* Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2015 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include "clifford.h"
#include "archive.h"
#include "utils.h"
+#include <stdexcept>
+
namespace GiNaC {
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(clifford, indexed,
// default constructors
//////////
-static ex default_metric()
-{
- static ex m = (new minkmetric)->setflag(status_flags::dynallocated);
- return m;
-}
-
-clifford::clifford() : representation_label(0), metric(default_metric())
+clifford::clifford() : representation_label(0), metric(0), commutator_sign(-1)
{
- tinfo_key = TINFO_clifford;
}
DEFAULT_CTOR(diracone)
/** Construct object without any indices. This constructor is for internal
* use only. Use the dirac_ONE() function instead.
* @see dirac_ONE */
-clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0)
+clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0), commutator_sign(-1)
{
- tinfo_key = TINFO_clifford;
}
/** Construct object with one Lorentz index. This constructor is for internal
* use only. Use the clifford_unit() or dirac_gamma() functions instead.
* @see clifford_unit
* @see dirac_gamma */
-clifford::clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl) : inherited(b, mu), representation_label(rl), metric(metr)
+clifford::clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl, int comm_sign) : inherited(b, mu), representation_label(rl), metric(metr), commutator_sign(comm_sign)
{
- GINAC_ASSERT(is_a<varidx>(mu));
- tinfo_key = TINFO_clifford;
+ GINAC_ASSERT(is_a<idx>(mu));
}
-clifford::clifford(unsigned char rl, const ex & metr, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr)
+clifford::clifford(unsigned char rl, const ex & metr, int comm_sign, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), commutator_sign(comm_sign)
{
- tinfo_key = TINFO_clifford;
}
-clifford::clifford(unsigned char rl, const ex & metr, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr)
+clifford::clifford(unsigned char rl, const ex & metr, int comm_sign, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), commutator_sign(comm_sign)
{
- tinfo_key = TINFO_clifford;
+}
+
+return_type_t clifford::return_type_tinfo() const
+{
+ return make_return_type_t<clifford>(representation_label);
}
//////////
// archiving
//////////
-clifford::clifford(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+void clifford::read_archive(const archive_node& n, lst& sym_lst)
{
+ inherited::read_archive(n, sym_lst);
unsigned rl;
n.find_unsigned("label", rl);
representation_label = rl;
n.find_ex("metric", metric, sym_lst);
+ n.find_unsigned("commutator_sign+1", rl);
+ commutator_sign = rl - 1;
}
-void clifford::archive(archive_node &n) const
+void clifford::archive(archive_node & n) const
{
inherited::archive(n);
n.add_unsigned("label", representation_label);
n.add_ex("metric", metric);
+ n.add_unsigned("commutator_sign+1", commutator_sign+1);
+}
+
+GINAC_BIND_UNARCHIVER(clifford);
+GINAC_BIND_UNARCHIVER(cliffordunit);
+GINAC_BIND_UNARCHIVER(diracone);
+GINAC_BIND_UNARCHIVER(diracgamma);
+GINAC_BIND_UNARCHIVER(diracgamma5);
+GINAC_BIND_UNARCHIVER(diracgammaL);
+GINAC_BIND_UNARCHIVER(diracgammaR);
+
+
+ex clifford::get_metric(const ex & i, const ex & j, bool symmetrised) const
+{
+ if (is_a<indexed>(metric)) {
+ if (symmetrised && !(ex_to<symmetry>(ex_to<indexed>(metric).get_symmetry()).has_symmetry())) {
+ if (is_a<matrix>(metric.op(0))) {
+ return indexed((ex_to<matrix>(metric.op(0)).add(ex_to<matrix>(metric.op(0)).transpose())).mul(numeric(1, 2)),
+ symmetric2(), i, j);
+ } else {
+ return simplify_indexed(indexed(metric.op(0)*_ex1_2, i, j) + indexed(metric.op(0)*_ex1_2, j, i));
+ }
+ } else {
+ return metric.subs(lst(metric.op(1) == i, metric.op(2) == j), subs_options::no_pattern);
+ }
+ } else {
+ exvector indices = metric.get_free_indices();
+ if (symmetrised)
+ return _ex1_2*simplify_indexed(metric.subs(lst(indices[0] == i, indices[1] == j), subs_options::no_pattern)
+ + metric.subs(lst(indices[0] == j, indices[1] == i), subs_options::no_pattern));
+ else
+ return metric.subs(lst(indices[0] == i, indices[1] == j), subs_options::no_pattern);
+ }
}
-DEFAULT_UNARCHIVE(clifford)
-DEFAULT_ARCHIVING(diracone)
-DEFAULT_ARCHIVING(cliffordunit)
-DEFAULT_ARCHIVING(diracgamma)
-DEFAULT_ARCHIVING(diracgamma5)
-DEFAULT_ARCHIVING(diracgammaL)
-DEFAULT_ARCHIVING(diracgammaR)
+bool clifford::same_metric(const ex & other) const
+{
+ ex metr;
+ if (is_a<clifford>(other))
+ metr = ex_to<clifford>(other).get_metric();
+ else
+ metr = other;
+
+ if (is_a<indexed>(metr))
+ return metr.op(0).is_equal(get_metric().op(0));
+ else {
+ exvector indices = metr.get_free_indices();
+ return (indices.size() == 2)
+ && simplify_indexed(get_metric(indices[0], indices[1])-metr).is_zero();
+ }
+}
//////////
// functions overriding virtual functions from base classes
//////////
-ex clifford::get_metric(const ex & i, const ex & j) const
+ex clifford::op(size_t i) const
{
- return indexed(metric, i, j);
+ GINAC_ASSERT(i<nops());
+ if (nops()-i == 1)
+ return representation_label;
+ else
+ return inherited::op(i);
}
-bool clifford::same_metric(const ex & other) const
+ex & clifford::let_op(size_t i)
{
- if (is_a<clifford>(other)) {
- return get_metric().is_equal(ex_to<clifford>(other).get_metric());
- } else if (is_a<indexed>(other)) {
- return get_metric(other.op(1), other.op(2)).is_equal(other);
- } else
- return false;
+ GINAC_ASSERT(i<nops());
+
+ static ex rl = numeric(representation_label);
+ ensure_if_modifiable();
+ if (nops()-i == 1)
+ return rl;
+ else
+ return inherited::let_op(i);
+}
+
+ex clifford::subs(const exmap & m, unsigned options) const
+{
+ ex subsed = inherited::subs(m, options);
+ if(is_a<clifford>(subsed)) {
+ ex prevmetric = ex_to<clifford>(subsed).metric;
+ ex newmetric = prevmetric.subs(m, options);
+ if(!are_ex_trivially_equal(prevmetric, newmetric)) {
+ clifford c = ex_to<clifford>(subsed);
+ c.metric = newmetric;
+ subsed = c;
+ }
+ }
+ return subsed;
}
int clifford::compare_same_type(const basic & other) const
GINAC_ASSERT(is_a<clifford>(other));
const clifford &o = static_cast<const clifford &>(other);
- return (representation_label == o.representation_label) && same_metric(o);
+ return ((representation_label == o.representation_label) && (commutator_sign == o.get_commutator_sign()) && same_metric(o));
}
static bool is_dirac_slash(const ex & seq0)
if (is_dirac_slash(seq[0])) {
seq[0].print(c, precedence());
c.s << "\\";
- } else
- this->print_dispatch<inherited>(c, level);
+ } else { // We do not print representation label if it is 0
+ if (representation_label == 0) {
+ this->print_dispatch<inherited>(c, level);
+ } else { // otherwise we put it before indices in square brackets; the code is borrowed from indexed.cpp
+ if (precedence() <= level) {
+ c.s << '(';
+ }
+ seq[0].print(c, precedence());
+ c.s << '[' << int(representation_label) << ']';
+ printindices(c, level);
+ if (precedence() <= level) {
+ c.s << ')';
+ }
+ }
+ }
}
void clifford::do_print_latex(const print_latex & c, unsigned level) const
static void base_and_index(const ex & c, ex & b, ex & i)
{
GINAC_ASSERT(is_a<clifford>(c));
- GINAC_ASSERT(c.nops() == 2);
+ GINAC_ASSERT(c.nops() == 2+1);
if (is_a<cliffordunit>(c.op(0))) { // proper dirac gamma object or clifford unit
i = c.op(1);
if (is_a<clifford>(*other)) {
- // Contraction only makes sense if the represenation labels are equal
+ // Contraction only makes sense if the representation labels are equal
if (ex_to<clifford>(*other).get_representation_label() != rl)
return false;
return false;
}
-/** An utility function looking for a given metric within an exvector,
- * used in cliffordunit::contract_with(). */
-static int find_same_metric(exvector & v, ex & c)
-{
- for (int i=0; i<v.size();i++) {
- if (!is_a<clifford>(v[i]) && is_a<indexed>(v[i])
- && ex_to<clifford>(c).same_metric(v[i])
- && (ex_to<varidx>(c.op(1)) == ex_to<indexed>(v[i]).get_indices()[0]
- || ex_to<varidx>(c.op(1)).toggle_variance() == ex_to<indexed>(v[i]).get_indices()[0])) {
- return ++i; // next to found
- }
- }
- return 0; //nothing found
-}
-
/** Contraction of a Clifford unit with something else. */
bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
unsigned char rl = unit.get_representation_label();
if (is_a<clifford>(*other)) {
- // Contraction only makes sense if the represenation labels are equal
+ // Contraction only makes sense if the representation labels are equal
// and the metrics are the same
if ((ex_to<clifford>(*other).get_representation_label() != rl)
&& unit.same_metric(*other))
return false;
- // Find if a previous contraction produces the square of self
- int prev_square = find_same_metric(v, self[0]);
- varidx d((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(self->op(1)).get_dim());
- ex squared_metric = unit.get_metric(self->op(1), d) * unit.get_metric(d.toggle_variance(), other->op(1));
+ exvector::iterator before_other = other - 1;
+ ex mu = self->op(1);
+ ex mu_toggle = other->op(1);
+ ex alpha = before_other->op(1);
// e~mu e.mu = Tr ONE
if (other - self == 1) {
- if (prev_square != 0) {
- *self = squared_metric;
- v[prev_square-1] = _ex1;
- } else
- *self = unit.get_metric(self->op(1), other->op(1));
+ *self = unit.get_metric(mu, mu_toggle, true);
*other = dirac_ONE(rl);
return true;
- // e~mu e~alpha e.mu = (2e~alpha^2-Tr) e~alpha
- } else if (other - self == 2
- && is_a<clifford>(self[1])) {
-
- const ex & ia = self[1].op(1);
- const ex & ib = self[1].op(1);
- if (is_a<tensmetric>(unit.get_metric()))
- *self = 2 - unit.get_metric(self->op(1), other->op(1));
- else if (prev_square != 0) {
- *self = 2-squared_metric;
- v[prev_square-1] = _ex1;
- } else
- *self = 2*unit.get_metric(ia, ib) - unit.get_metric(self->op(1), other->op(1));
- *other = _ex1;
- return true;
+ } else if (other - self == 2) {
+ if (is_a<clifford>(*before_other) && ex_to<clifford>(*before_other).get_representation_label() == rl) {
+ // e~mu e~alpha e.mu = 2*e~mu B(alpha, mu.toggle_variance())-Tr(B) e~alpha
+ *self = 2 * (*self) * unit.get_metric(alpha, mu_toggle, true) - unit.get_metric(mu, mu_toggle, true) * (*before_other);
+ *before_other = _ex1;
+ *other = _ex1;
+ return true;
- // e~mu S e~alpha e.mu = 2 e~alpha^3 S - e~mu S e.mu e~alpha
+ } else {
+ // e~mu S e.mu = Tr S ONE
+ *self = unit.get_metric(mu, mu_toggle, true);
+ *other = dirac_ONE(rl);
+ return true;
+ }
+ } else {
+ // e~mu S e~alpha e.mu = 2 e~mu S B(alpha, mu.toggle_variance()) - e~mu S e.mu e~alpha
// (commutate contracted indices towards each other, simplify_indexed()
// will re-expand and re-run the simplification)
- } else {
- exvector::iterator it = self + 1, next_to_last = other - 1;
- while (it != other) {
- if (!is_a<clifford>(*it))
- return false;
- ++it;
+ if (std::find_if(self + 1, other, is_not_a_clifford()) != other) {
+ return false;
}
+
+ ex S = ncmul(exvector(self + 1, before_other), true);
- it = self + 1;
- ex S = _ex1;
- while (it != next_to_last) {
- S *= *it;
- *it++ = _ex1;
+ if (is_a<clifford>(*before_other) && ex_to<clifford>(*before_other).get_representation_label() == rl) {
+ *self = 2 * (*self) * S * unit.get_metric(alpha, mu_toggle, true) - (*self) * S * (*other) * (*before_other);
+ } else {
+ // simply commutes
+ *self = (*self) * S * (*other) * (*before_other);
}
-
- const ex & ia = next_to_last->op(1);
- const ex & ib = next_to_last->op(1);
- if (is_a<tensmetric>(unit.get_metric()))
- *self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last);
- else if (prev_square != 0) {
- *self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last)*unit.get_metric(self->op(1),self->op(1));
- v[prev_square-1] = _ex1;
- } else
- *self = 2 * (*next_to_last) * S* unit.get_metric(ia,ib) - (*self) * S * (*other) * (*next_to_last);
- *next_to_last = _ex1;
- *other = _ex1;
+
+ std::fill(self + 1, other + 1, _ex1);
return true;
}
-
- }
-
+ }
return false;
}
bool a_is_cliffordunit = is_a<cliffordunit>(ag);
bool b_is_cliffordunit = is_a<cliffordunit>(bg);
- if (a_is_cliffordunit && b_is_cliffordunit && ex_to<clifford>(a).same_metric(b)) {
-
+ if (a_is_cliffordunit && b_is_cliffordunit && ex_to<clifford>(a).same_metric(b)
+ && (ex_to<clifford>(a).get_commutator_sign() == -1)) {
+ // This is done only for Clifford algebras
+
const ex & ia = a.op(1);
const ex & ib = b.op(1);
if (ia.is_equal(ib)) { // gamma~alpha gamma~alpha -> g~alpha~alpha
- a = ex_to<clifford>(a).get_metric(ia, ib);
+ a = ex_to<clifford>(a).get_metric(ia, ib, true);
b = dirac_ONE(representation_label);
something_changed = true;
}
}
if (s.empty())
- return clifford(diracone(), representation_label) * sign;
+ return dirac_ONE(representation_label) * sign;
if (something_changed)
return reeval_ncmul(s) * sign;
else
ex clifford::thiscontainer(const exvector & v) const
{
- return clifford(representation_label, get_metric(), v);
+ return clifford(representation_label, metric, commutator_sign, v);
}
ex clifford::thiscontainer(std::auto_ptr<exvector> vp) const
{
- return clifford(representation_label, get_metric(), vp);
+ return clifford(representation_label, metric, commutator_sign, vp);
}
ex diracgamma5::conjugate() const
return clifford(ONE, rl);
}
+static unsigned get_dim_uint(const ex& e)
+{
+ if (!is_a<idx>(e))
+ throw std::invalid_argument("get_dim_uint: argument is not an index");
+ ex dim = ex_to<idx>(e).get_dim();
+ if (!dim.info(info_flags::posint))
+ throw std::invalid_argument("get_dim_uint: dimension of index should be a positive integer");
+ unsigned d = ex_to<numeric>(dim).to_int();
+ return d;
+}
+
ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl)
{
- static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
+ //static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
+ ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
- if (!is_a<varidx>(mu))
- throw(std::invalid_argument("index of Clifford unit must be of type varidx"));
+ if (!is_a<idx>(mu))
+ throw(std::invalid_argument("clifford_unit(): index of Clifford unit must be of type idx or varidx"));
- if (is_a<indexed>(metr))
- return clifford(unit, mu, metr.op(0), rl);
- else if(is_a<tensmetric>(metr) || is_a<matrix>(metr))
+ exvector indices = metr.get_free_indices();
+
+ if (indices.size() == 2) {
return clifford(unit, mu, metr, rl);
- else
- throw(std::invalid_argument("metric for Clifford unit must be of type indexed, tensormetric or matrix"));
+ } else if (is_a<matrix>(metr)) {
+ matrix M = ex_to<matrix>(metr);
+ unsigned n = M.rows();
+ bool symmetric = true;
+
+ //static idx xi((new symbol)->setflag(status_flags::dynallocated), n),
+ // chi((new symbol)->setflag(status_flags::dynallocated), n);
+ idx xi((new symbol)->setflag(status_flags::dynallocated), n),
+ chi((new symbol)->setflag(status_flags::dynallocated), n);
+ if ((n == M.cols()) && (n == get_dim_uint(mu))) {
+ for (unsigned i = 0; i < n; i++) {
+ for (unsigned j = i+1; j < n; j++) {
+ if (!M(i, j).is_equal(M(j, i))) {
+ symmetric = false;
+ }
+ }
+ }
+ return clifford(unit, mu, indexed(metr, symmetric?symmetric2():not_symmetric(), xi, chi), rl);
+ } else {
+ throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be a square matrix with the same dimensions as index"));
+ }
+ } else if (indices.size() == 0) { // a tensor or other expression without indices
+ //static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim()),
+ // chi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim());
+ varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim()),
+ chi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim());
+ return clifford(unit, mu, indexed(metr, xi, chi), rl);
+ } else
+ throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be of type tensor, matrix or an expression with two free indices"));
}
ex dirac_gamma(const ex & mu, unsigned char rl)
static ex gamma = (new diracgamma)->setflag(status_flags::dynallocated);
if (!is_a<varidx>(mu))
- throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
+ throw(std::invalid_argument("dirac_gamma(): index of Dirac gamma must be of type varidx"));
- return clifford(gamma, mu, default_metric(), rl);
+ static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<varidx>(mu).get_dim()),
+ chi((new symbol)->setflag(status_flags::dynallocated), ex_to<varidx>(mu).get_dim());
+ return clifford(gamma, mu, indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl);
}
ex dirac_gamma5(unsigned char rl)
// Slashed vectors are actually stored as a clifford object with the
// vector as its base expression and a (dummy) index that just serves
// for storing the space dimensionality
- return clifford(e, varidx(0, dim), default_metric(), rl);
-}
-/** Check whether a given tinfo key (as returned by return_type_tinfo()
- * is that of a clifford object with the specified representation label. */
-static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
-{
- return ti == (TINFO_clifford + rl);
-}
-
-/** Check whether a given tinfo key (as returned by return_type_tinfo()
- * is that of a clifford object (with an arbitrary representation label). */
-static bool is_clifford_tinfo(unsigned ti)
-{
- return (ti & ~0xff) == TINFO_clifford;
+ static varidx xi((new symbol)->setflag(status_flags::dynallocated), dim),
+ chi((new symbol)->setflag(status_flags::dynallocated), dim);
+ return clifford(e, varidx(0, dim), indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl);
}
/** Extract representation label from tinfo key (as returned by
* return_type_tinfo()). */
-static unsigned char get_representation_label(unsigned ti)
+static unsigned char get_representation_label(const return_type_t& ti)
{
- return ti & 0xff;
+ return (unsigned char)ti.rl;
}
/** Take trace of a string of an even number of Dirac gammas given a vector
pointer_to_map_function fcn(canonicalize_clifford);
if (is_a<matrix>(e_) // || is_a<pseries>(e) || is_a<integral>(e)
- || is_a<lst>(e_)) {
+ || e_.info(info_flags::list)) {
return e_.map(fcn);
} else {
ex e=simplify_indexed(e_);
exvector::iterator it = v.begin(), next_to_last = v.end() - 1;
if (is_a<diracgamma5>(it->op(0)) || is_a<diracgammaL>(it->op(0)) || is_a<diracgammaR>(it->op(0)))
++it;
+
while (it != next_to_last) {
if (it[0].compare(it[1]) > 0) {
+
ex save0 = it[0], save1 = it[1];
ex b1, i1, b2, i2;
base_and_index(it[0], b1, i1);
base_and_index(it[1], b2, i2);
- it[0] = (ex_to<clifford>(save0).get_metric(i1, i2) * b1 * b2).simplify_indexed();
- it[1] = v.size() == 2 ? _ex2 * dirac_ONE(ex_to<clifford>(it[1]).get_representation_label()) : _ex2;
+ // for Clifford algebras (commutator_sign == -1) metric should be symmetrised
+ it[0] = (ex_to<clifford>(save0).get_metric(i1, i2, ex_to<clifford>(save0).get_commutator_sign() == -1) * b1 * b2).simplify_indexed();
+ it[1] = v.size() ? _ex2 * dirac_ONE(ex_to<clifford>(save0).get_representation_label()) : _ex2;
ex sum = ncmul(v);
it[0] = save1;
it[1] = save0;
- sum -= ncmul(v, true);
+ sum += ex_to<clifford>(save0).get_commutator_sign() * ncmul(v, true);
i->second = canonicalize_clifford(sum);
goto next_sym;
}
if (is_a<clifford>(e) && is_a<cliffordunit>(e.op(0))) {
return -e;
} else if (is_a<add>(e) || is_a<ncmul>(e) || is_a<mul>(e) //|| is_a<pseries>(e) || is_a<integral>(e)
- || is_a<matrix>(e) || is_a<lst>(e)) {
+ || is_a<matrix>(e) || e.info(info_flags::list)) {
return e.map(fcn);
} else if (is_a<power>(e)) {
return pow(clifford_prime(e.op(0)), e.op(1));
return e;
}
-ex remove_dirac_ONE(const ex & e, unsigned char rl)
+ex remove_dirac_ONE(const ex & e, unsigned char rl, unsigned options)
{
- pointer_to_map_function_1arg<unsigned char> fcn(remove_dirac_ONE, rl);
- if (is_a<clifford>(e) && ex_to<clifford>(e).get_representation_label() >= rl) {
- if (is_a<diracone>(e.op(0)))
+ pointer_to_map_function_2args<unsigned char, unsigned> fcn(remove_dirac_ONE, rl, options | 1);
+ bool need_reevaluation = false;
+ ex e1 = e;
+ if (! (options & 1) ) { // is not a child
+ if (options & 2)
+ e1 = expand_dummy_sum(e, true);
+ e1 = canonicalize_clifford(e1);
+ }
+
+ if (is_a<clifford>(e1) && ex_to<clifford>(e1).get_representation_label() >= rl) {
+ if (is_a<diracone>(e1.op(0)))
return 1;
+ else
+ throw(std::invalid_argument("remove_dirac_ONE(): expression is a non-scalar Clifford number!"));
+ } else if (is_a<add>(e1) || is_a<ncmul>(e1) || is_a<mul>(e1)
+ || is_a<matrix>(e1) || e1.info(info_flags::list)) {
+ if (options & 3) // is a child or was already expanded
+ return e1.map(fcn);
else
- throw(std::invalid_argument("Expression is a non-scalar Clifford number!"));
- } else if (is_a<add>(e) || is_a<ncmul>(e) || is_a<mul>(e) // || is_a<pseries>(e) || is_a<integral>(e)
- || is_a<matrix>(e) || is_a<lst>(e)) {
- return e.map(fcn);
- } else if (is_a<power>(e)) {
- return pow(remove_dirac_ONE(e.op(0)), e.op(1));
- } else
- return e;
+ try {
+ return e1.map(fcn);
+ } catch (std::exception &p) {
+ need_reevaluation = true;
+ }
+ } else if (is_a<power>(e1)) {
+ if (options & 3) // is a child or was already expanded
+ return pow(remove_dirac_ONE(e1.op(0), rl, options | 1), e1.op(1));
+ else
+ try {
+ return pow(remove_dirac_ONE(e1.op(0), rl, options | 1), e1.op(1));
+ } catch (std::exception &p) {
+ need_reevaluation = true;
+ }
+ }
+ if (need_reevaluation)
+ return remove_dirac_ONE(e, rl, options | 2);
+ return e1;
}
-ex clifford_norm(const ex & e)
+int clifford_max_label(const ex & e, bool ignore_ONE)
{
- return sqrt(remove_dirac_ONE(canonicalize_clifford(e * clifford_bar(e)).simplify_indexed()));
+ if (is_a<clifford>(e))
+ if (ignore_ONE && is_a<diracone>(e.op(0)))
+ return -1;
+ else
+ return ex_to<clifford>(e).get_representation_label();
+ else {
+ int rl = -1;
+ for (size_t i=0; i < e.nops(); i++)
+ rl = (rl > clifford_max_label(e.op(i), ignore_ONE)) ? rl : clifford_max_label(e.op(i), ignore_ONE);
+ return rl;
+ }
}
+ex clifford_norm(const ex & e)
+{
+ return sqrt(remove_dirac_ONE(e * clifford_bar(e)));
+}
+
ex clifford_inverse(const ex & e)
{
ex norm = clifford_norm(e);
if (!norm.is_zero())
return clifford_bar(e) / pow(norm, 2);
else
- throw(std::invalid_argument("Cannot find inverse of Clifford number with zero norm!"));
+ throw(std::invalid_argument("clifford_inverse(): cannot find inverse of Clifford number with zero norm!"));
}
ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl)
{
if (!ex_to<idx>(mu).is_dim_numeric())
- throw(std::invalid_argument("Index should have a numeric dimension"));
+ throw(std::invalid_argument("lst_to_clifford(): Index should have a numeric dimension"));
ex e = clifford_unit(mu, metr, rl);
return lst_to_clifford(v, e);
}
unsigned min, max;
if (is_a<clifford>(e)) {
- varidx mu = ex_to<varidx>(e.op(1));
- unsigned dim = (ex_to<numeric>(mu.get_dim())).to_int();
+ ex mu = e.op(1);
+ ex mu_toggle
+ = is_a<varidx>(mu) ? ex_to<varidx>(mu).toggle_variance() : mu;
+ unsigned dim = get_dim_uint(mu);
if (is_a<matrix>(v)) {
if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) {
}
if (min == 1) {
if (dim == max)
- return indexed(v, ex_to<varidx>(mu).toggle_variance()) * e;
- else
- throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch"));
+ return indexed(v, mu_toggle) * e;
+ else if (max - dim == 1) {
+ if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows())
+ return v.op(0) * dirac_ONE(ex_to<clifford>(e).get_representation_label()) + indexed(sub_matrix(ex_to<matrix>(v), 0, 1, 1, dim), mu_toggle) * e;
+ else
+ return v.op(0) * dirac_ONE(ex_to<clifford>(e).get_representation_label()) + indexed(sub_matrix(ex_to<matrix>(v), 1, dim, 0, 1), mu_toggle) * e;
+ } else
+ throw(std::invalid_argument("lst_to_clifford(): dimensions of vector and clifford unit mismatch"));
} else
- throw(std::invalid_argument("First argument should be a vector vector"));
- } else if (is_a<lst>(v)) {
+ throw(std::invalid_argument("lst_to_clifford(): first argument should be a vector (nx1 or 1xn matrix)"));
+ } else if (v.info(info_flags::list)) {
if (dim == ex_to<lst>(v).nops())
- return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * e;
+ return indexed(matrix(dim, 1, ex_to<lst>(v)), mu_toggle) * e;
+ else if (ex_to<lst>(v).nops() - dim == 1)
+ return v.op(0) * dirac_ONE(ex_to<clifford>(e).get_representation_label()) + indexed(sub_matrix(matrix(dim+1, 1, ex_to<lst>(v)), 1, dim, 0, 1), mu_toggle) * e;
else
- throw(std::invalid_argument("List length and dimension of clifford unit mismatch"));
+ throw(std::invalid_argument("lst_to_clifford(): list length and dimension of clifford unit mismatch"));
} else
- throw(std::invalid_argument("Cannot construct from anything but list or vector"));
+ throw(std::invalid_argument("lst_to_clifford(): cannot construct from anything but list or vector"));
} else
- throw(std::invalid_argument("The second argument should be a Clifford unit"));
+ throw(std::invalid_argument("lst_to_clifford(): the second argument should be a Clifford unit"));
}
-
+
/** Auxiliary structure to define a function for striping one Clifford unit
* from vectors. Used in clifford_to_lst(). */
static ex get_clifford_comp(const ex & e, const ex & c)
{
pointer_to_map_function_1arg<const ex &> fcn(get_clifford_comp, c);
- int ival = ex_to<numeric>(ex_to<varidx>(c.op(1)).get_value()).to_int();
+ int ival = ex_to<numeric>(ex_to<idx>(c.op(1)).get_value()).to_int();
- if (is_a<add>(e) ||
is_a<lst>(e) // || is_a<pseries>(e) || is_a<integral>(e)
+ if (is_a<add>(e) ||
e.info(info_flags::list) // || is_a<pseries>(e) || is_a<integral>(e)
|| is_a<matrix>(e))
return e.map(fcn);
else if (is_a<ncmul>(e) || is_a<mul>(e)) {
// find a Clifford unit with the same metric, delete it and substitute its index
size_t ind = e.nops() + 1;
- for (size_t j = 0; j < e.nops(); j++)
- if (is_a<clifford>(e.op(j)) && ex_to<clifford>(c).same_metric(e.op(j)))
- if (ind > e.nops())
+ for (size_t j = 0; j < e.nops(); j++) {
+ if (is_a<clifford>(e.op(j)) && ex_to<clifford>(c).same_metric(e.op(j))) {
+ if (ind > e.nops()) {
ind = j;
- else
- throw(std::invalid_argument("Expression is a Clifford multi-vector"));
+ } else {
+ throw(std::invalid_argument("get_clifford_comp(): expression is a Clifford multi-vector"));
+ }
+ }
+ }
if (ind < e.nops()) {
ex S = 1;
bool same_value_index, found_dummy;
- same_value_index = ( ex_to<varidx>(e.op(ind).op(1)).is_numeric()
- && (ival == ex_to<numeric>(ex_to<varidx>(e.op(ind).op(1)).get_value()).to_int()) );
+ same_value_index = ( ex_to<idx>(e.op(ind).op(1)).is_numeric()
+ && (ival == ex_to<numeric>(ex_to<idx>(e.op(ind).op(1)).get_value()).to_int()) );
found_dummy = same_value_index;
- for(size_t j=0; j < e.nops(); j++)
- if (j != ind)
- if (same_value_index)
+ // Run through the expression collecting all non-clifford factors
+ for (size_t j=0; j < e.nops(); j++) {
+ if (j != ind) {
+ if (same_value_index) {
S = S * e.op(j);
- else {
- exvector ind_vec = ex_to<indexed>(e.op(j)).get_dummy_indices(ex_to<indexed>(e.op(ind)));
+ } else {
+ exvector ind_vec;
+ if (is_a<indexed>(e.op(j)))
+ ind_vec = ex_to<indexed>(e.op(j)).get_dummy_indices(ex_to<indexed>(e.op(ind)));
+
if (ind_vec.size() > 0) {
found_dummy = true;
exvector::const_iterator it = ind_vec.begin(), itend = ind_vec.end();
while (it != itend) {
- S = S * e.op(j).subs(lst(ex_to<varidx>(*it) == ival, ex_to<varidx>(*it).toggle_variance() == ival), subs_options::no_pattern);
+ ex curridx = *it;
+ ex curridx_toggle = is_a<varidx>(curridx)
+ ? ex_to<varidx>(curridx).toggle_variance()
+ : curridx;
+ S = S * e.op(j).subs(lst(curridx == ival,
+ curridx_toggle == ival), subs_options::no_pattern);
++it;
}
} else
S = S * e.op(j);
}
+ }
+ }
return (found_dummy ? S : 0);
} else
- throw(std::invalid_argument("Expression is not a Clifford vector to the given units"));
+ throw(std::invalid_argument("get_clifford_comp(): expression is not a Clifford vector to the given units"));
} else if (e.is_zero())
return e;
else if (is_a<clifford>(e) && ex_to<clifford>(e).same_metric(c))
- if ( ex_to<varidx>(e.op(1)).is_numeric() &&
- (ival != ex_to<numeric>(ex_to<varidx>(e.op(1)).get_value()).to_int()) )
+ if ( ex_to<idx>(e.op(1)).is_numeric() &&
+ (ival != ex_to<numeric>(ex_to<idx>(e.op(1)).get_value()).to_int()) )
return 0;
else
return 1;
else
- throw(std::invalid_argument("Expression is not usable as a Clifford vector"));
+ throw(std::invalid_argument("get_clifford_comp(): expression is not usable as a Clifford vector"));
}
lst clifford_to_lst(const ex & e, const ex & c, bool algebraic)
{
GINAC_ASSERT(is_a<clifford>(c));
- varidx mu = ex_to<varidx>(c.op(1));
- if (! mu.is_dim_numeric())
- throw(std::invalid_argument("Index should have a numeric dimension"));
- unsigned int D = ex_to<numeric>(mu.get_dim()).to_int();
+ ex mu = c.op(1);
+ if (! ex_to<idx>(mu).is_dim_numeric())
+ throw(std::invalid_argument("clifford_to_lst(): index should have a numeric dimension"));
+ unsigned int D = ex_to<numeric>(ex_to<idx>(mu).get_dim()).to_int();
if (algebraic) // check if algebraic method is applicable
for (unsigned int i = 0; i < D; i++)
- if (pow(c.subs(mu == i), 2).is_zero()
- or (not is_a<numeric>(pow(c.subs(mu == i), 2))))
+ if (pow(c.subs(mu == i, subs_options::no_pattern), 2).is_zero()
+ || (! is_a<numeric>(pow(c.subs(mu == i, subs_options::no_pattern), 2))))
algebraic = false;
lst V;
- if (algebraic)
+ ex v0 = remove_dirac_ONE(canonicalize_clifford(e+clifford_prime(e)).normal())/2;
+ if (! v0.is_zero())
+ V.append(v0);
+ ex e1 = canonicalize_clifford(e - v0 * dirac_ONE(ex_to<clifford>(c).get_representation_label()));
+ if (algebraic) {
for (unsigned int i = 0; i < D; i++)
V.append(remove_dirac_ONE(
- simplify_indexed(canonicalize_clifford(e * c.subs(mu == i) + c.subs(mu == i) * e))
- / (2*pow(c.subs(mu == i), 2))));
- else {
- ex e1 = canonicalize_clifford(e);
- for (unsigned int i = 0; i < D; i++)
- V.append(get_clifford_comp(e1, c.subs(c.op(1) == i)));
+ simplify_indexed(canonicalize_clifford(e1 * c.subs(mu == i, subs_options::no_pattern) + c.subs(mu == i, subs_options::no_pattern) * e1))
+ / (2*pow(c.subs(mu == i, subs_options::no_pattern), 2))));
+ } else {
+ try {
+ for (unsigned int i = 0; i < D; i++)
+ V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern)));
+ } catch (std::exception &p) {
+ /* Try to expand dummy summations to simplify the expression*/
+ e1 = canonicalize_clifford(expand_dummy_sum(e, true));
+ V.remove_all();
+ v0 = remove_dirac_ONE(canonicalize_clifford(e1+clifford_prime(e1)).normal())/2;
+ if (! v0.is_zero()) {
+ V.append(v0);
+ e1 = canonicalize_clifford(e1 - v0 * dirac_ONE(ex_to<clifford>(c).get_representation_label()));
+ }
+ for (unsigned int i = 0; i < D; i++)
+ V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern)));
+ }
}
return V;
}
{
ex x, D, cu;
- if (! is_a<matrix>(v) && ! is_a<lst>(v))
- throw(std::invalid_argument("parameter v should be either vector or list"));
+ if (! is_a<matrix>(v) && ! v.info(info_flags::list))
+ throw(std::invalid_argument("clifford_moebius_map(): parameter v should be either vector or list"));
if (is_a<clifford>(G)) {
cu = G;
} else {
- if (is_a<indexed>(G))
- D = ex_to<varidx>(G.op(1)).get_dim();
- else if (is_a<matrix>(G))
+ if (is_a<indexed>(G)) {
+ D = ex_to<idx>(G.op(1)).get_dim();
+ varidx mu((new symbol)->setflag(status_flags::dynallocated), D);
+ cu = clifford_unit(mu, G, rl);
+ } else if (is_a<matrix>(G)) {
D = ex_to<matrix>(G).rows();
- else throw(std::invalid_argument("metric should be an indexed object, matrix, or a Clifford unit"));
+ idx mu((new symbol)->setflag(status_flags::dynallocated), D);
+ cu = clifford_unit(mu, G, rl);
+ } else throw(std::invalid_argument("clifford_moebius_map(): metric should be an indexed object, matrix, or a Clifford unit"));
- varidx mu((new symbol)->setflag(status_flags::dynallocated), D);
- cu = clifford_unit(mu, G, rl);
}
-
+
x = lst_to_clifford(v, cu);
- ex e = simplify_indexed(canonicalize_clifford((a * x + b) * clifford_inverse(c * x + d)));
- return clifford_to_lst(e, cu, false);
+ ex e = clifford_to_lst(simplify_indexed(canonicalize_clifford((a * x + b) * clifford_inverse(c * x + d))), cu, false);
+ return (is_a<matrix>(v) ? matrix(ex_to<matrix>(v).rows(), ex_to<matrix>(v).cols(), ex_to<lst>(e)) : e);
}
ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl)
{
- if (is_a<matrix>(M))
- return clifford_moebius_map(ex_to<matrix>(M)(0,0), ex_to<matrix>(M)(0,1),
- ex_to<matrix>(M)(1,0), ex_to<matrix>(M)(1,1), v, G, rl);
+ if (is_a<matrix>(M) && (ex_to<matrix>(M).rows() == 2) && (ex_to<matrix>(M).cols() == 2))
+ return clifford_moebius_map(M.op(0), M.op(1), M.op(2), M.op(3), v, G, rl);
else
- throw(std::invalid_argument("parameter M should be a matrix"));
+ throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a 2x2 matrix"));
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff