GINAC_IMPLEMENT_REGISTERED_CLASS(tensor, basic)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensdelta, tensor)
+GINAC_IMPLEMENT_REGISTERED_CLASS(tens4delta, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensmetric, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(minkmetric, tensmetric)
+GINAC_IMPLEMENT_REGISTERED_CLASS(mink4metric, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(spinmetric, tensmetric)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor)
DEFAULT_CTORS(tensor)
DEFAULT_CTORS(tensdelta)
+DEFAULT_CTORS(tens4delta)
DEFAULT_CTORS(tensmetric)
DEFAULT_COPY(spinmetric)
DEFAULT_DESTROY(spinmetric)
DEFAULT_DESTROY(minkmetric)
+DEFAULT_DESTROY(mink4metric)
DEFAULT_DESTROY(tensepsilon)
minkmetric::minkmetric() : pos_sig(false)
tinfo_key = TINFO_minkmetric;
}
+mink4metric::mink4metric() : pos_sig(false)
+{
+ tinfo_key = TINFO_mink4metric;
+}
+
spinmetric::spinmetric()
{
tinfo_key = TINFO_spinmetric;
tinfo_key = TINFO_minkmetric;
}
+mink4metric::mink4metric(bool ps) : pos_sig(ps)
+{
+ tinfo_key = TINFO_mink4metric;
+}
+
void minkmetric::copy(const minkmetric & other)
{
inherited::copy(other);
pos_sig = other.pos_sig;
}
-tensepsilon::tensepsilon() : minkowski(false), pos_sig(false)
+void mink4metric::copy(const mink4metric & other)
+{
+ inherited::copy(other);
+ pos_sig = other.pos_sig;
+}
+
+tensepsilon::tensepsilon() : minkowski(false), pos_sig(false), four_dim(false)
{
tinfo_key = TINFO_tensepsilon;
}
-tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps)
+tensepsilon::tensepsilon(bool mink, bool ps, bool fd) : minkowski(mink), pos_sig(ps), four_dim(fd)
{
tinfo_key = TINFO_tensepsilon;
}
inherited::copy(other);
minkowski = other.minkowski;
pos_sig = other.pos_sig;
+ four_dim = other.four_dim;
}
//////////
DEFAULT_ARCHIVING(tensor)
DEFAULT_ARCHIVING(tensdelta)
+DEFAULT_ARCHIVING(tens4delta)
DEFAULT_ARCHIVING(tensmetric)
DEFAULT_ARCHIVING(spinmetric)
DEFAULT_UNARCHIVE(minkmetric)
+DEFAULT_UNARCHIVE(mink4metric)
DEFAULT_UNARCHIVE(tensepsilon)
minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
n.add_bool("pos_sig", pos_sig);
}
+mink4metric::mink4metric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+{
+ n.find_bool("pos_sig", pos_sig);
+}
+
+void mink4metric::archive(archive_node &n) const
+{
+ inherited::archive(n);
+ n.add_bool("pos_sig", pos_sig);
+}
+
tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
n.find_bool("minkowski", minkowski);
n.find_bool("pos_sig", pos_sig);
+ n.find_bool("4dim", four_dim);
}
void tensepsilon::archive(archive_node &n) const
inherited::archive(n);
n.add_bool("minkowski", minkowski);
n.add_bool("pos_sig", pos_sig);
+ n.add_bool("4dim", four_dim);
}
//////////
DEFAULT_COMPARE(tensor)
DEFAULT_COMPARE(tensdelta)
+DEFAULT_COMPARE(tens4delta)
DEFAULT_COMPARE(tensmetric)
DEFAULT_COMPARE(spinmetric)
return inherited::compare_same_type(other);
}
+int mink4metric::compare_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_a<mink4metric>(other));
+ const mink4metric &o = static_cast<const mink4metric &>(other);
+
+ if (pos_sig != o.pos_sig)
+ return pos_sig ? -1 : 1;
+ else
+ return inherited::compare_same_type(other);
+}
+
int tensepsilon::compare_same_type(const basic & other) const
{
GINAC_ASSERT(is_a<tensepsilon>(other));
return minkowski ? -1 : 1;
else if (pos_sig != o.pos_sig)
return pos_sig ? -1 : 1;
+ else if (four_dim != o.four_dim)
+ return four_dim ? -1 : 1;
else
return inherited::compare_same_type(other);
}
DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta")
+DEFAULT_PRINT_LATEX(tens4delta, "delta4", "{\\delta^{(4)}}")
DEFAULT_PRINT(tensmetric, "g")
DEFAULT_PRINT_LATEX(minkmetric, "eta", "\\eta")
+DEFAULT_PRINT_LATEX(mink4metric, "eta4", "{\\eta^{(4)}}")
DEFAULT_PRINT_LATEX(spinmetric, "eps", "\\varepsilon")
DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\varepsilon")
return i.hold();
}
+/** Automatic symbolic evaluation of an indexed 4-dimensional delta tensor. */
+ex tens4delta::eval_indexed(const basic & i) const
+{
+ GINAC_ASSERT(is_a<indexed>(i));
+ GINAC_ASSERT(i.nops() == 3);
+ GINAC_ASSERT(is_a<tens4delta>(i.op(0)));
+
+ const idx & i1 = ex_to<idx>(i.op(1));
+ const idx & i2 = ex_to<idx>(i.op(2));
+
+ // Trace of 4-dimensional delta tensor is four
+ if (is_dummy_pair(i1, i2))
+ return _ex4;
+
+ // 4-dimensional delta tensor with numeric index dimension of four or
+ // less gets replaced by ordinary delta tensor
+ if (i1.get_dim().is_equal(i2.get_dim()) && is_a<numeric>(i1.get_dim())
+ && ex_to<numeric>(i1.get_dim()).to_int() <= 4)
+ return indexed(tensdelta(), sy_symm(), i.op(1), i.op(2));
+
+ // 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 && n1 < 4)
+ return _ex1;
+ else
+ return _ex0;
+ }
+
+ // No further simplifications
+ return i.hold();
+}
+
/** Automatic symbolic evaluation of an indexed metric tensor. */
ex tensmetric::eval_indexed(const basic & i) const
{
return inherited::eval_indexed(i);
}
+/** Automatic symbolic evaluation of an indexed 4-dimensional Lorentz metric
+ * tensor. */
+ex mink4metric::eval_indexed(const basic & i) const
+{
+ GINAC_ASSERT(is_a<indexed>(i));
+ GINAC_ASSERT(i.nops() == 3);
+ GINAC_ASSERT(is_a<mink4metric>(i.op(0)));
+ GINAC_ASSERT(is_a<varidx>(i.op(1)));
+ GINAC_ASSERT(is_a<varidx>(i.op(2)));
+
+ const varidx & i1 = ex_to<varidx>(i.op(1));
+ const varidx & i2 = ex_to<varidx>(i.op(2));
+
+ // 4-dimensional Lorentz metric tensor with numeric index dimension of
+ // four or less gets replaced by ordinary Lorentz metric tensor
+ if (i1.get_dim().is_equal(i2.get_dim()) && is_a<numeric>(i1.get_dim())
+ && ex_to<numeric>(i1.get_dim()).to_int() <= 4)
+ return indexed(minkmetric(pos_sig), sy_symm(), i.op(1), i.op(2));
+
+ // A metric tensor with one covariant and one contravariant index gets
+ // replaced by a delta tensor
+ if (i1.is_covariant() != i2.is_covariant())
+ return indexed(tens4delta(), sy_symm(), i.op(1), i.op(2));
+
+ // Numeric evaluation
+ if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
+ int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
+ if (n1 != n2 || n1 > 3)
+ return _ex0;
+ else if (n1 == 0)
+ return pos_sig ? _ex_1 : _ex1;
+ else
+ return pos_sig ? _ex1 : _ex_1;
+ }
+
+ // No further simplifications
+ return i.hold();
+}
+
/** Automatic symbolic evaluation of an indexed metric tensor. */
ex spinmetric::eval_indexed(const basic & i) const
{
return false;
}
+/** Contraction of an indexed 4-dimensional delta tensor with something else. */
+bool tens4delta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+ GINAC_ASSERT(is_a<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(self->nops() == 3);
+ GINAC_ASSERT(is_a<tens4delta>(self->op(0)));
+
+ // Only contract with 4-dimensional delta, metric and epsilon tensors
+ if (!(is_a<tens4delta>(other->op(0)) || is_a<mink4metric>(other->op(0)) || is_a<tensepsilon>(other->op(0))))
+ 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));
+ bool first_index_tried = false;
+
+again:
+ if (self_idx->is_symbolic()) {
+ for (unsigned 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);
+ return true;
+ }
+ }
+ }
+
+ 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));
+ first_index_tried = true;
+ goto again;
+ }
+
+ return false;
+}
+
/** Contraction of an indexed metric tensor with something else. */
bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
return false;
}
+/** Contraction of an indexed 4-dimensional Lorentz metric tensor with something else. */
+bool mink4metric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+ GINAC_ASSERT(is_a<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(self->nops() == 3);
+ GINAC_ASSERT(is_a<mink4metric>(self->op(0)));
+
+ // Only contract with 4-dimensional metric and epsilon tensors
+ if (!(is_a<mink4metric>(other->op(0)) || is_a<tensepsilon>(other->op(0))))
+ 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));
+ bool first_index_tried = false;
+
+again:
+ if (self_idx->is_symbolic()) {
+ for (unsigned 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);
+ return true;
+ }
+ }
+ }
+
+ 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));
+ first_index_tried = true;
+ goto again;
+ }
+
+ return false;
+}
+
+
/** Contraction of an indexed spinor metric with something else. */
bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
if (is_exactly_a<tensepsilon>(other->op(0)) && num+1 == other->nops()) {
// Contraction of two epsilon tensors is a determinant
- ex dim = ex_to<idx>(self->op(1)).get_dim();
matrix M(num, num);
for (int i=0; i<num; i++) {
for (int j=0; j<num; j++) {
- if (minkowski)
+ if (four_dim)
+ M(i, j) = indexed(mink4metric(pos_sig), sy_symm(), self->op(i+1), other->op(j+1));
+ else if (minkowski)
M(i, j) = lorentz_g(self->op(i+1), other->op(j+1), pos_sig);
else
M(i, j) = metric_tensor(self->op(i+1), other->op(j+1));
*self = sign * M.determinant().simplify_indexed();
*other = _ex1;
return true;
-
- } else if (other->return_type() == return_types::commutative) {
-
-#if 0
- // This handles eps.i.j.k * p.j * p.k = 0
- // Maybe something like this should go to simplify_indexed() because
- // such relations are true for any antisymmetric tensors...
- exvector c;
-
- // Handle all indices of the epsilon tensor
- for (int i=0; i<num; i++) {
- ex idx = self->op(i+1);
-
- // Look whether there's a contraction with this index
- exvector::const_iterator ait, aitend = v.end();
- for (ait = v.begin(); ait != aitend; ait++) {
- if (ait == self)
- continue;
- if (is_a<indexed>(*ait) && ait->return_type() == return_types::commutative && ex_to<indexed>(*ait).has_dummy_index_for(idx) && ait->nops() == 2) {
-
- // Yes, did we already have another contraction with the same base expression?
- ex base = ait->op(0);
- if (std::find_if(c.begin(), c.end(), bind2nd(ex_is_equal(), base)) == c.end()) {
-
- // No, add the base expression to the list
- c.push_back(base);
-
- } else {
-
- // Yes, the contraction is zero
- *self = _ex0;
- *other = _ex0;
- return true;
- }
- }
- }
- }
-#endif
}
return false;
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), sy_anti(), i1, i2, i3, i4);
+ return indexed(tensepsilon(true, pos_sig, false), sy_anti(), i1, i2, i3, i4);
}
ex eps0123(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
if (dim.is_equal(4))
return lorentz_eps(i1, i2, i3, i4, pos_sig);
else
- return indexed(tensepsilon(true, pos_sig), sy_anti(), i1, i2, i3, i4);
+ return indexed(tensepsilon(true, pos_sig, true), sy_anti(), i1, i2, i3, i4);
}
} // namespace GiNaC
};
+/** This class represents a 4-dimensional delta tensor embedded in a
+ * higher-dimensional space. Its matrix representation is
+ * diag(1,1,1,1,0,0...). */
+class tens4delta : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(tens4delta, tensor)
+
+ // functions overriding virtual functions from base classes
+public:
+ void print(const print_context & c, unsigned level = 0) const;
+ ex eval_indexed(const basic & i) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+};
+
+
+/** This class represents a 4-dimensional Minkowski tensor embedded in
+ * a higher-dimensional space (so it's not really a metric for that space;
+ * that's why this is not a subclass of tensmetric). Its matrix representation
+ * is diag(1,-1,-1,-1,0,0,...) or diag(-1,1,1,1,0,0,...). */
+class mink4metric : public tensor
+{
+ GINAC_DECLARE_REGISTERED_CLASS(mink4metric, tensor)
+
+ // other constructors
+public:
+ /** Construct Lorentz metric tensor with given signature. */
+ mink4metric(bool pos_sig);
+
+ // functions overriding virtual functions from base classes
+public:
+ void print(const print_context & c, unsigned level = 0) const;
+ ex eval_indexed(const basic & i) const;
+ bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
+
+ // member variables
+private:
+ bool pos_sig; /**< If true, the metric is diag(-1,1,...). Otherwise it is diag(1,-1,...). */
+};
+
+
/** 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. */
// other constructors
public:
- tensepsilon(bool minkowski, bool pos_sig);
+ tensepsilon(bool minkowski, bool pos_sig, bool four_dim);
// functions overriding virtual functions from base classes
public:
// 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. */
+ 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. */
+ bool four_dim; /**< If true, this is a four-dimensional object embedded in a higher-dimensional space */
};
git://www.ginac.de / ginac.git / commitdiff