* Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2006 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
print_func<print_dflt>(&clifford::do_print_dflt).
print_func<print_latex>(&clifford::do_print_latex))
+const tinfo_static_t clifford::return_type_tinfo_static[256] = {{}};
+
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracone, tensor,
print_func<print_dflt>(&diracone::do_print).
print_func<print_latex>(&diracone::do_print_latex))
// 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()), anticommuting(false)
+clifford::clifford() : representation_label(0), metric(0), commutator_sign(-1)
{
- tinfo_key = TINFO_clifford;
+ tinfo_key = &clifford::tinfo_static;
}
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, bool anticommut) : inherited(b), representation_label(rl), metric(0), anticommuting(anticommut)
+clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0), commutator_sign(-1)
{
- tinfo_key = TINFO_clifford;
+ tinfo_key = &clifford::tinfo_static;
}
/** 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, bool anticommut) : inherited(b, mu), representation_label(rl), metric(metr), anticommuting(anticommut)
+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;
+ tinfo_key = &clifford::tinfo_static;
}
-clifford::clifford(unsigned char rl, const ex & metr, bool anticommut, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), anticommuting(anticommut)
+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;
+ tinfo_key = &clifford::tinfo_static;
}
-clifford::clifford(unsigned char rl, const ex & metr, bool anticommut, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), anticommuting(anticommut)
+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;
+ tinfo_key = &clifford::tinfo_static;
}
//////////
n.find_unsigned("label", rl);
representation_label = rl;
n.find_ex("metric", metric, sym_lst);
- n.find_bool("anticommuting", anticommuting);
+ n.find_unsigned("commutator_sign+1", rl);
+ commutator_sign = rl - 1;
}
void clifford::archive(archive_node & n) const
inherited::archive(n);
n.add_unsigned("label", representation_label);
n.add_ex("metric", metric);
- n.add_bool("anticommuting", anticommuting);
+ n.add_unsigned("commutator_sign+1", commutator_sign+1);
}
DEFAULT_UNARCHIVE(clifford)
DEFAULT_ARCHIVING(diracgammaL)
DEFAULT_ARCHIVING(diracgammaR)
-//////////
-// functions overriding virtual functions from base classes
-//////////
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)),
+ 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 indexed(metric.op(0), ex_to<symmetry>(ex_to<indexed>(metric).get_symmetry()), i, j);
+ return metric.subs(lst(metric.op(1) == i, metric.op(2) == j), subs_options::no_pattern);
}
} else {
- // should not really happen since all constructors but clifford() make the metric an indexed object
- return indexed(metric, i, j);
+ 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);
}
}
bool clifford::same_metric(const ex & other) const
{
- if (is_a<clifford>(other)) {
- return same_metric(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;
+ 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::op(size_t i) const
+{
+ GINAC_ASSERT(i<nops());
+ if (nops()-i == 1)
+ return representation_label;
+ else
+ return inherited::op(i);
+}
+
+ex & clifford::let_op(size_t i)
+{
+ 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)
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);
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 (size_t i=0; i<v.size(); i++) {
- if (is_a<indexed>(v[i]) && !is_a<clifford>(v[i])
- && ((ex_to<varidx>(c.op(1)) == ex_to<indexed>(v[i]).get_indices()[0]
- && ex_to<varidx>(c.op(1)) == ex_to<indexed>(v[i]).get_indices()[1])
- || (ex_to<varidx>(c.op(1)).toggle_variance() == ex_to<indexed>(v[i]).get_indices()[0]
- && ex_to<varidx>(c.op(1)).toggle_variance() == ex_to<indexed>(v[i]).get_indices()[1]))) {
- return i; // the index of the found
- }
- }
- return -1; //nothing found
-}
-
/** Contraction of a Clifford unit with something else. */
bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
&& unit.same_metric(*other))
return false;
- // Find if a previous contraction produces the square of self
- int prev_square = find_same_metric(v, *self);
- const varidx d((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(self->op(1)).get_dim()),
- in1((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(self->op(1)).get_dim()),
- in2((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(self->op(1)).get_dim());
- ex squared_metric;
- if (prev_square > -1)
- squared_metric = simplify_indexed(indexed(v[prev_square].op(0), in1, d)
- * unit.get_metric(d.toggle_variance(), in2, true)).op(0);
-
exvector::iterator before_other = other - 1;
- const varidx & mu = ex_to<varidx>(self->op(1));
- const varidx & mu_toggle = ex_to<varidx>(other->op(1));
- const varidx & alpha = ex_to<varidx>(before_other->op(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 > -1) {
- *self = indexed(squared_metric, mu, mu_toggle);
- v[prev_square] = _ex1;
- } else {
- *self = unit.get_metric(mu, mu_toggle, true);
- }
+ *self = unit.get_metric(mu, mu_toggle, true);
*other = dirac_ONE(rl);
return true;
} else if (other - self == 2) {
if (is_a<clifford>(*before_other) && ex_to<clifford>(*before_other).get_representation_label() == rl) {
- if (ex_to<clifford>(*self).is_anticommuting()) {
- // e~mu e~alpha e.mu = (2*pow(e~alpha, 2) -Tr(B)) e~alpha
- if (prev_square > -1) {
- *self = 2 * indexed(squared_metric, alpha, alpha)
- - indexed(squared_metric, mu, mu_toggle);
- v[prev_square] = _ex1;
- } else {
- *self = 2 * unit.get_metric(alpha, alpha, true) - unit.get_metric(mu, mu_toggle, true);
- }
- *other = _ex1;
- return true;
-
- } else {
- // 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 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;
+
} else {
// e~mu S e.mu = Tr S ONE
*self = unit.get_metric(mu, mu_toggle, true);
ex S = ncmul(exvector(self + 1, before_other), true);
if (is_a<clifford>(*before_other) && ex_to<clifford>(*before_other).get_representation_label() == rl) {
- if (ex_to<clifford>(*self).is_anticommuting()) {
- if (prev_square > -1) {
- *self = 2 * (*before_other) * S * indexed(squared_metric, alpha, alpha)
- - (*self) * S * (*other) * (*before_other);
- } else {
- *self = 2 * (*before_other) * S * unit.get_metric(alpha, alpha, true) - (*self) * S * (*other) * (*before_other);
- }
- } else {
- *self = 2 * (*self) * S * unit.get_metric(alpha, mu_toggle, true) - (*self) * S * (*other) * (*before_other);
- }
+ *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);
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
ex clifford::thiscontainer(const exvector & v) const
{
- return clifford(representation_label, get_metric(), is_anticommuting(), v);
+ return clifford(representation_label, metric, commutator_sign, v);
}
ex clifford::thiscontainer(std::auto_ptr<exvector> vp) const
{
- return clifford(representation_label, get_metric(), is_anticommuting(), vp);
+ return clifford(representation_label, metric, commutator_sign, vp);
}
ex diracgamma5::conjugate() const
ex dirac_ONE(unsigned char rl)
{
static ex ONE = (new diracone)->setflag(status_flags::dynallocated);
- return clifford(ONE, rl, false);
+ return clifford(ONE, rl);
}
-ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl, bool anticommuting)
+ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl)
{
static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
if (!is_a<idx>(mu))
throw(std::invalid_argument("clifford_unit(): index of Clifford unit must be of type idx or varidx"));
- if (ex_to<idx>(mu).is_symbolic() && !is_a<varidx>(mu))
- throw(std::invalid_argument("clifford_unit(): symbolic index of Clifford unit must be of type varidx (not idx)"));
+ exvector indices = metr.get_free_indices();
- if (is_a<indexed>(metr)) {
- exvector indices = ex_to<indexed>(metr).get_indices();
- if ((indices.size() == 2) && is_a<varidx>(indices[0]) && is_a<varidx>(indices[1])) {
- return clifford(unit, mu, metr, rl, anticommuting);
- } else {
- throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be indexed exactly by two indices of same type as the given index"));
- }
- } else if (is_a<tensmetric>(metr)) {
- 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(unit, mu, indexed(metr, xi, chi), rl, anticommuting);
+ if ((indices.size() == 2) && is_a<varidx>(indices[0]) && is_a<varidx>(indices[1])) {
+ return clifford(unit, mu, metr, rl);
} else if (is_a<matrix>(metr)) {
matrix M = ex_to<matrix>(metr);
unsigned n = M.rows();
bool symmetric = true;
- anticommuting = true;
static varidx xi((new symbol)->setflag(status_flags::dynallocated), n),
chi((new symbol)->setflag(status_flags::dynallocated), n);
- if ((n == M.cols()) && (n == ex_to<varidx>(mu).get_dim())) {
+ if ((n == M.cols()) && (n == ex_to<idx>(mu).get_dim())) {
for (unsigned i = 0; i < n; i++) {
for (unsigned j = i+1; j < n; j++) {
if (M(i, j) != M(j, i)) {
symmetric = false;
}
- if (M(i, j) != -M(j, i)) {
- anticommuting = false;
- }
}
}
- return clifford(unit, mu, indexed(metr, symmetric?symmetric2():not_symmetric(), xi, chi), rl, anticommuting);
+ 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 {
- throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be of type indexed, tensormetric or matrix"));
- }
+ } else if (indices.size() == 0) { // a tensor or other expression without indices
+ 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(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 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(default_metric(), symmetric2(), xi, chi), rl, true);
+ 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);
+ 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);
}
/** 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)
+bool is_clifford_tinfo(tinfo_t ti)
{
- return (ti & ~0xff) == TINFO_clifford;
+ p_int start_loc=(p_int)&clifford::return_type_tinfo_static;
+ return (p_int)ti>=start_loc && (p_int)ti<start_loc+256;
}
/** 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(tinfo_t ti)
{
- return ti & 0xff;
+ return (unsigned char)((p_int)ti-(p_int)&clifford::return_type_tinfo_static);
}
/** 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, true) * 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));
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) || is_a<lst>(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("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, bool anticommuting)
+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("lst_to_clifford(): Index should have a numeric dimension"));
- ex e = clifford_unit(mu, metr, rl, anticommuting);
+ 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 = (ex_to<numeric>(ex_to<idx>(mu).get_dim())).to_int();
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;
+ return indexed(v, mu_toggle) * e;
else
throw(std::invalid_argument("lst_to_clifford(): dimensions of vector and clifford unit mismatch"));
} else
- throw(std::invalid_argument("lst_to_clifford(): 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
throw(std::invalid_argument("lst_to_clifford(): list length and dimension of clifford unit mismatch"));
} else
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)) {
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)
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
} 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;
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())
+ 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>(mu.get_dim()).to_int();
+ 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()
+ or (not is_a<numeric>(pow(c.subs(mu == i, subs_options::no_pattern), 2))))
algebraic = false;
lst V;
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))));
+ simplify_indexed(canonicalize_clifford(e * c.subs(mu == i, subs_options::no_pattern) + c.subs(mu == i, subs_options::no_pattern) * e))
+ / (2*pow(c.subs(mu == i, subs_options::no_pattern), 2))));
} else {
ex e1 = canonicalize_clifford(e);
try {
for (unsigned int i = 0; i < D; i++)
- V.append(get_clifford_comp(e1, c.subs(c.op(1) == 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(e1, true));
for (unsigned int i = 0; i < D; i++)
- V.append(get_clifford_comp(e1, c.subs(c.op(1) == i)));
+ V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern)));
}
}
return V;
}
-ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G, unsigned char rl, bool anticommuting)
+ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G, unsigned char rl)
{
ex x, D, cu;
- if (! is_a<matrix>(v) && ! is_a<lst>(v))
+ 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)) {
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, anticommuting);
+ 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, bool anticommuting)
+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, anticommuting);
+ ex_to<matrix>(M)(1,0), ex_to<matrix>(M)(1,1), v, G, rl);
else
throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a matrix"));
}
git://www.ginac.de / ginac.git / blobdiff