ser_carry_pth_root_reg_op Struct Reference

#include <p_adic.hpp>

Static Public Member Functions

template<typename M , typename V > static series< M, V > binpow_no_tangent_normalized (const series< M, V > &x0, const series< M, V > &x1, const integer &r, const integer &p)
static generic name ()
template<typename M > static M op (const M &a, const pair< integer, integer > &p)
template<typename M , typename V > static series< M, V > op (const series< M, V > &a, const pair< integer, integer > &p)
template<typename M , typename V > static series< M, V > op_init (const series< M, V > &a, const pair< integer, integer > &p, const M &init)
static syntactic op (const syntactic &a, const syntactic &p)
static nat nr_init ()
template<typename M , typename V > static series< M, V > def (const series< M, V > &me, const series< M, V > &a, const pair< integer, integer > &p_b0)

Detailed Description

Definition at line 134 of file p_adic.hpp.

Member Function Documentation

static series<M,V> binpow_no_tangent_normalized	(	const series< M, V > &	x0,
		const series< M, V > &	x1,
		const integer &	r,
		const integer &	p
	)			`[inline, static]`

Definition at line 138 of file p_adic.hpp.

References binpow(), mmx::coefficients(), default_p_expansion, mmx::lshiftz(), M, mmx::rshiftz(), Series, and mmx::square().

Referenced by ser_carry_pth_root_reg_op::def().

00140 00141 00142 00143 00144 00145 00146 00147 00148 00149 00150 00151 00152 00153 00154 00155 00156 00157     } 00158 00159 00160 00161 00162 00163 00164 00165 00166 00167 00168 00169   }

class="fragment">00139 { // ((x0 + p * x1)^r - r * p * x1 * x0^(r-1) - x0^r) / p^2 // x1 has valuation at least 1 ASSERT (p >= 3, "bug"); if (r <= 1) return Series (0); Series x1_2= lshiftz (square (rshiftz (x1, 1)), 2); if (r == 2) return x1_2; Series s_p (coefficients (as<default_p_expansion(M)> (p))); if ((r & 1) == 1) { integer h= r - 1; Series w= binpow_no_tangent_normalized (x0, x1, h, p); Series s_h (coefficients (as<default_p_expansion(M)> (h))); Series x0_h_1= binpow (x0, h - 1); return lshiftz ((x0 + s_p * x1) * rshiftz (w, 1), 1) + s_h * x0_h_1 * x1_2; integer h= r >> 1; // r is now even Series s_h (coefficients (as<default_p_expansion(M)> (h))); Series s_p_2 (coefficients (as<default_p_expansion(M)> (square (p)))); Series x0_h_1= binpow (x0, h - 1); Series x0_h= x0 * x0_h_1; Series d= binpow_no_tangent_normalized (x0, x1, h, p); Series l= s_h * s_p * x0_h_1 * x1 + x0_h; return lshiftz (rshiftz (d, 1) * (s_p_2 * d + l + l), 1) + square (s_h * x0_h_1) * x1_2;

static series<M,V> def	(	const series< M, V > &	me,
		const series< M, V > &	a,
		const pair< integer, integer > &	p_b0
	)			`[inline, static]`

Definition at line 194 of file p_adic.hpp.

References binpow(), ser_carry_pth_root_reg_op::binpow_no_tangent_normalized(), car(), cdr(), mmx::coefficients(), default_p_expansion, mmx::lshiftz(), M, mmx::rshiftz(), Series, and mmx::square().

00194                                                             {
00195     integer p= car (p_b0); integer b0= cdr (p_b0);
00196     integer q= as<integer> (* M::get_modulus ());
00197     Series ser_p (coefficients (as<default_p_expansion(M)> (p)));
00198     if (p == 2)
00199       return (a - me[0] - ser_p
00200               * (square (Series (me[0]))
00201                  + lshiftz (square (rshiftz (me, 1)), 2)))
00202         / (M(1) + square (ser_p) * me[0]);
00203 
00204     Series tmp= binpow (Series (M(b0) + ser_p * me[0]), p)
00205       - binpow (Series (M(b0)), p);
00206     tmp= q == p ? rshiftz (tmp, 2): rshiftz (M (q / square (p)) * tmp, 1);
00207     Series ap= a - tmp;
00208     Series c= M (b0) + ser_p * me[0];
00209     return (ap - binpow_no_tangent_normalized (c, me - me[0], p, p))
00210       / binpow (c, p - 1); }

static generic name ( ) [inline, static]

Definition at line 171 of file p_adic.hpp.

00171 { return "pth_root"; }

static nat nr_init ( ) [inline, static]

Definition at line 191 of file p_adic.hpp.

00191 { return 1; }

static syntactic op	(	const syntactic &	a,
		const syntactic &	p
	)			`[inline, static]`

Definition at line 188 of file p_adic.hpp.

00188                                               {
00189     return apply ("pth_root_reg", a, p); }

static series<M,V> op	(	const series< M, V > &	a,
		const pair< integer, integer > &	p
	)			`[inline, static]`

Definition at line 178 of file p_adic.hpp.

00178                                       {
00179     typedef implementation<series_pth_root_reg,V> Ser;
00180     return Ser::unsep_root_reg (a, p); }

static M op	(	const M &	a,
		const pair< integer, integer > &	p
	)			`[inline, static]`

Definition at line 174 of file p_adic.hpp.

00174                                  {
00175     (void) p; return a; }

static series<M,V> op_init	(	const series< M, V > &	a,
		const pair< integer, integer > &	p,
		const M &	init
	)			`[inline, static]`

Definition at line 183 of file p_adic.hpp.

00183                                                           {
00184     typedef implementation<series_pth_root_reg,V> Ser;
00185     return Ser::unsep_root_reg (a, p, init); }

The documentation for this struct was generated from the following file:

include/algebramix/p_adic.hpp