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virtual | ~clifford_algebra () |
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virtual bool | operator== (const multivector_t &val) const =0 |
| Test for equality of multivectors. More...
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virtual bool | operator== (const Scalar_T &scr) const =0 |
| Test for equality of multivector and scalar. More...
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virtual multivector_t & | operator+= (const multivector_t &rhs)=0 |
| Geometric sum. More...
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virtual multivector_t & | operator+= (const Scalar_T &scr)=0 |
| Geometric sum of multivector and scalar. More...
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virtual multivector_t & | operator-= (const multivector_t &rhs)=0 |
| Geometric difference. More...
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virtual const multivector_t | operator- () const =0 |
| Unary -. More...
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virtual multivector_t & | operator*= (const Scalar_T &scr)=0 |
| Product of multivector and scalar. More...
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virtual multivector_t & | operator*= (const multivector_t &rhs)=0 |
| Geometric product. More...
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virtual multivector_t & | operator%= (const multivector_t &rhs)=0 |
| Contraction. More...
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virtual multivector_t & | operator &= (const multivector_t &rhs)=0 |
| Inner product. More...
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virtual multivector_t & | operator^= (const multivector_t &rhs)=0 |
| Outer product. More...
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virtual multivector_t & | operator/= (const Scalar_T &scr)=0 |
| Quotient of multivector and scalar. More...
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virtual multivector_t & | operator/= (const multivector_t &rhs)=0 |
| Geometric quotient. More...
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virtual multivector_t & | operator|= (const multivector_t &rhs)=0 |
| Transformation via twisted adjoint action. More...
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virtual const multivector_t | inv () const =0 |
| Geometric multiplicative inverse. More...
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virtual const multivector_t | pow (int m) const =0 |
| *this to the m More...
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virtual const multivector_t | outer_pow (int m) const =0 |
| Outer product power. More...
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virtual const index_set_t | frame () const =0 |
| Subalgebra generated by all generators of terms of given multivector. More...
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virtual index_t | grade () const =0 |
| Maximum of the grades of each term. More...
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virtual Scalar_T | operator[] (const index_set_t ist) const =0 |
| Subscripting: map from index set to scalar coordinate. More...
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virtual const multivector_t | operator() (index_t grade) const =0 |
| Pure grade-vector part. More...
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virtual Scalar_T | scalar () const =0 |
| Scalar part. More...
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virtual const multivector_t | pure () const =0 |
| Pure part. More...
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virtual const multivector_t | even () const =0 |
| Even part of multivector, sum of even grade terms. More...
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virtual const multivector_t | odd () const =0 |
| Odd part of multivector, sum of odd grade terms. More...
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virtual const vector_t | vector_part () const =0 |
| Vector part of multivector, as a vector_t with respect to frame() More...
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virtual const vector_t | vector_part (const index_set_t frm, const bool prechecked) const =0 |
| Vector part of multivector, as a vector_t with respect to frm. More...
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virtual const multivector_t | involute () const =0 |
| Main involution, each {i} is replaced by -{i} in each term, eg. {1} -> -{1}. More...
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virtual const multivector_t | reverse () const =0 |
| Reversion, eg. {1}*{2} -> {2}*{1}. More...
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virtual const multivector_t | conj () const =0 |
| Conjugation, reverse o involute == involute o reverse. More...
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virtual Scalar_T | quad () const =0 |
| Scalar_T quadratic form == (rev(x)*x)(0) More...
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virtual Scalar_T | norm () const =0 |
| Scalar_T norm == sum of norm of coordinates. More...
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virtual Scalar_T | max_abs () const =0 |
| Maximum of absolute values of components of multivector: multivector infinity norm. More...
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virtual const multivector_t | truncated (const Scalar_T &limit=Scalar_T(DEFAULT_TRUNCATION)) const =0 |
| Remove all terms with relative size smaller than limit. More...
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virtual bool | isnan () const =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 42 of file clifford_algebra.h.