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/*
Copyright (C) 2011, 2013 Sebastian Pancratz
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
/*
Demo FLINT program to demonstrate some use of the qadic module.
*/
#include <stdlib.h>
#include <stdio.h>
#include <flint/qadic.h>
int main(void)
{
fmpz_t p;
slong d, N;
qadic_ctx_t ctx;
qadic_t a, b, c;
int ans;
/*************************************************************************/
fmpz_t e = {WORD(4)};
fmpz_t nine = {WORD(9)};
fmpz_init_set_ui(p, 3);
d = 2;
N = 5;
qadic_ctx_init_conway(ctx, p, d, 0, N, "a", PADIC_SERIES);
qadic_init2(a, N);
qadic_init2(b, N);
qadic_init2(c, N);
flint_printf("Compute a power and a sum\n");
padic_poly_fit_length(a, 2);
fmpz_one(a->coeffs + 0);
fmpz_set_ui(a->coeffs + 1, 2);
a->val = 0;
_padic_poly_set_length(a, 2);
qadic_print_pretty(a, ctx); flint_printf("\n");
qadic_pow(a, a, e, ctx);
padic_poly_set_ui(b, 3249, &ctx->pctx);
qadic_add(c, a, b, ctx);
qadic_print_pretty(a, ctx); flint_printf("\n");
qadic_print_pretty(b, ctx); flint_printf("\n");
qadic_print_pretty(c, ctx); flint_printf("\n");
flint_printf("\n");
flint_printf("Compute a Teichmuller lift\n");
padic_poly_fit_length(a, 2);
fmpz_one(a->coeffs + 0);
fmpz_set_ui(a->coeffs + 1, 2);
a->val = 0;
_padic_poly_set_length(a, 2);
qadic_teichmuller(b, a, ctx);
qadic_pow(c, b, nine, ctx);
qadic_print_pretty(a, ctx); flint_printf("\n");
qadic_print_pretty(b, ctx); flint_printf("\n");
qadic_print_pretty(c, ctx); flint_printf("\n");
flint_printf("\n");
flint_printf("Compute an inverse\n");
qadic_set(a, b, ctx);
qadic_inv(b, a, ctx);
qadic_mul(c, a, b, ctx);
qadic_print_pretty(a, ctx); flint_printf("\n");
qadic_print_pretty(b, ctx); flint_printf("\n");
qadic_print_pretty(c, ctx); flint_printf("\n");
flint_printf("\n");
qadic_clear(a);
qadic_clear(b);
qadic_clear(c);
qadic_ctx_clear(ctx);
fmpz_clear(p);
/*************************************************************************/
flint_printf("Compute a Frobenius image\n");
fmpz_init_set_ui(p, 3);
d = 2;
N = 5;
qadic_ctx_init_conway(ctx, p, d, 0, N, "X", PADIC_TERSE);
qadic_init2(a, N);
qadic_init2(b, N);
padic_poly_fit_length(a, 2);
a->coeffs[0] = WORD(78);
a->coeffs[1] = WORD(45);
a->val = 0;
_padic_poly_set_length(a, 2);
qadic_frobenius(b, a, 1, ctx);
flint_printf("a = "), qadic_print_pretty(a, ctx), flint_printf("\n");
flint_printf("b = "), qadic_print_pretty(b, ctx), flint_printf("\n");
flint_printf("Context:\n"), qadic_ctx_print(ctx);
flint_printf("\n");
qadic_clear(a);
qadic_clear(b);
qadic_ctx_clear(ctx);
fmpz_clear(p);
/*************************************************************************/
flint_printf("Compute a square root\n");
fmpz_init_set_ui(p, 2);
d = 3;
N = 2;
qadic_ctx_init_conway(ctx, p, d, 0, N, "X", PADIC_SERIES);
qadic_init2(a, N);
qadic_init2(b, N);
padic_poly_fit_length(a, d);
a->coeffs[0] = WORD(1);
a->coeffs[1] = WORD(3);
a->coeffs[2] = WORD(1);
a->val = 0;
_padic_poly_set_length(a, d);
ans = qadic_sqrt(b, a, ctx);
flint_printf("a = "), qadic_print_pretty(a, ctx), flint_printf("\n");
flint_printf("b = "), qadic_print_pretty(b, ctx), flint_printf("\n");
flint_printf("ans = %d\n", ans);
flint_printf("Context:\n"), qadic_ctx_print(ctx);
flint_printf("\n");
qadic_clear(a);
qadic_clear(b);
qadic_ctx_clear(ctx);
fmpz_clear(p);
return 0;
}
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