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virtual | ~clifford_algebra ()=default |
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virtual auto | operator== (const multivector_t &val) const -> bool=0 |
| Test for equality of multivectors. More...
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virtual auto | operator== (const Scalar_T &scr) const -> bool=0 |
| Test for equality of multivector and scalar. More...
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virtual auto | operator+= (const multivector_t &rhs) -> multivector_t &=0 |
| Geometric sum. More...
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virtual auto | operator+= (const Scalar_T &scr) -> multivector_t &=0 |
| Geometric sum of multivector and scalar. More...
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virtual auto | operator-= (const multivector_t &rhs) -> multivector_t &=0 |
| Geometric difference. More...
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virtual auto | operator-= (const Scalar_T &scr) -> multivector_t &=0 |
| Geometric difference of multivector and scalar. More...
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virtual auto | operator- () const -> const multivector_t=0 |
| Unary -. More...
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virtual auto | operator*= (const Scalar_T &scr) -> multivector_t &=0 |
| Product of multivector and scalar. More...
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virtual auto | operator*= (const multivector_t &rhs) -> multivector_t &=0 |
| Geometric product. More...
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virtual auto | operator%= (const multivector_t &rhs) -> multivector_t &=0 |
| Contraction. More...
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virtual auto | operator &= (const multivector_t &rhs) -> multivector_t &=0 |
| Inner product. More...
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virtual auto | operator^= (const multivector_t &rhs) -> multivector_t &=0 |
| Outer product. More...
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virtual auto | operator/= (const Scalar_T &scr) -> multivector_t &=0 |
| Quotient of multivector and scalar. More...
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virtual auto | operator/= (const multivector_t &rhs) -> multivector_t &=0 |
| Geometric quotient. More...
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virtual auto | operator|= (const multivector_t &rhs) -> multivector_t &=0 |
| Transformation via twisted adjoint action. More...
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virtual auto | inv () const -> const multivector_t=0 |
| Geometric multiplicative inverse. More...
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virtual auto | pow (int m) const -> const multivector_t=0 |
| *this to the m More...
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virtual auto | outer_pow (int m) const -> const multivector_t=0 |
| Outer product power. More...
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virtual auto | frame () const -> const index_set_t=0 |
| Subalgebra generated by all generators of terms of given multivector. More...
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virtual auto | grade () const -> index_t=0 |
| Maximum of the grades of each term. More...
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virtual auto | operator[] (const index_set_t ist) const -> Scalar_T=0 |
| Subscripting: map from index set to scalar coordinate. More...
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virtual auto | operator() (index_t grade) const -> const multivector_t=0 |
| Pure grade-vector part. More...
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virtual auto | scalar () const -> Scalar_T=0 |
| Scalar part. More...
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virtual auto | pure () const -> const multivector_t=0 |
| Pure part. More...
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virtual auto | even () const -> const multivector_t=0 |
| Even part of multivector, sum of even grade terms. More...
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virtual auto | odd () const -> const multivector_t=0 |
| Odd part of multivector, sum of odd grade terms. More...
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virtual auto | vector_part () const -> const vector_t=0 |
| Vector part of multivector, as a vector_t with respect to frame() More...
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virtual auto | vector_part (const index_set_t frm, const bool prechecked) const -> const vector_t=0 |
| Vector part of multivector, as a vector_t with respect to frm. More...
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virtual auto | involute () const -> const multivector_t=0 |
| Main involution, each {i} is replaced by -{i} in each term, eg. {1} -> -{1}. More...
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virtual auto | reverse () const -> const multivector_t=0 |
| Reversion, eg. {1}*{2} -> {2}*{1}. More...
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virtual auto | conj () const -> const multivector_t=0 |
| Conjugation, reverse o involute == involute o reverse. More...
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virtual auto | quad () const -> Scalar_T=0 |
| Scalar_T quadratic form == (rev(x)*x)(0) More...
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virtual auto | norm () const -> Scalar_T=0 |
| Scalar_T norm == sum of norm of coordinates. More...
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virtual auto | max_abs () const -> Scalar_T=0 |
| Maximum of absolute values of components of multivector: multivector infinity norm. More...
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virtual auto | truncated (const Scalar_T &limit=default_truncation) const -> const multivector_t=0 |
| Remove all terms with relative size smaller than limit. More...
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virtual auto | isinf () const -> bool=0 |
| Check if a multivector contains any infinite values. More...
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virtual auto | isnan () const -> bool=0 |
| Check if a multivector contains any IEEE NaN values. More...
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virtual void | write (const std::string &msg="") const =0 |
| Write formatted multivector to output. More...
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virtual void | write (std::ofstream &ofile, const std::string &msg="") const =0 |
| Write formatted multivector to file. More...
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template<typename Scalar_T, typename Index_Set_T, typename Multivector_T>
class glucat::clifford_algebra< Scalar_T, Index_Set_T, Multivector_T >
clifford_algebra<> declares the operations of a Clifford algebra
Definition at line 45 of file clifford_algebra.h.