- dirac_trace() handles arbitrary expressions (even unexpanded), including
[ginac.git] / ginac / tensor.cpp
index 28b520f1bc57242c716b1d8369f17e0b3b8e34e7..d16bbfce4b7949b85359f926767673c5f66c839f 100644 (file)
  */
 
 #include <stdexcept>
+#include <vector>
 
 #include "tensor.h"
 #include "idx.h"
 #include "indexed.h"
 #include "relational.h"
+#include "lst.h"
 #include "numeric.h"
+#include "print.h"
 #include "archive.h"
 #include "utils.h"
 #include "debugmsg.h"
@@ -43,21 +46,6 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor)
 // default constructor, destructor, copy constructor assignment operator and helpers
 //////////
 
-#define DEFAULT_CTORS(classname) \
-classname::classname() : inherited(TINFO_##classname) \
-{ \
-       debugmsg(#classname " default constructor", LOGLEVEL_CONSTRUCT); \
-} \
-void classname::copy(const classname & other) \
-{ \
-       inherited::copy(other); \
-} \
-void classname::destroy(bool call_parent) \
-{ \
-       if (call_parent) \
-               inherited::destroy(call_parent); \
-}
-
 tensor::tensor(unsigned ti) : inherited(ti)
 {
        debugmsg("tensor constructor from unsigned", LOGLEVEL_CONSTRUCT); \
@@ -66,7 +54,8 @@ 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)
 {
@@ -86,34 +75,34 @@ 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_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); \
-} \
-void classname::archive(archive_node &n) const \
-{ \
-       inherited::archive(n); \
-}
-
 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 +110,23 @@ 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);
 }
 
@@ -136,17 +134,9 @@ void minkmetric::archive(archive_node &n) const
 // functions overriding virtual functions from bases classes
 //////////
 
-#define DEFAULT_COMPARE(classname) \
-int classname::compare_same_type(const basic & other) const \
-{ \
-       /* by default, two tensors of the same class are always identical */ \
-       return 0; \
-}
-
 DEFAULT_COMPARE(tensor)
 DEFAULT_COMPARE(tensdelta)
 DEFAULT_COMPARE(tensmetric)
-DEFAULT_COMPARE(tensepsilon)
 
 int minkmetric::compare_same_type(const basic & other) const
 {
@@ -159,29 +149,23 @@ int minkmetric::compare_same_type(const basic & other) const
                return inherited::compare_same_type(other);
 }
 
-void tensdelta::print(std::ostream & os, unsigned upper_precedence) const
+int tensepsilon::compare_same_type(const basic & other) const
 {
-       debugmsg("tensdelta print",LOGLEVEL_PRINT);
-       os << "delta";
-}
+       GINAC_ASSERT(is_of_type(other, tensepsilon));
+       const tensepsilon &o = static_cast<const tensepsilon &>(other);
 
-void tensmetric::print(std::ostream & os, unsigned upper_precedence) const
-{
-       debugmsg("tensmetric print",LOGLEVEL_PRINT);
-       os << "g";
-}
-
-void minkmetric::print(std::ostream & os, unsigned upper_precedence) const
-{
-       debugmsg("minkmetric print",LOGLEVEL_PRINT);
-       os << "eta";
+       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 tensepsilon::print(std::ostream & os, unsigned upper_precedence) const
-{
-       debugmsg("tensepsilon print",LOGLEVEL_PRINT);
-       os << "eps";
-}
+DEFAULT_PRINT(tensdelta, "delta")
+DEFAULT_PRINT(tensmetric, "g")
+DEFAULT_PRINT(minkmetric, "eta")
+DEFAULT_PRINT(tensepsilon, "eps")
 
 /** Automatic symbolic evaluation of an indexed delta tensor. */
 ex tensdelta::eval_indexed(const basic & i) const
@@ -197,6 +181,15 @@ ex tensdelta::eval_indexed(const basic & i) const
        if (is_dummy_pair(i1, i2))
                return i1.get_dim();
 
+       // Numeric evaluation
+       if (static_cast<const indexed &>(i).all_index_values_are(info_flags::integer)) {
+               int n1 = ex_to_numeric(i1.get_value()).to_int(), n2 = ex_to_numeric(i2.get_value()).to_int();
+               if (n1 == n2)
+                       return _ex1();
+               else
+                       return _ex0();
+       }
+
        // No further simplifications
        return i.hold();
 }
@@ -249,29 +242,72 @@ 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)
+               std::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(ex & self, ex & other) const
+bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
-       GINAC_ASSERT(is_ex_of_type(self, indexed));
-       GINAC_ASSERT(is_ex_of_type(other, indexed));
-       GINAC_ASSERT(self.nops() == 3);
-       GINAC_ASSERT(is_ex_of_type(self.op(0), tensdelta));
+       GINAC_ASSERT(is_ex_of_type(*self, indexed));
+       GINAC_ASSERT(is_ex_of_type(*other, indexed));
+       GINAC_ASSERT(self->nops() == 3);
+       GINAC_ASSERT(is_ex_of_type(self->op(0), tensdelta));
 
        // Try to contract first index
-       const idx *self_idx = &ex_to_idx(self.op(1));
-       const idx *free_idx = &ex_to_idx(self.op(2));
+       const idx *self_idx = &ex_to_idx(self->op(1));
+       const idx *free_idx = &ex_to_idx(self->op(2));
        bool first_index_tried = false;
 
 again:
        if (self_idx->is_symbolic()) {
-               for (int i=1; i<other.nops(); i++) {
-                       const idx &other_idx = ex_to_idx(other.op(i));
+               for (int i=1; i<other->nops(); i++) {
+                       const idx &other_idx = ex_to_idx(other->op(i));
                        if (is_dummy_pair(*self_idx, other_idx)) {
 
                                // Contraction found, remove delta tensor and substitute
                                // index in second object
-                               self = _ex1();
-                               other = other.subs(other_idx == *free_idx);
+                               *self = _ex1();
+                               *other = other->subs(other_idx == *free_idx);
                                return true;
                        }
                }
@@ -280,8 +316,8 @@ again:
        if (!first_index_tried) {
 
                // No contraction with first index found, try second index
-               self_idx = &ex_to_idx(self.op(2));
-               free_idx = &ex_to_idx(self.op(1));
+               self_idx = &ex_to_idx(self->op(2));
+               free_idx = &ex_to_idx(self->op(1));
                first_index_tried = true;
                goto again;
        }
@@ -290,33 +326,33 @@ again:
 }
 
 /** Contraction of an indexed metric tensor with something else. */
-bool tensmetric::contract_with(ex & self, ex & other) const
+bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
-       GINAC_ASSERT(is_ex_of_type(self, indexed));
-       GINAC_ASSERT(is_ex_of_type(other, indexed));
-       GINAC_ASSERT(self.nops() == 3);
-       GINAC_ASSERT(is_ex_of_type(self.op(0), tensmetric));
+       GINAC_ASSERT(is_ex_of_type(*self, indexed));
+       GINAC_ASSERT(is_ex_of_type(*other, indexed));
+       GINAC_ASSERT(self->nops() == 3);
+       GINAC_ASSERT(is_ex_of_type(self->op(0), tensmetric));
 
        // If contracting with the delta tensor, let the delta do it
        // (don't raise/lower delta indices)
-       if (is_ex_exactly_of_type(other.op(0), tensdelta))
+       if (is_ex_of_type(other->op(0), tensdelta))
                return false;
 
        // Try to contract first index
-       const idx *self_idx = &ex_to_idx(self.op(1));
-       const idx *free_idx = &ex_to_idx(self.op(2));
+       const idx *self_idx = &ex_to_idx(self->op(1));
+       const idx *free_idx = &ex_to_idx(self->op(2));
        bool first_index_tried = false;
 
 again:
        if (self_idx->is_symbolic()) {
-               for (int i=1; i<other.nops(); i++) {
-                       const idx &other_idx = ex_to_idx(other.op(i));
+               for (int i=1; i<other->nops(); i++) {
+                       const idx &other_idx = ex_to_idx(other->op(i));
                        if (is_dummy_pair(*self_idx, other_idx)) {
 
                                // Contraction found, remove metric tensor and substitute
                                // index in second object
-                               self = _ex1();
-                               other = other.subs(other_idx == *free_idx);
+                               *self = _ex1();
+                               *other = other->subs(other_idx == *free_idx);
                                return true;
                        }
                }
@@ -325,8 +361,8 @@ again:
        if (!first_index_tried) {
 
                // No contraction with first index found, try second index
-               self_idx = &ex_to_idx(self.op(2));
-               free_idx = &ex_to_idx(self.op(1));
+               self_idx = &ex_to_idx(self->op(2));
+               free_idx = &ex_to_idx(self->op(1));
                first_index_tried = true;
                goto again;
        }
@@ -351,7 +387,7 @@ ex metric_tensor(const ex & i1, const ex & i2)
        if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
                throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
 
-       return indexed(tensmetric(), i1, i2);
+       return indexed(tensmetric(), indexed::symmetric, i1, i2);
 }
 
 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig)
@@ -366,10 +402,54 @@ 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);
+}
+
+ex eps0123(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 epsilon tensor must be of type varidx"));
+
+       ex dim = ex_to_idx(i1).get_dim();
+       if (dim.is_equal(4))
+               return lorentz_eps(i1, i2, i3, i4, pos_sig);
+       else
+               return indexed(tensepsilon(true, pos_sig), indexed::antisymmetric, i1, i2, i3, i4);
+}
+
 } // namespace GiNaC