From: Christian Bauer <Christian.Bauer@uni-mainz.de>
Date: Wed, 14 Mar 2001 23:05:10 +0000 (+0000)
Subject: added predefined epsilon tensor
X-Git-Tag: release_0-8-0~25
X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=745d46b8492878030cc0decd1cb9bf2de2de03ff

added predefined epsilon tensor
---

diff --git a/ginac/idx.h b/ginac/idx.h
index c760f67b..ea885fee 100644
--- a/ginac/idx.h
+++ b/ginac/idx.h
@@ -80,7 +80,6 @@ public:
 	/** Check whether the dimension is symbolic. */
 	bool is_dim_symbolic(void) const {return !is_ex_exactly_of_type(dim, numeric);}
 
-	// member variables
 protected:
 	ex value; /**< Expression that constitutes the index (numeric or symbolic name) */
 	ex dim;   /**< Dimension of space (can be symbolic or numeric) */
diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp
index c3fe1d9a..fb34df95 100644
--- a/ginac/indexed.cpp
+++ b/ginac/indexed.cpp
@@ -66,56 +66,56 @@ indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
 {
 	debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
 {
 	debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
 {
 	debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
 {
 	debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(unknown)
 {
 	debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
 {
 	debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
 {
 	debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(symm)
 {
 	debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
@@ -123,7 +123,7 @@ indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unkn
 	debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
 	seq.insert(seq.end(), v.begin(), v.end());
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
@@ -131,28 +131,28 @@ indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherit
 	debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
 	seq.insert(seq.end(), v.begin(), v.end());
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
 {
 	debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
 {
 	debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
 {
 	debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	GINAC_ASSERT(all_indices_of_type_idx());
+	assert_all_indices_of_type_idx();
 }
 
 //////////
@@ -426,16 +426,15 @@ void indexed::printindices(std::ostream & os) const
 /** Check whether all indices are of class idx. This function is used
  *  internally to make sure that all constructed indexed objects really
  *  carry indices and not some other classes. */
-bool indexed::all_indices_of_type_idx(void) const
+void indexed::assert_all_indices_of_type_idx(void) const
 {
 	GINAC_ASSERT(seq.size() > 0);
 	exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 	while (it != itend) {
 		if (!is_ex_of_type(*it, idx))
-			return false;
+			throw(std::invalid_argument("indices of indexed object must be of type idx"));
 		it++;
 	}
-	return true;
 }
 
 //////////
@@ -502,6 +501,13 @@ static bool indices_consistent(const exvector & v1, const exvector & v2)
 	return true;
 }
 
+exvector indexed::get_dummy_indices(void) const
+{
+	exvector free_indices, dummy_indices;
+	find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
+	return dummy_indices;
+}
+
 exvector indexed::get_free_indices(void) const
 {
 	exvector free_indices, dummy_indices;
diff --git a/ginac/indexed.h b/ginac/indexed.h
index b15ed8b3..b06fad10 100644
--- a/ginac/indexed.h
+++ b/ginac/indexed.h
@@ -173,11 +173,14 @@ public:
 	 *  @see class info_flags */
 	bool all_index_values_are(unsigned inf) const;
 
+	/** Return a vector containing the dummy indices of the object, if any. */
+	exvector get_dummy_indices(void) const;
+
 protected:
 	void printrawindices(std::ostream & os) const;
 	void printtreeindices(std::ostream & os, unsigned indent) const;
 	void printindices(std::ostream & os) const;
-	bool all_indices_of_type_idx(void) const;
+	void assert_all_indices_of_type_idx(void) const;
 
 	// member variables
 protected:
diff --git a/ginac/tensor.cpp b/ginac/tensor.cpp
index 9d5feb63..cf0204b5 100644
--- a/ginac/tensor.cpp
+++ b/ginac/tensor.cpp
@@ -21,6 +21,7 @@
  */
 
 #include <stdexcept>
+#include <vector>
 
 #include "tensor.h"
 #include "idx.h"
@@ -43,6 +44,13 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor)
 // default constructor, destructor, copy constructor assignment operator and helpers
 //////////
 
+#define DEFAULT_DESTROY(classname) \
+void classname::destroy(bool call_parent) \
+{ \
+	if (call_parent) \
+		inherited::destroy(call_parent); \
+}
+
 #define DEFAULT_CTORS(classname) \
 classname::classname() : inherited(TINFO_##classname) \
 { \
@@ -52,11 +60,7 @@ void classname::copy(const classname & other) \
 { \
 	inherited::copy(other); \
 } \
-void classname::destroy(bool call_parent) \
-{ \
-	if (call_parent) \
-		inherited::destroy(call_parent); \
-}
+DEFAULT_DESTROY(classname)
 
 tensor::tensor(unsigned ti) : inherited(ti)
 {
@@ -66,7 +70,8 @@ tensor::tensor(unsigned ti) : inherited(ti)
 DEFAULT_CTORS(tensor)
 DEFAULT_CTORS(tensdelta)
 DEFAULT_CTORS(tensmetric)
-DEFAULT_CTORS(tensepsilon)
+DEFAULT_DESTROY(minkmetric)
+DEFAULT_DESTROY(tensepsilon)
 
 minkmetric::minkmetric() : pos_sig(false)
 {
@@ -86,25 +91,41 @@ void minkmetric::copy(const minkmetric & other)
 	pos_sig = other.pos_sig;
 }
 
-void minkmetric::destroy(bool call_parent)
+tensepsilon::tensepsilon() : minkowski(false), pos_sig(false)
+{
+	debugmsg("tensepsilon default constructor", LOGLEVEL_CONSTRUCT);
+	tinfo_key = TINFO_tensepsilon;
+}
+
+tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps)
 {
-	if (call_parent)
-		inherited::destroy(call_parent);
+	debugmsg("tensepsilon constructor from bool,bool", LOGLEVEL_CONSTRUCT);
+	tinfo_key = TINFO_tensepsilon;
+}
+
+void tensepsilon::copy(const tensepsilon & other)
+{
+	inherited::copy(other);
+	minkowski = other.minkowski;
+	pos_sig = other.pos_sig;
 }
 
 //////////
 // archiving
 //////////
 
+#define DEFAULT_UNARCHIVE(classname) \
+ex classname::unarchive(const archive_node &n, const lst &sym_lst) \
+{ \
+	return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
+}
+
 #define DEFAULT_ARCHIVING(classname) \
 classname::classname(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) \
 { \
 	debugmsg(#classname " constructor from archive_node", LOGLEVEL_CONSTRUCT); \
 } \
-ex classname::unarchive(const archive_node &n, const lst &sym_lst) \
-{ \
-	return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
-} \
+DEFAULT_UNARCHIVE(classname) \
 void classname::archive(archive_node &n) const \
 { \
 	inherited::archive(n); \
@@ -113,7 +134,8 @@ void classname::archive(archive_node &n) const \
 DEFAULT_ARCHIVING(tensor)
 DEFAULT_ARCHIVING(tensdelta)
 DEFAULT_ARCHIVING(tensmetric)
-DEFAULT_ARCHIVING(tensepsilon)
+DEFAULT_UNARCHIVE(minkmetric)
+DEFAULT_UNARCHIVE(tensepsilon)
 
 minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
@@ -121,14 +143,23 @@ minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n,
 	n.find_bool("pos_sig", pos_sig);
 }
 
-ex minkmetric::unarchive(const archive_node &n, const lst &sym_lst)
+void minkmetric::archive(archive_node &n) const
 {
-	return (new minkmetric(n, sym_lst))->setflag(status_flags::dynallocated);
+	inherited::archive(n);
+	n.add_bool("pos_sig", pos_sig);
 }
 
-void minkmetric::archive(archive_node &n) const
+tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+{
+	debugmsg("tensepsilon constructor from archive_node", LOGLEVEL_CONSTRUCT);
+	n.find_bool("minkowski", minkowski);
+	n.find_bool("pos_sig", pos_sig);
+}
+
+void tensepsilon::archive(archive_node &n) const
 {
 	inherited::archive(n);
+	n.add_bool("minkowski", minkowski);
 	n.add_bool("pos_sig", pos_sig);
 }
 
@@ -146,7 +177,6 @@ int classname::compare_same_type(const basic & other) const \
 DEFAULT_COMPARE(tensor)
 DEFAULT_COMPARE(tensdelta)
 DEFAULT_COMPARE(tensmetric)
-DEFAULT_COMPARE(tensepsilon)
 
 int minkmetric::compare_same_type(const basic & other) const
 {
@@ -159,6 +189,19 @@ int minkmetric::compare_same_type(const basic & other) const
 		return inherited::compare_same_type(other);
 }
 
+int tensepsilon::compare_same_type(const basic & other) const
+{
+	GINAC_ASSERT(is_of_type(other, tensepsilon));
+	const tensepsilon &o = static_cast<const tensepsilon &>(other);
+
+	if (minkowski != o.minkowski)
+		return minkowski ? -1 : 1;
+	else if (pos_sig != o.pos_sig)
+		return pos_sig ? -1 : 1;
+	else
+		return inherited::compare_same_type(other);
+}
+
 void tensdelta::print(std::ostream & os, unsigned upper_precedence) const
 {
 	debugmsg("tensdelta print",LOGLEVEL_PRINT);
@@ -249,6 +292,49 @@ ex minkmetric::eval_indexed(const basic & i) const
 	return inherited::eval_indexed(i);
 }
 
+/** Automatic symbolic evaluation of an indexed epsilon tensor. */
+ex tensepsilon::eval_indexed(const basic & i) const
+{
+	GINAC_ASSERT(is_of_type(i, indexed));
+	GINAC_ASSERT(i.nops() > 1);
+	GINAC_ASSERT(is_ex_of_type(i.op(0), tensepsilon));
+
+	// Convolutions are zero
+	if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
+		return _ex0();
+
+	// Numeric evaluation
+	if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
+
+		// Get sign of index permutation (the indices should already be in
+		// a canonic order but we can't assume what exactly that order is)
+		vector<int> v;
+		v.reserve(i.nops() - 1);
+		for (unsigned j=1; j<i.nops(); j++)
+			v.push_back(ex_to_numeric(ex_to_idx(i.op(j)).get_value()).to_int());
+		int sign = permutation_sign(v);
+
+		// In a Minkowski space, check for covariant indices
+		if (minkowski) {
+			for (unsigned j=1; j<i.nops(); j++) {
+				const ex & x = i.op(j);
+				if (!is_ex_of_type(x, varidx))
+					throw(std::runtime_error("indices of epsilon tensor in Minkowski space must be of type varidx"));
+				if (ex_to_varidx(x).is_covariant())
+					if (ex_to_idx(x).get_value().is_zero())
+						sign = (pos_sig ? -sign : sign);
+					else
+						sign = (pos_sig ? sign : -sign);
+			}
+		}
+
+		return sign;
+	}
+
+	// No further simplifications
+	return i.hold();
+}
+
 /** Contraction of an indexed delta tensor with something else. */
 bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
@@ -366,10 +452,42 @@ ex epsilon_tensor(const ex & i1, const ex & i2)
 {
 	if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
 		throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
-	if (!ex_to_idx(i1).get_dim().is_equal(_ex2()) || !ex_to_idx(i2).get_dim().is_equal(_ex2()))
-		throw(std::invalid_argument("index dimension of epsilon tensor must match number of indices"));
+
+	ex dim = ex_to_idx(i1).get_dim();
+	if (!dim.is_equal(ex_to_idx(i2).get_dim()))
+		throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
+	if (!ex_to_idx(i1).get_dim().is_equal(_ex2()))
+		throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
 
 	return indexed(tensepsilon(), indexed::antisymmetric, i1, i2);
 }
 
+ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3)
+{
+	if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx) || !is_ex_of_type(i3, idx))
+		throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
+
+	ex dim = ex_to_idx(i1).get_dim();
+	if (!dim.is_equal(ex_to_idx(i2).get_dim()) || !dim.is_equal(ex_to_idx(i3).get_dim()))
+		throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
+	if (!ex_to_idx(i1).get_dim().is_equal(_ex3()))
+		throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
+
+	return indexed(tensepsilon(), indexed::antisymmetric, i1, i2, i3);
+}
+
+ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
+{
+	if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx) || !is_ex_of_type(i3, varidx) || !is_ex_of_type(i4, varidx))
+		throw(std::invalid_argument("indices of Lorentz epsilon tensor must be of type varidx"));
+
+	ex dim = ex_to_idx(i1).get_dim();
+	if (!dim.is_equal(ex_to_idx(i2).get_dim()) || !dim.is_equal(ex_to_idx(i3).get_dim()) || !dim.is_equal(ex_to_idx(i4).get_dim()))
+		throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
+	if (!ex_to_idx(i1).get_dim().is_equal(_ex4()))
+		throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
+
+	return indexed(tensepsilon(true, pos_sig), indexed::antisymmetric, i1, i2, i3, i4);
+}
+
 } // namespace GiNaC
diff --git a/ginac/tensor.h b/ginac/tensor.h
index 9c4d2c36..b8a65455 100644
--- a/ginac/tensor.h
+++ b/ginac/tensor.h
@@ -104,9 +104,19 @@ class tensepsilon : public tensor
 {
 	GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
 
+	// other constructors
+public:
+	tensepsilon(bool minkowski, bool pos_sig);
+
 	// functions overriding virtual functions from bases classes
 public:
 	void print(std::ostream & os, unsigned upper_precedence=0) const;
+	ex eval_indexed(const basic & i) 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. */
 };
 
 
@@ -145,14 +155,34 @@ ex metric_tensor(const ex & i1, const ex & i2);
  *  @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 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__