ser_polynomial_regular_root_op Struct Reference

#include <series_naive.hpp>

Static Public Member Functions

static generic name ()
template<typename C > static C op (const polynomial< Lift_type(C)> &P)
static syntactic op (const syntactic &P)
template<typename R , typename L > static void set_op (R &x, const polynomial< L > &P)
template<typename C , typename V , typename L > static series< C, V > op_init (const polynomial< L > &P, const C &i)
static nat nr_init ()
template<typename S , typename L > static S def (const S &me, const polynomial< L > &P)

Detailed Description

Definition at line 653 of file series_naive.hpp.

Member Function Documentation

static S def	(	const S &	me,
		const polynomial< L > &	P
	)			`[inline, static]`

Definition at line 683 of file series_naive.hpp.

References mmx::C, mmx::eval(), mmx::lshiftz(), mmx::N(), R, mmx::rem(), mmx::rshiftz(), and mmx::square().

00683                                             {
00684     typedef Scalar_type (S) C;
00685     L y0 (* me[0]);
00686     polynomial<L> Q;
00687     polynomial<L> sqr (vec<L> (square (y0), - 2 * y0, 1)); // (X-y_O)²
00688     polynomial<L> R= rem (P, sqr, Q);
00689     S Py0 (R[0]);
00690     S dPy0 (R[1]);
00691     nat n = N(Q);
00692     vector<S> vs (S(0), n);
00693     for (nat i= 0; i<n; i++)
00694       vs[i] = S (Q[i]);
00695     polynomial<S> sQ (vs);
00696     return ((Py0 - me[0] * dPy0 + lshiftz (square (rshiftz (me))
00697                                            * eval (sQ, me), 2)) / (-dPy0));
00698   }

static generic name ( ) [inline, static]

Definition at line 656 of file series_naive.hpp.

00656 { return "polynomial_regular_root"; }

static nat nr_init ( ) [inline, static]

Definition at line 680 of file series_naive.hpp.

00680 { return 1; }

static syntactic op ( const syntactic & P ) [inline, static]

Definition at line 669 of file series_naive.hpp.

00669                           {
00670     return apply ("polynomial_regular_root", P); }

static C op ( const polynomial< Lift_type(C)> & P ) [inline, static]

Definition at line 659 of file series_naive.hpp.

References mmx::polynomial_modular_root().

00659                                           {
00660     //TODO: try this!
00661     return polynomial_modular_root (as<polynomial<C> > (P)); }

static series<C,V> op_init	(	const polynomial< L > &	P,
		const C &	i
	)			`[inline, static]`

Definition at line 677 of file series_naive.hpp.

References mmx::polynomial_regular_root_init().

00677                                                {
00678     return polynomial_regular_root_init (P, i); }

static void set_op	(	R &	x,
		const polynomial< L > &	P
	)			`[inline, static]`

Definition at line 673 of file series_naive.hpp.

References mmx::polynomial_regular_root().

00673                                         {
00674     x= polynomial_regular_root (P); }

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

include/algebramix/series_naive.hpp