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Namespaces | |
| glucat | |
Functions | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| bool | glucat::operator!= (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Test for inequality of multivectors. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| bool | glucat::operator!= (const Multivector< Scalar_T, LO, HI > &lhs, const Scalar_T &scr) |
| Test for inequality of multivector and scalar. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| bool | glucat::operator!= (const Scalar_T &scr, const Multivector< Scalar_T, LO, HI > &rhs) |
| Test for inequality of scalar and multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator+ (const Multivector< Scalar_T, LO, HI > &lhs, const Scalar_T &scr) |
| Geometric sum of multivector and scalar. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator+ (const Scalar_T &scr, const Multivector< Scalar_T, LO, HI > &rhs) |
| Geometric sum of scalar and multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator+ (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Geometric sum. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator- (const Multivector< Scalar_T, LO, HI > &lhs, const Scalar_T &scr) |
| Geometric difference of multivector and scalar. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator- (const Scalar_T &scr, const Multivector< Scalar_T, LO, HI > &rhs) |
| Geometric difference of scalar and multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator- (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Geometric difference. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator* (const Multivector< Scalar_T, LO, HI > &lhs, const Scalar_T &scr) |
| Product of multivector and scalar. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator* (const Scalar_T &scr, const Multivector< Scalar_T, LO, HI > &rhs) |
| Product of scalar and multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator* (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Geometric product. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator^ (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Outer product. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator & (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Inner product. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator% (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Left contraction. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| Scalar_T | glucat::star (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Hestenes scalar product. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator/ (const Multivector< Scalar_T, LO, HI > &lhs, const Scalar_T &scr) |
| Quotient of multivector and scalar. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator/ (const Scalar_T &scr, const Multivector< Scalar_T, LO, HI > &rhs) |
| Quotient of scalar and multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator/ (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Geometric quotient. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::operator| (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Transformation via twisted adjoint action. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::inv (const Multivector< Scalar_T, LO, HI > &val) |
| Geometric multiplicative inverse. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::pow (const Multivector< Scalar_T, LO, HI > &lhs, int rhs) |
| Integer power of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, template< typename, const index_t, const index_t > class RHS, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::pow (const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs) |
| Multivector power of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::outer_pow (const Multivector< Scalar_T, LO, HI > &lhs, int rhs) |
| Outer product power of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| Scalar_T | glucat::scalar (const Multivector< Scalar_T, LO, HI > &val) |
| Scalar part. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| Scalar_T | glucat::real (const Multivector< Scalar_T, LO, HI > &val) |
| Real part: synonym for scalar part. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| Scalar_T | glucat::imag (const Multivector< Scalar_T, LO, HI > &val) |
| Imaginary part: deprecated (always 0) More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::pure (const Multivector< Scalar_T, LO, HI > &val) |
| Pure part. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::even (const Multivector< Scalar_T, LO, HI > &val) |
| Even part. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::odd (const Multivector< Scalar_T, LO, HI > &val) |
| Odd part. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const std::vector< Scalar_T > | glucat::vector_part (const Multivector< Scalar_T, LO, HI > &val) |
| Vector part of multivector, as a vector_t with respect to frame() More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::involute (const Multivector< Scalar_T, LO, HI > &val) |
| Main involution, each {i} is replaced by -{i} in each term, eg. {1}*{2} -> (-{2})*(-{1}) More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::reverse (const Multivector< Scalar_T, LO, HI > &val) |
| Reversion, eg. {1}*{2} -> {2}*{1}. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::conj (const Multivector< Scalar_T, LO, HI > &val) |
| Conjugation, rev o invo == invo o rev. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| Scalar_T | glucat::quad (const Multivector< Scalar_T, LO, HI > &val) |
| Scalar_T quadratic form == (rev(x)*x)(0) More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| Scalar_T | glucat::norm (const Multivector< Scalar_T, LO, HI > &val) |
| Scalar_T norm == sum of norm of coordinates. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| Scalar_T | glucat::abs (const Multivector< Scalar_T, LO, HI > &val) |
| Absolute value == sqrt(norm) More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| Scalar_T | glucat::max_abs (const Multivector< Scalar_T, LO, HI > &val) |
| Maximum of absolute values of components of multivector: multivector infinity norm. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::complexifier (const Multivector< Scalar_T, LO, HI > &val) |
| Square root of -1 which commutes with all members of the frame of the given multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::elliptic (const Multivector< Scalar_T, LO, HI > &val) |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| static void | glucat::check_complex (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Check that i is a valid complexifier for val. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::sqrt (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Square root of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::sqrt (const Multivector< Scalar_T, LO, HI > &val) |
| Square root of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::clifford_exp (const Multivector< Scalar_T, LO, HI > &val) |
| Exponential of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::log (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Natural logarithm of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::log (const Multivector< Scalar_T, LO, HI > &val) |
| Natural logarithm of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::cosh (const Multivector< Scalar_T, LO, HI > &val) |
| Hyperbolic cosine of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::acosh (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Inverse hyperbolic cosine of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::acosh (const Multivector< Scalar_T, LO, HI > &val) |
| Inverse hyperbolic cosine of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::cos (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Cosine of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::cos (const Multivector< Scalar_T, LO, HI > &val) |
| Cosine of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::acos (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Inverse cosine of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::acos (const Multivector< Scalar_T, LO, HI > &val) |
| Inverse cosine of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::sinh (const Multivector< Scalar_T, LO, HI > &val) |
| Hyperbolic sine of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::asinh (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Inverse hyperbolic sine of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::asinh (const Multivector< Scalar_T, LO, HI > &val) |
| Inverse hyperbolic sine of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::sin (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Sine of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::sin (const Multivector< Scalar_T, LO, HI > &val) |
| Sine of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::asin (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Inverse sine of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::asin (const Multivector< Scalar_T, LO, HI > &val) |
| Inverse sine of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::tanh (const Multivector< Scalar_T, LO, HI > &val) |
| Hyperbolic tangent of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::atanh (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Inverse hyperbolic tangent of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::atanh (const Multivector< Scalar_T, LO, HI > &val) |
| Inverse hyperbolic tangent of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::tan (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Tangent of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::tan (const Multivector< Scalar_T, LO, HI > &val) |
| Tangent of multivector. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::atan (const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false) |
| Inverse tangent of multivector with specified complexifier. More... | |
| template<template< typename, const index_t, const index_t > class Multivector, typename Scalar_T , const index_t LO, const index_t HI> | |
| const Multivector< Scalar_T, LO, HI > | glucat::atan (const Multivector< Scalar_T, LO, HI > &val) |
| Inverse tangent of multivector. More... | |
