* Interface to GiNaC's special tensors. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
// other constructors
protected:
- tensor(unsigned ti);
+ tensor(unsigned ti) : inherited(ti) {}
- // functions overriding virtual functions from bases classes
+ // functions overriding virtual functions from base classes
protected:
- unsigned return_type(void) const { return return_types::noncommutative_composite; }
+ unsigned return_type() const { return return_types::noncommutative_composite; }
+
+ // non-virtual functions in this class
+public:
+ /** Replace dummy index in contracted-with object by the contracting
+ * object's second index (used internally for delta and metric tensor
+ * contractions. */
+ bool replace_contr_index(exvector::iterator self, exvector::iterator other) const;
};
{
GINAC_DECLARE_REGISTERED_CLASS(tensdelta, tensor)
- // functions overriding virtual functions from bases classes
+ // functions overriding virtual functions from base classes
public:
- void print(std::ostream & os, unsigned upper_precedence=0) const;
ex eval_indexed(const basic & i) const;
bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
};
{
GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
- // functions overriding virtual functions from bases classes
+ // functions overriding virtual functions from base classes
public:
- void print(std::ostream & os, unsigned upper_precedence=0) const;
ex eval_indexed(const basic & i) const;
bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
};
/** Construct Lorentz metric tensor with given signature. */
minkmetric(bool pos_sig);
- // functions overriding virtual functions from bases classes
+ // functions overriding virtual functions from base classes
public:
- void print(std::ostream & os, unsigned upper_precedence=0) const;
ex eval_indexed(const basic & i) const;
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+
// member variables
private:
bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
};
+/** This class represents an antisymmetric spinor metric tensor which
+ * can be used to raise/lower indices of 2-component Weyl spinors. If
+ * indexed, it must have exactly two indices of the same type which
+ * must be of class spinidx or a subclass and have dimension 2. */
+class spinmetric : public tensmetric
+{
+ GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
+
+ // functions overriding virtual functions from base classes
+public:
+ ex eval_indexed(const basic & i) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+};
+
+
/** This class represents the totally antisymmetric epsilon tensor. If
* indexed, all indices must be of the same type and their number must
* be equal to the dimension of the index space. */
{
GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
- // functions overriding virtual functions from bases classes
+ // other constructors
public:
- void print(std::ostream & os, unsigned upper_precedence=0) const;
+ tensepsilon(bool minkowski, bool pos_sig);
+
+ // functions overriding virtual functions from base classes
+public:
+ ex eval_indexed(const basic & i) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
+ // non-virtual functions in this class
+protected:
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+
+ // member variables
+private:
+ bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
+ bool pos_sig; /**< If true, the metric is assumed to be diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). This is only relevant if minkowski = true. */
};
// utility functions
-inline const tensor &ex_to_tensor(const ex &e)
-{
- return static_cast<const tensor &>(*e.bp);
-}
/** Create a delta tensor with specified indices. The indices must be of class
* idx or a subclass. The delta tensor is always symmetric and its trace is
* @return newly constructed delta tensor */
ex delta_tensor(const ex & i1, const ex & i2);
-/** Create a metric tensor with specified indices. The indices must be of
- * class varidx or a subclass. A metric tensor with one covariant and one
- * contravariant index is equivalent to the delta tensor.
+/** Create a symmetric metric tensor with specified indices. The indices
+ * must be of class varidx or a subclass. A metric tensor with one
+ * covariant and one contravariant index is equivalent to the delta tensor.
*
* @param i1 First index
* @param i2 Second index
* @return newly constructed Lorentz metric tensor */
ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
-/** Create an epsilon tensor with two indices. The indices must be of class
- * idx or a subclass, and have a dimension of 2.
+/** Create a spinor metric tensor with specified indices. The indices must be
+ * of class spinidx or a subclass and have a dimension of 2. The spinor
+ * metric is an antisymmetric tensor with a matrix representation of
+ * [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].
+ *
+ * @param i1 First index
+ * @param i2 Second index
+ * @return newly constructed spinor metric tensor */
+ex spinor_metric(const ex & i1, const ex & i2);
+
+/** Create an epsilon tensor in a Euclidean space with two indices. The
+ * indices must be of class idx or a subclass, and have a dimension of 2.
*
* @param i1 First index
* @param i2 Second index
* @return newly constructed epsilon tensor */
ex epsilon_tensor(const ex & i1, const ex & i2);
+/** Create an epsilon tensor in a Euclidean space with three indices. The
+ * indices must be of class idx or a subclass, and have a dimension of 3.
+ *
+ * @param i1 First index
+ * @param i2 Second index
+ * @param i3 Third index
+ * @return newly constructed epsilon tensor */
+ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
+
+/** Create an epsilon tensor in a Minkowski space with four indices. The
+ * indices must be of class varidx or a subclass, and have a dimension of 4.
+ *
+ * @param i1 First index
+ * @param i2 Second index
+ * @param i3 Third index
+ * @param i4 Fourth index
+ * @param pos_sig Whether the signature of the metric is positive
+ * @return newly constructed epsilon tensor */
+ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
+
} // namespace GiNaC
#endif // ndef __GINAC_TENSOR_H__
git://www.ginac.de / ginac.git / blobdiff