/** Create a symbol for replacing the expression "e" (or return a previously
- * assigned symbol). The symbol is appended to sym_lst and returned, the
- * expression is appended to repl_lst.
+ * assigned symbol). The symbol and expression are appended to repl, for
+ * a later application of subs().
* @see ex::normal */
-static ex replace_with_symbol(const ex &e, lst &sym_lst, lst &repl_lst)
+static ex replace_with_symbol(const ex & e, exmap & repl)
{
- // Expression already in repl_lst? Then return the assigned symbol
- lst::const_iterator its, itr;
- for (its = sym_lst.begin(), itr = repl_lst.begin(); itr != repl_lst.end(); ++its, ++itr)
- if (itr->is_equal(e))
- return *its;
+ // Expression already in repl? Then return the assigned symbol
+ for (exmap::const_iterator it = repl.begin(); it != repl.end(); ++it)
+ if (it->second.is_equal(e))
+ return it->first;
// Otherwise create new symbol and add to list, taking care that the
- // replacement expression doesn't contain symbols from the sym_lst
+ // replacement expression doesn't itself contain symbols from repl,
// because subs() is not recursive
- symbol s;
- ex es(s);
- ex e_replaced = e.subs(sym_lst, repl_lst);
- sym_lst.append(es);
- repl_lst.append(e_replaced);
+ ex es = (new symbol)->setflag(status_flags::dynallocated);
+ ex e_replaced = e.subs(repl);
+ repl[es] = e_replaced;
return es;
}
* to repl_lst and the symbol is returned.
* @see basic::to_rational
* @see basic::to_polynomial */
-static ex replace_with_symbol(const ex &e, lst &repl_lst)
+static ex replace_with_symbol(const ex & e, lst & repl_lst)
{
// Expression already in repl_lst? Then return the assigned symbol
for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it)
return it->op(0);
// Otherwise create new symbol and add to list, taking care that the
- // replacement expression doesn't contain symbols from the sym_lst
+ // replacement expression doesn't itself contain symbols from the repl_lst,
// because subs() is not recursive
- symbol s;
- ex es(s);
+ ex es = (new symbol)->setflag(status_flags::dynallocated);
ex e_replaced = e.subs(repl_lst);
repl_lst.append(es == e_replaced);
return es;
/** Default implementation of ex::normal(). It normalizes the children and
* replaces the object with a temporary symbol.
* @see ex::normal */
-ex basic::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex basic::normal(exmap & repl, int level) const
{
if (nops() == 0)
- return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(*this, repl), _ex1))->setflag(status_flags::dynallocated);
else {
if (level == 1)
- return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(*this, repl), _ex1))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
else {
normal_map_function map_normal(level - 1);
- return (new lst(replace_with_symbol(map(map_normal), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(map(map_normal), repl), _ex1))->setflag(status_flags::dynallocated);
}
}
}
/** Implementation of ex::normal() for symbols. This returns the unmodified symbol.
* @see ex::normal */
-ex symbol::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex symbol::normal(exmap & repl, int level) const
{
return (new lst(*this, _ex1))->setflag(status_flags::dynallocated);
}
* into re+I*im and replaces I and non-rational real numbers with a temporary
* symbol.
* @see ex::normal */
-ex numeric::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex numeric::normal(exmap & repl, int level) const
{
numeric num = numer();
ex numex = num;
if (num.is_real()) {
if (!num.is_integer())
- numex = replace_with_symbol(numex, sym_lst, repl_lst);
+ numex = replace_with_symbol(numex, repl);
} else { // complex
numeric re = num.real(), im = num.imag();
- ex re_ex = re.is_rational() ? re : replace_with_symbol(re, sym_lst, repl_lst);
- ex im_ex = im.is_rational() ? im : replace_with_symbol(im, sym_lst, repl_lst);
- numex = re_ex + im_ex * replace_with_symbol(I, sym_lst, repl_lst);
+ ex re_ex = re.is_rational() ? re : replace_with_symbol(re, repl);
+ ex im_ex = im.is_rational() ? im : replace_with_symbol(im, repl);
+ numex = re_ex + im_ex * replace_with_symbol(I, repl);
}
// Denominator is always a real integer (see numeric::denom())
/** Implementation of ex::normal() for a sum. It expands terms and performs
* fractional addition.
* @see ex::normal */
-ex add::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex add::normal(exmap & repl, int level) const
{
if (level == 1)
- return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(*this, repl), _ex1))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
dens.reserve(seq.size()+1);
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- ex n = ex_to<basic>(recombine_pair_to_ex(*it)).normal(sym_lst, repl_lst, level-1);
+ ex n = ex_to<basic>(recombine_pair_to_ex(*it)).normal(repl, level-1);
nums.push_back(n.op(0));
dens.push_back(n.op(1));
it++;
}
- ex n = ex_to<numeric>(overall_coeff).normal(sym_lst, repl_lst, level-1);
+ ex n = ex_to<numeric>(overall_coeff).normal(repl, level-1);
nums.push_back(n.op(0));
dens.push_back(n.op(1));
GINAC_ASSERT(nums.size() == dens.size());
/** Implementation of ex::normal() for a product. It cancels common factors
* from fractions.
* @see ex::normal() */
-ex mul::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex mul::normal(exmap & repl, int level) const
{
if (level == 1)
- return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(*this, repl), _ex1))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
ex n;
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- n = ex_to<basic>(recombine_pair_to_ex(*it)).normal(sym_lst, repl_lst, level-1);
+ n = ex_to<basic>(recombine_pair_to_ex(*it)).normal(repl, level-1);
num.push_back(n.op(0));
den.push_back(n.op(1));
it++;
}
- n = ex_to<numeric>(overall_coeff).normal(sym_lst, repl_lst, level-1);
+ n = ex_to<numeric>(overall_coeff).normal(repl, level-1);
num.push_back(n.op(0));
den.push_back(n.op(1));
* distributes integer exponents to numerator and denominator, and replaces
* non-integer powers by temporary symbols.
* @see ex::normal */
-ex power::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex power::normal(exmap & repl, int level) const
{
if (level == 1)
- return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(*this, repl), _ex1))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
// Normalize basis and exponent (exponent gets reassembled)
- ex n_basis = ex_to<basic>(basis).normal(sym_lst, repl_lst, level-1);
- ex n_exponent = ex_to<basic>(exponent).normal(sym_lst, repl_lst, level-1);
+ ex n_basis = ex_to<basic>(basis).normal(repl, level-1);
+ ex n_exponent = ex_to<basic>(exponent).normal(repl, level-1);
n_exponent = n_exponent.op(0) / n_exponent.op(1);
if (n_exponent.info(info_flags::integer)) {
if (n_exponent.info(info_flags::positive)) {
// (a/b)^x -> {sym((a/b)^x), 1}
- return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl), _ex1))->setflag(status_flags::dynallocated);
} else if (n_exponent.info(info_flags::negative)) {
if (n_basis.op(1).is_equal(_ex1)) {
// a^-x -> {1, sym(a^x)}
- return (new lst(_ex1, replace_with_symbol(power(n_basis.op(0), -n_exponent), sym_lst, repl_lst)))->setflag(status_flags::dynallocated);
+ return (new lst(_ex1, replace_with_symbol(power(n_basis.op(0), -n_exponent), repl)))->setflag(status_flags::dynallocated);
} else {
// (a/b)^-x -> {sym((b/a)^x), 1}
- return (new lst(replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), repl), _ex1))->setflag(status_flags::dynallocated);
}
}
}
// (a/b)^x -> {sym((a/b)^x, 1}
- return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl), _ex1))->setflag(status_flags::dynallocated);
}
/** Implementation of ex::normal() for pseries. It normalizes each coefficient
* and replaces the series by a temporary symbol.
* @see ex::normal */
-ex pseries::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex pseries::normal(exmap & repl, int level) const
{
epvector newseq;
epvector::const_iterator i = seq.begin(), end = seq.end();
++i;
}
ex n = pseries(relational(var,point), newseq);
- return (new lst(replace_with_symbol(n, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(n, repl), _ex1))->setflag(status_flags::dynallocated);
}
* @return normalized expression */
ex ex::normal(int level) const
{
- lst sym_lst, repl_lst;
+ exmap repl;
- ex e = bp->normal(sym_lst, repl_lst, level);
+ ex e = bp->normal(repl, level);
GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
- if (sym_lst.nops() > 0)
- e = e.subs(sym_lst, repl_lst);
+ if (!repl.empty())
+ e = e.subs(repl);
// Convert {numerator, denominator} form back to fraction
return e.op(0) / e.op(1);
* @return numerator */
ex ex::numer() const
{
- lst sym_lst, repl_lst;
+ exmap repl;
- ex e = bp->normal(sym_lst, repl_lst, 0);
+ ex e = bp->normal(repl, 0);
GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
- if (sym_lst.nops() > 0)
- return e.op(0).subs(sym_lst, repl_lst);
- else
+ if (repl.empty())
return e.op(0);
+ else
+ return e.op(0).subs(repl);
}
/** Get denominator of an expression. If the expression is not of the normal
* @return denominator */
ex ex::denom() const
{
- lst sym_lst, repl_lst;
+ exmap repl;
- ex e = bp->normal(sym_lst, repl_lst, 0);
+ ex e = bp->normal(repl, 0);
GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
- if (sym_lst.nops() > 0)
- return e.op(1).subs(sym_lst, repl_lst);
- else
+ if (repl.empty())
return e.op(1);
+ else
+ return e.op(1).subs(repl);
}
/** Get numerator and denominator of an expression. If the expresison is not
* @return a list [numerator, denominator] */
ex ex::numer_denom() const
{
- lst sym_lst, repl_lst;
+ exmap repl;
- ex e = bp->normal(sym_lst, repl_lst, 0);
+ ex e = bp->normal(repl, 0);
GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
- if (sym_lst.nops() > 0)
- return e.subs(sym_lst, repl_lst);
- else
+ if (repl.empty())
return e;
+ else
+ return e.subs(repl);
}
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