sbasis.h File Reference

Polynomial in symmetric power basis (S-basis) More...

Go to the source code of this file.

Classes
class	Geom::SBasis
	Polynomial in symmetric power basis. More...

Namespaces
namespace	Geom
	Various utility functions.

Functions
OptInterval	Geom::bounds_exact (SBasis const &a)
OptInterval	Geom::bounds_fast (SBasis const &a, int order=0)
OptInterval	Geom::bounds_local (SBasis const &a, const OptInterval &t, int order=0)
SBasis	Geom::operator- (const SBasis &p)
SBasis	Geom::operator* (SBasis const &a, double k)
	Compute the pointwise product of a and b (Exact)
SBasis	Geom::operator* (double k, SBasis const &a)
SBasis	Geom::operator/ (SBasis const &a, double k)
SBasis &	Geom::operator*= (SBasis &a, double b)
	Compute the pointwise product of a and b and store the value in a (Exact)
SBasis &	Geom::operator/= (SBasis &a, double b)
SBasis	Geom::operator+ (const SBasis &a, const SBasis &b)
	Compute the pointwise sum of a and b (Exact)
SBasis	Geom::operator- (const SBasis &a, const SBasis &b)
	Compute the pointwise difference of a and b (Exact)
SBasis &	Geom::operator+= (SBasis &a, const SBasis &b)
	Compute the pointwise sum of a and b and store in a (Exact)
SBasis &	Geom::operator-= (SBasis &a, const SBasis &b)
	Compute the pointwise difference of a and b and store in a (Exact)
SBasis	Geom::operator+ (const SBasis &a, double b)
SBasis	Geom::operator- (const SBasis &a, double b)
SBasis &	Geom::operator+= (SBasis &a, double b)
SBasis &	Geom::operator-= (SBasis &a, double b)
SBasis	Geom::shift (SBasis const &a, int sh)
	multiply a by x^sh in place (Exact)
SBasis	Geom::shift (Linear const &a, int sh)
	multiply a by x^sh (Exact)
SBasis	Geom::truncate (SBasis const &a, unsigned terms)
SBasis	Geom::multiply (SBasis const &a, SBasis const &b)
	Compute the pointwise product of a and b (Exact)
SBasis	Geom::multiply_add (SBasis const &a, SBasis const &b, SBasis c)
	Compute the pointwise product of a and b adding c (Exact)
SBasis	Geom::integral (SBasis const &c)
	Compute the integral of a (Exact)
SBasis	Geom::derivative (SBasis const &a)
	Compute the derivative of a (Exact)
SBasis	Geom::sqrt (SBasis const &a, int k)
	Compute the sqrt of a.
SBasis	Geom::reciprocal (Linear const &a, int k)
	Compute the recpirocal of a.
SBasis	Geom::divide (SBasis const &a, SBasis const &b, int k)
	Compute a / b to k terms.
SBasis	Geom::operator* (SBasis const &a, SBasis const &b)
SBasis &	Geom::operator*= (SBasis &a, SBasis const &b)
SBasis	Geom::compose (SBasis const &a, SBasis const &b)
	Compute a composed with b.
SBasis	Geom::compose (SBasis const &a, SBasis const &b, unsigned k)
	Compute a composed with b to k terms.
SBasis	Geom::inverse (SBasis a, int k)
	find the function a^-1 such that a^-1 composed with a to k terms is the identity function
SBasis	Geom::compose_inverse (SBasis const &f, SBasis const &g, unsigned order, double zero)
	compute fog^-1.
SBasis	Geom::portion (const SBasis &t, Interval const &ivl)
std::ostream &	Geom::operator<< (std::ostream &out_file, const Linear &bo)
std::ostream &	Geom::operator<< (std::ostream &out_file, const SBasis &p)
SBasis	Geom::sin (Linear b, int k)
	Compute the sine of a to k terms.
SBasis	Geom::cos (Linear bo, int k)
	Compute the cosine of a.
std::vector< double >	Geom::roots (SBasis const &s)
std::vector< double >	Geom::roots (SBasis const &s, Interval const inside)
std::vector< std::vector< double > >	Geom::multi_roots (SBasis const &f, std::vector< double > const &levels, double htol=1e-7, double vtol=1e-7, double a=0, double b=1)
std::vector< Interval >	Geom::level_set (SBasis const &f, double level, double vtol=1e-5, double a=0., double b=1., double tol=1e-5)
	Solve f(t) = v +/- tolerance.
std::vector< Interval >	Geom::level_set (SBasis const &f, Interval const &level, double a=0., double b=1., double tol=1e-5)
	Solve f(t)\in I=[u,v], which defines a collection of intervals (J_k).
std::vector< std::vector< Interval > >	Geom::level_sets (SBasis const &f, std::vector< double > const &levels, double a=0., double b=1., double vtol=1e-5, double tol=1e-5)
	'Solve' f(t) = v +/- tolerance for several values of v at once.
std::vector< std::vector< Interval > >	Geom::level_sets (SBasis const &f, std::vector< Interval > const &levels, double a=0., double b=1., double tol=1e-5)
	'Solve' f(t)\in I=[u,v] for several intervals I at once.

Detailed Description

Polynomial in symmetric power basis (S-basis)

Definition in file sbasis.h.