly_t f,
const padic_poly_t g, const padic_poly_t h,
const padic_ctx_t ctx)
{
const slong lenG = g->length;
const slong lenH = h->length;
const slong lenF = FLINT_MAX(lenG, lenH);
if (lenG == 0)
{
padic_poly_neg(f, h, ctx);
return;
}
if (lenH == 0)
{
padic_poly_set(f, g, ctx);
return;
}
if ((lenG == 0 && lenH == 0) || (FLINT_MIN(g->val, h->val) >= f->N))
{
padic_poly_zero(f);
return;
}
padic_poly_fit_length(f, lenF);
_padic_poly_sub(f->coeffs, &(f->val), f->N,
g->coeffs, g->val, lenG, g->N,
h->coeffs, h->val, lenH, h->N, ctx);
_padic_poly_set_length(f, lenF);
_padic_poly_normalise(f);
}
int qadic_exp_balanced(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
const slong N = qadic_prec(rop);
const slong v = op->val;
const fmpz *p = (&ctx->pctx)->p;
if (padic_poly_is_zero(op))
{
padic_poly_one(rop);
return 1;
}
if ((*p == WORD(2) && v <= 1) || (v <= 0))
{
return 0;
}
else
{
if (v < N)
{
const slong d = qadic_ctx_degree(ctx);
fmpz_t pN;
int alloc;
alloc = _padic_ctx_pow_ui(pN, N, &ctx->pctx);
padic_poly_fit_length(rop, d);
_qadic_exp_balanced(rop->coeffs, op->coeffs, v, op->length,
ctx->a, ctx->j, ctx->len, p, N, pN);
rop->val = 0;
_padic_poly_set_length(rop, d);
_padic_poly_normalise(rop);
if (alloc)
fmpz_clear(pN);
}
else
{
padic_poly_one(rop);
}
return 1;
}
}
void padic_poly_randtest_val(padic_poly_t f, flint_rand_t state,
slong val, slong len, const padic_ctx_t ctx)
{
const slong N = padic_poly_prec(f);
if (len == 0)
return;
if (val >= N)
{
padic_poly_zero(f);
}
else
{
slong i;
fmpz_t pow;
int alloc;
f->val = val;
padic_poly_fit_length(f, len);
alloc = _padic_ctx_pow_ui(pow, N - f->val, ctx);
for (i = 0; i < len; i++)
fmpz_randm(f->coeffs + i, state, pow);
if (alloc)
fmpz_clear(pow);
for (i = 0; i < len; i++)
if (!fmpz_divisible(f->coeffs + i, ctx->p))
break;
if (i == len)
fmpz_one(f->coeffs + n_randint(state, len));
_padic_poly_set_length(f, len);
_padic_poly_normalise(f);
padic_poly_reduce(f, ctx);
}
}
static
void fmpz_poly_evaluate_qadic(qadic_t rop,
const fmpz_poly_t op1, const qadic_t op2, const qadic_ctx_t ctx)
{
const long N = qadic_prec(rop);
const long d = qadic_ctx_degree(ctx);
if (N <= 0 || op2->val != 0 || rop == op2)
{
printf("Exception (fmpz_poly_evaluate_qadic):\n");
printf("Currently assumes that N > 0 and op2->val == 0, \n");
printf("and does not support aliasing.\n");
abort();
}
if (fmpz_poly_is_zero(op1))
{
qadic_zero(rop);
}
else if (qadic_is_zero(op2))
{
padic_poly_set_fmpz(rop, op1->coeffs + 0, &ctx->pctx);
}
else
{
fmpz_t pN;
fmpz_init(pN);
fmpz_pow_ui(pN, (&ctx->pctx)->p, N);
padic_poly_fit_length(rop, d);
_fmpz_mod_poly_compose_smod(rop->coeffs,
op1->coeffs, op1->length, op2->coeffs, op2->length,
ctx->a, ctx->j, ctx->len, pN);
_padic_poly_set_length(rop, d);
qadic_reduce(rop, ctx);
fmpz_clear(pN);
}
}
void padic_poly_randtest_not_zero(padic_poly_t f, flint_rand_t state,
slong len, const padic_ctx_t ctx)
{
slong i;
if (len == 0)
{
flint_printf("Exception (padic_poly_randtest_not_zero). len == 0.\n");
abort();
}
padic_poly_randtest(f, state, len, ctx);
for (i = 0; !padic_poly_is_zero(f) && (i < 10); i++)
padic_poly_randtest(f, state, len, ctx);
if (padic_poly_is_zero(f))
{
padic_poly_fit_length(f, 1);
_padic_poly_set_length(f, 1);
fmpz_one(f->coeffs + 0);
f->val = f->N - 1;
}
}
int qadic_exp(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
const slong N = qadic_prec(rop);
const slong v = op->val;
const fmpz *p = (&ctx->pctx)->p;
if (padic_poly_is_zero(op))
{
padic_poly_one(rop);
return 1;
}
if ((*p == WORD(2) && v <= 1) || (v <= 0))
{
return 0;
}
else
{
if (v < N)
{
const slong d = qadic_ctx_degree(ctx);
fmpz *t;
fmpz_t pN;
int alloc;
alloc = _padic_ctx_pow_ui(pN, N, &ctx->pctx);
if (rop == op)
{
t = _fmpz_vec_init(2 * d - 1);
}
else
{
padic_poly_fit_length(rop, 2 * d - 1);
t = rop->coeffs;
}
_qadic_exp(t, op->coeffs, v, op->length,
ctx->a, ctx->j, ctx->len, p, N, pN);
rop->val = 0;
if (rop == op)
{
_fmpz_vec_clear(rop->coeffs, rop->alloc);
rop->coeffs = t;
rop->alloc = 2 * d - 1;
rop->length = d;
}
_padic_poly_set_length(rop, d);
_padic_poly_normalise(rop);
if (alloc)
fmpz_clear(pN);
}
else
{
padic_poly_one(rop);
}
return 1;
}
}
int
main(void)
{
int i, result;
padic_ctx_t ctx;
fmpz_t p;
slong N;
FLINT_TEST_INIT(state);
flint_printf("inv_series... ");
fflush(stdout);
/* Check aliasing */
for (i = 0; i < 1000; i++)
{
padic_poly_t a, b, c;
slong n;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_randtest(a, state, n_randint(state, 100) + 1, ctx);
if (fmpz_is_zero(a->coeffs))
{
fmpz_randtest_not_zero(a->coeffs, state, 20);
fmpz_remove(a->coeffs, a->coeffs, p);
padic_poly_reduce(a, ctx);
} else
fmpz_remove(a->coeffs, a->coeffs, p);
padic_poly_set(b, a, ctx);
n = n_randint(state, 100) + 1;
padic_poly_inv_series(c, b, n, ctx);
padic_poly_inv_series(b, b, n, ctx);
result = (padic_poly_equal(b, c) && padic_poly_is_reduced(b, ctx));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), padic_poly_print(a, ctx), flint_printf("\n\n");
flint_printf("b = "), padic_poly_print(b, ctx), flint_printf("\n\n");
flint_printf("c = "), padic_poly_print(c, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
/*
Check correctness:
If ord_p(a) = v then we can compute b = a^{-1} mod p^N
and we will have a b = 1 mod p^{N-|v|}. Thus, require
that N - |v| > 0.
*/
for (i = 0; i < 1000; i++)
{
padic_poly_t a, b, c;
slong n, N2;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - 1) + 1;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
{
slong i, len = n_randint(state, 10) + 1;
int alloc;
fmpz_t pow;
padic_poly_fit_length(a, len);
_padic_poly_set_length(a, len);
a->val = n_randint(state, N);
if (n_randint(state, 2))
a->val = - a->val;
alloc = _padic_ctx_pow_ui(pow, N - a->val, ctx);
for (i = 0; i < len; i++)
fmpz_randm(a->coeffs + i, state, pow);
while (fmpz_is_zero(a->coeffs))
fmpz_randm(a->coeffs, state, pow);
fmpz_remove(a->coeffs, a->coeffs, p);
_padic_poly_normalise(a);
if (alloc)
fmpz_clear(pow);
}
n = n_randint(state, 100) + 1;
N2 = N - FLINT_ABS(a->val);
padic_poly_init2(c, 0, N2);
padic_poly_inv_series(b, a, n, ctx);
padic_poly_mul(c, a, b, ctx);
padic_poly_truncate(c, n, p);
result = (padic_poly_is_one(c) && padic_poly_is_reduced(b, ctx));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), padic_poly_print(a, ctx), flint_printf("\n\n");
flint_printf("b = "), padic_poly_print(b, ctx), flint_printf("\n\n");
flint_printf("c = "), padic_poly_print(c, ctx), flint_printf("\n\n");
flint_printf("N = %wd\n", N);
flint_printf("N2 = %wd\n", N2);
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
