void arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, long n, long prec) { if (n == 0 || B->length == 0) { printf("arb_poly_inv_series: require n > 0 and nonzero input\n"); abort(); } if (A->length == 0) { arb_poly_zero(Q); return; } if (Q == A || Q == B) { arb_poly_t t; arb_poly_init(t); arb_poly_div_series(t, A, B, n, prec); arb_poly_swap(Q, t); arb_poly_clear(t); return; } arb_poly_fit_length(Q, n); _arb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec); _arb_poly_set_length(Q, n); _arb_poly_normalise(Q); }
void _arb_poly_div(arb_ptr Q, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) { slong lenQ, lenB2; arb_ptr Arev, Brev; lenQ = lenA - lenB + 1; Arev = _arb_vec_init(2 * lenQ); Brev = Arev + lenQ; _arb_poly_reverse(Arev, A + (lenA - lenQ), lenQ, lenQ); if (lenB >= lenQ) { _arb_poly_reverse(Brev, B + (lenB - lenQ), lenQ, lenQ); lenB2 = lenQ; } else { _arb_poly_reverse(Brev, B, lenB, lenB); lenB2 = lenB; } _arb_poly_div_series(Q, Arev, lenQ, Brev, lenB2, lenQ, prec); _arb_poly_reverse(Q, Q, lenQ, lenQ); _arb_vec_clear(Arev, 2 * lenQ); }
void _arb_poly_tan_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); if (hlen == 1) { arb_tan(g, h, prec); _arb_vec_zero(g + 1, len - 1); } else if (len == 2) { arb_t t; arb_init(t); arb_tan(g, h, prec); arb_mul(t, g, g, prec); arb_add_ui(t, t, 1, prec); arb_mul(g + 1, t, h + 1, prec); /* safe since hlen >= 2 */ arb_clear(t); } else { arb_ptr t, u; t = _arb_vec_init(2 * len); u = t + len; NEWTON_INIT(TAN_NEWTON_CUTOFF, len) NEWTON_BASECASE(n) _arb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec, 0); _arb_poly_div_series(g, t, n, u, n, n, prec); NEWTON_END_BASECASE NEWTON_LOOP(m, n) _arb_poly_mullow(u, g, m, g, m, n, prec); arb_add_ui(u, u, 1, prec); _arb_poly_atan_series(t, g, m, n, prec); _arb_poly_sub(t + m, h + m, FLINT_MAX(0, hlen - m), t + m, n - m, prec); _arb_poly_mullow(g + m, u, n, t + m, n - m, n - m, prec); NEWTON_END_LOOP NEWTON_END _arb_vec_clear(t, 2 * len); } }
void arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, long n, long prec) { if (n == 0) { arb_poly_zero(Q); return; } if (B->length == 0) { arb_poly_fit_length(Q, n); _arb_vec_indeterminate(Q->coeffs, n); _arb_poly_set_length(Q, n); return; } if (A->length == 0) { arb_poly_zero(Q); return; } if (Q == A || Q == B) { arb_poly_t t; arb_poly_init(t); arb_poly_div_series(t, A, B, n, prec); arb_poly_swap(Q, t); arb_poly_clear(t); return; } arb_poly_fit_length(Q, n); _arb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec); _arb_poly_set_length(Q, n); _arb_poly_normalise(Q); }
void _arb_poly_cot_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); if (hlen == 1) { arb_cot_pi(g, h, prec); _arb_vec_zero(g + 1, len - 1); } else { arb_ptr t, u; t = _arb_vec_init(len); u = _arb_vec_init(len); _arb_poly_sin_cos_pi_series(t, u, h, hlen, len, prec); _arb_poly_div_series(g, u, len, t, len, len, prec); _arb_vec_clear(t, len); _arb_vec_clear(u, len); } }