#include "numeric.h"
#include "power.h"
#include "relational.h"
+#include "operators.h"
#include "matrix.h"
#include "pseries.h"
#include "symbol.h"
x = &ex_to<symbol>(e);
return true;
} else if (is_exactly_a<add>(e) || is_exactly_a<mul>(e)) {
- for (unsigned i=0; i<e.nops(); i++)
+ for (size_t i=0; i<e.nops(); i++)
if (get_first_symbol(e.op(i), x))
return true;
} else if (is_exactly_a<power>(e)) {
int max_deg;
/** Maximum number of terms of leading coefficient of symbol in both polynomials */
- int max_lcnops;
+ size_t max_lcnops;
/** Commparison operator for sorting */
bool operator<(const sym_desc &x) const
if (is_a<symbol>(e)) {
add_symbol(&ex_to<symbol>(e), v);
} else if (is_exactly_a<add>(e) || is_exactly_a<mul>(e)) {
- for (unsigned i=0; i<e.nops(); i++)
+ for (size_t i=0; i<e.nops(); i++)
collect_symbols(e.op(i), v);
} else if (is_exactly_a<power>(e)) {
collect_symbols(e.op(0), v);
++it;
}
std::sort(v.begin(), v.end());
+
#if 0
std::clog << "Symbols:\n";
it = v.begin(); itend = v.end();
return lcm(ex_to<numeric>(e).denom(), l);
else if (is_exactly_a<add>(e)) {
numeric c = _num1;
- for (unsigned i=0; i<e.nops(); i++)
+ for (size_t i=0; i<e.nops(); i++)
c = lcmcoeff(e.op(i), c);
return lcm(c, l);
} else if (is_exactly_a<mul>(e)) {
numeric c = _num1;
- for (unsigned i=0; i<e.nops(); i++)
+ for (size_t i=0; i<e.nops(); i++)
c *= lcmcoeff(e.op(i), _num1);
return lcm(c, l);
} else if (is_exactly_a<power>(e)) {
static ex multiply_lcm(const ex &e, const numeric &lcm)
{
if (is_exactly_a<mul>(e)) {
- unsigned num = e.nops();
+ size_t num = e.nops();
exvector v; v.reserve(num + 1);
numeric lcm_accum = _num1;
- for (unsigned i=0; i<e.nops(); i++) {
+ for (size_t i=0; i<num; i++) {
numeric op_lcm = lcmcoeff(e.op(i), _num1);
v.push_back(multiply_lcm(e.op(i), op_lcm));
lcm_accum *= op_lcm;
v.push_back(lcm / lcm_accum);
return (new mul(v))->setflag(status_flags::dynallocated);
} else if (is_exactly_a<add>(e)) {
- unsigned num = e.nops();
+ size_t num = e.nops();
exvector v; v.reserve(num);
- for (unsigned i=0; i<num; i++)
+ for (size_t i=0; i<num; i++)
v.push_back(multiply_lcm(e.op(i), lcm));
return (new add(v))->setflag(status_flags::dynallocated);
} else if (is_exactly_a<power>(e)) {
*
* @param e expanded polynomial
* @return integer content */
-numeric ex::integer_content(void) const
+numeric ex::integer_content() const
{
- GINAC_ASSERT(bp!=0);
return bp->integer_content();
}
-numeric basic::integer_content(void) const
+numeric basic::integer_content() const
{
return _num1;
}
-numeric numeric::integer_content(void) const
+numeric numeric::integer_content() const
{
return abs(*this);
}
-numeric add::integer_content(void) const
+numeric add::integer_content() const
{
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
return c;
}
-numeric mul::integer_content(void) const
+numeric mul::integer_content() const
{
#ifdef DO_GINAC_ASSERT
epvector::const_iterator it = seq.begin();
numeric point = _num0;
ex c;
for (i=0; i<=adeg; i++) {
- ex bs = b.subs(*x == point);
+ ex bs = b.subs(*x == point, subs_options::no_pattern);
while (bs.is_zero()) {
point += _num1;
- bs = b.subs(*x == point);
+ bs = b.subs(*x == point, subs_options::no_pattern);
}
- if (!divide_in_z(a.subs(*x == point), bs, c, var+1))
+ if (!divide_in_z(a.subs(*x == point, subs_options::no_pattern), bs, c, var+1))
return false;
alpha.push_back(point);
u.push_back(c);
* GCD of multivariate polynomials
*/
-/** Compute GCD of polynomials in Q[X] using the Euclidean algorithm (not
- * really suited for multivariate GCDs). This function is only provided for
- * testing purposes.
- *
- * @param a first multivariate polynomial
- * @param b second multivariate polynomial
- * @param x pointer to symbol (main variable) in which to compute the GCD in
- * @return the GCD as a new expression
- * @see gcd */
-
-static ex eu_gcd(const ex &a, const ex &b, const symbol *x)
-{
-//std::clog << "eu_gcd(" << a << "," << b << ")\n";
-
- // Sort c and d so that c has higher degree
- ex c, d;
- int adeg = a.degree(*x), bdeg = b.degree(*x);
- if (adeg >= bdeg) {
- c = a;
- d = b;
- } else {
- c = b;
- d = a;
- }
-
- // Normalize in Q[x]
- c = c / c.lcoeff(*x);
- d = d / d.lcoeff(*x);
-
- // Euclidean algorithm
- ex r;
- for (;;) {
-//std::clog << " d = " << d << endl;
- r = rem(c, d, *x, false);
- if (r.is_zero())
- return d / d.lcoeff(*x);
- c = d;
- d = r;
- }
-}
-
-
-/** Compute GCD of multivariate polynomials using the Euclidean PRS algorithm
- * with pseudo-remainders ("World's Worst GCD Algorithm", staying in Z[X]).
- * This function is only provided for testing purposes.
- *
- * @param a first multivariate polynomial
- * @param b second multivariate polynomial
- * @param x pointer to symbol (main variable) in which to compute the GCD in
- * @return the GCD as a new expression
- * @see gcd */
-
-static ex euprem_gcd(const ex &a, const ex &b, const symbol *x)
-{
-//std::clog << "euprem_gcd(" << a << "," << b << ")\n";
-
- // Sort c and d so that c has higher degree
- ex c, d;
- int adeg = a.degree(*x), bdeg = b.degree(*x);
- if (adeg >= bdeg) {
- c = a;
- d = b;
- } else {
- c = b;
- d = a;
- }
-
- // Calculate GCD of contents
- ex gamma = gcd(c.content(*x), d.content(*x), NULL, NULL, false);
-
- // Euclidean algorithm with pseudo-remainders
- ex r;
- for (;;) {
-//std::clog << " d = " << d << endl;
- r = prem(c, d, *x, false);
- if (r.is_zero())
- return d.primpart(*x) * gamma;
- c = d;
- d = r;
- }
-}
-
-
-/** Compute GCD of multivariate polynomials using the primitive Euclidean
- * PRS algorithm (complete content removal at each step). This function is
- * only provided for testing purposes.
- *
- * @param a first multivariate polynomial
- * @param b second multivariate polynomial
- * @param x pointer to symbol (main variable) in which to compute the GCD in
- * @return the GCD as a new expression
- * @see gcd */
-
-static ex peu_gcd(const ex &a, const ex &b, const symbol *x)
-{
-//std::clog << "peu_gcd(" << a << "," << b << ")\n";
-
- // Sort c and d so that c has higher degree
- ex c, d;
- int adeg = a.degree(*x), bdeg = b.degree(*x);
- int ddeg;
- if (adeg >= bdeg) {
- c = a;
- d = b;
- ddeg = bdeg;
- } else {
- c = b;
- d = a;
- ddeg = adeg;
- }
-
- // Remove content from c and d, to be attached to GCD later
- ex cont_c = c.content(*x);
- ex cont_d = d.content(*x);
- ex gamma = gcd(cont_c, cont_d, NULL, NULL, false);
- if (ddeg == 0)
- return gamma;
- c = c.primpart(*x, cont_c);
- d = d.primpart(*x, cont_d);
-
- // Euclidean algorithm with content removal
- ex r;
- for (;;) {
-//std::clog << " d = " << d << endl;
- r = prem(c, d, *x, false);
- if (r.is_zero())
- return gamma * d;
- c = d;
- d = r.primpart(*x);
- }
-}
-
-
-/** Compute GCD of multivariate polynomials using the reduced PRS algorithm.
- * This function is only provided for testing purposes.
- *
- * @param a first multivariate polynomial
- * @param b second multivariate polynomial
- * @param x pointer to symbol (main variable) in which to compute the GCD in
- * @return the GCD as a new expression
- * @see gcd */
-
-static ex red_gcd(const ex &a, const ex &b, const symbol *x)
-{
-//std::clog << "red_gcd(" << a << "," << b << ")\n";
-
- // Sort c and d so that c has higher degree
- ex c, d;
- int adeg = a.degree(*x), bdeg = b.degree(*x);
- int cdeg, ddeg;
- if (adeg >= bdeg) {
- c = a;
- d = b;
- cdeg = adeg;
- ddeg = bdeg;
- } else {
- c = b;
- d = a;
- cdeg = bdeg;
- ddeg = adeg;
- }
-
- // Remove content from c and d, to be attached to GCD later
- ex cont_c = c.content(*x);
- ex cont_d = d.content(*x);
- ex gamma = gcd(cont_c, cont_d, NULL, NULL, false);
- if (ddeg == 0)
- return gamma;
- c = c.primpart(*x, cont_c);
- d = d.primpart(*x, cont_d);
-
- // First element of divisor sequence
- ex r, ri = _ex1;
- int delta = cdeg - ddeg;
-
- for (;;) {
- // Calculate polynomial pseudo-remainder
-//std::clog << " d = " << d << endl;
- r = prem(c, d, *x, false);
- if (r.is_zero())
- return gamma * d.primpart(*x);
- c = d;
- cdeg = ddeg;
-
- if (!divide(r, pow(ri, delta), d, false))
- throw(std::runtime_error("invalid expression in red_gcd(), division failed"));
- ddeg = d.degree(*x);
- if (ddeg == 0) {
- if (is_exactly_a<numeric>(r))
- return gamma;
- else
- return gamma * r.primpart(*x);
- }
-
- ri = c.expand().lcoeff(*x);
- delta = cdeg - ddeg;
- }
-}
-
-
/** Compute GCD of multivariate polynomials using the subresultant PRS
* algorithm. This function is used internally by gcd().
*
static ex sr_gcd(const ex &a, const ex &b, sym_desc_vec::const_iterator var)
{
-//std::clog << "sr_gcd(" << a << "," << b << ")\n";
#if STATISTICS
sr_gcd_called++;
#endif
return gamma;
c = c.primpart(x, cont_c);
d = d.primpart(x, cont_d);
-//std::clog << " content " << gamma << " removed, continuing with sr_gcd(" << c << "," << d << ")\n";
// First element of subresultant sequence
ex r = _ex0, ri = _ex1, psi = _ex1;
int delta = cdeg - ddeg;
for (;;) {
+
// Calculate polynomial pseudo-remainder
-//std::clog << " start of loop, psi = " << psi << ", calculating pseudo-remainder...\n";
-//std::clog << " d = " << d << endl;
r = prem(c, d, x, false);
if (r.is_zero())
return gamma * d.primpart(x);
+
c = d;
cdeg = ddeg;
-//std::clog << " dividing...\n";
if (!divide_in_z(r, ri * pow(psi, delta), d, var))
throw(std::runtime_error("invalid expression in sr_gcd(), division failed"));
ddeg = d.degree(x);
}
// Next element of subresultant sequence
-//std::clog << " calculating next subresultant...\n";
ri = c.expand().lcoeff(x);
if (delta == 1)
psi = ri;
* @param e expanded multivariate polynomial
* @return maximum coefficient
* @see heur_gcd */
-numeric ex::max_coefficient(void) const
+numeric ex::max_coefficient() const
{
- GINAC_ASSERT(bp!=0);
return bp->max_coefficient();
}
/** Implementation ex::max_coefficient().
* @see heur_gcd */
-numeric basic::max_coefficient(void) const
+numeric basic::max_coefficient() const
{
return _num1;
}
-numeric numeric::max_coefficient(void) const
+numeric numeric::max_coefficient() const
{
return abs(*this);
}
-numeric add::max_coefficient(void) const
+numeric add::max_coefficient() const
{
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
return cur_max;
}
-numeric mul::max_coefficient(void) const
+numeric mul::max_coefficient() const
{
#ifdef DO_GINAC_ASSERT
epvector::const_iterator it = seq.begin();
* @exception gcdheu_failed() */
static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const_iterator var)
{
-//std::clog << "heur_gcd(" << a << "," << b << ")\n";
#if STATISTICS
heur_gcd_called++;
#endif
// 6 tries maximum
for (int t=0; t<6; t++) {
if (xi.int_length() * maxdeg > 100000) {
-//std::clog << "giving up heur_gcd, xi.int_length = " << xi.int_length() << ", maxdeg = " << maxdeg << std::endl;
throw gcdheu_failed();
}
// Apply evaluation homomorphism and calculate GCD
ex cp, cq;
- ex gamma = heur_gcd(p.subs(x == xi), q.subs(x == xi), &cp, &cq, var+1).expand();
+ ex gamma = heur_gcd(p.subs(x == xi, subs_options::no_pattern), q.subs(x == xi, subs_options::no_pattern), &cp, &cq, var+1).expand();
if (!is_exactly_a<fail>(gamma)) {
// Reconstruct polynomial from GCD of mapped polynomials
else
return g;
}
-#if 0
- cp = interpolate(cp, xi, x);
- if (divide_in_z(cp, p, g, var)) {
- if (divide_in_z(g, q, cb ? *cb : dummy, var)) {
- g *= gc;
- if (ca)
- *ca = cp;
- ex lc = g.lcoeff(x);
- if (is_exactly_a<numeric>(lc) && ex_to<numeric>(lc).is_negative())
- return -g;
- else
- return g;
- }
- }
- cq = interpolate(cq, xi, x);
- if (divide_in_z(cq, q, g, var)) {
- if (divide_in_z(g, p, ca ? *ca : dummy, var)) {
- g *= gc;
- if (cb)
- *cb = cq;
- ex lc = g.lcoeff(x);
- if (is_exactly_a<numeric>(lc) && ex_to<numeric>(lc).is_negative())
- return -g;
- else
- return g;
- }
- }
-#endif
}
// Next evaluation point
* @return the GCD as a new expression */
ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args)
{
-//std::clog << "gcd(" << a << "," << b << ")\n";
#if STATISTICS
gcd_called++;
#endif
if (is_exactly_a<mul>(b) && b.nops() > a.nops())
goto factored_b;
factored_a:
- unsigned num = a.nops();
+ size_t num = a.nops();
exvector g; g.reserve(num);
exvector acc_ca; acc_ca.reserve(num);
ex part_b = b;
- for (unsigned i=0; i<num; i++) {
+ for (size_t i=0; i<num; i++) {
ex part_ca, part_cb;
g.push_back(gcd(a.op(i), part_b, &part_ca, &part_cb, check_args));
acc_ca.push_back(part_ca);
if (is_exactly_a<mul>(a) && a.nops() > b.nops())
goto factored_a;
factored_b:
- unsigned num = b.nops();
+ size_t num = b.nops();
exvector g; g.reserve(num);
exvector acc_cb; acc_cb.reserve(num);
ex part_a = a;
- for (unsigned i=0; i<num; i++) {
+ for (size_t i=0; i<num; i++) {
ex part_ca, part_cb;
g.push_back(gcd(part_a, b.op(i), &part_ca, &part_cb, check_args));
acc_cb.push_back(part_cb);
int min_ldeg = std::min(ldeg_a,ldeg_b);
if (min_ldeg > 0) {
ex common = power(x, min_ldeg);
-//std::clog << "trivial common factor " << common << std::endl;
return gcd((aex / common).expand(), (bex / common).expand(), ca, cb, false) * common;
}
// Try to eliminate variables
if (var->deg_a == 0) {
-//std::clog << "eliminating variable " << x << " from b" << std::endl;
ex c = bex.content(x);
ex g = gcd(aex, c, ca, cb, false);
if (cb)
*cb *= bex.unit(x) * bex.primpart(x, c);
return g;
} else if (var->deg_b == 0) {
-//std::clog << "eliminating variable " << x << " from a" << std::endl;
ex c = aex.content(x);
ex g = gcd(c, bex, ca, cb, false);
if (ca)
return g;
}
- ex g;
-#if 1
// Try heuristic algorithm first, fall back to PRS if that failed
+ ex g;
try {
g = heur_gcd(aex, bex, ca, cb, var);
} catch (gcdheu_failed) {
g = fail();
}
if (is_exactly_a<fail>(g)) {
-//std::clog << "heuristics failed" << std::endl;
#if STATISTICS
heur_gcd_failed++;
#endif
-#endif
-// g = heur_gcd(aex, bex, ca, cb, var);
-// g = eu_gcd(aex, bex, &x);
-// g = euprem_gcd(aex, bex, &x);
-// g = peu_gcd(aex, bex, &x);
-// g = red_gcd(aex, bex, &x);
g = sr_gcd(aex, bex, var);
if (g.is_equal(_ex1)) {
// Keep cofactors factored if possible
if (cb)
divide(bex, g, *cb, false);
}
-#if 1
} else {
if (g.is_equal(_ex1)) {
// Keep cofactors factored if possible
*cb = b;
}
}
-#endif
+
return g;
}
}
// Find the symbol to factor in at this stage
- if (!is_ex_of_type(args.op(0), symbol))
+ if (!is_a<symbol>(args.op(0)))
throw (std::runtime_error("sqrfree(): invalid factorization variable"));
const symbol &x = ex_to<symbol>(args.op(0));
// Factorize denominator and compute cofactors
exvector yun = sqrfree_yun(denom, x);
//clog << "yun factors: " << exprseq(yun) << endl;
- unsigned num_yun = yun.size();
+ size_t num_yun = yun.size();
exvector factor; factor.reserve(num_yun);
exvector cofac; cofac.reserve(num_yun);
- for (unsigned i=0; i<num_yun; i++) {
+ for (size_t i=0; i<num_yun; i++) {
if (!yun[i].is_equal(_ex1)) {
- for (unsigned j=0; j<=i; j++) {
+ for (size_t j=0; j<=i; j++) {
factor.push_back(pow(yun[i], j+1));
ex prod = _ex1;
- for (unsigned k=0; k<num_yun; k++) {
+ for (size_t k=0; k<num_yun; k++) {
if (k == i)
prod *= pow(yun[k], i-j);
else
}
}
}
- unsigned num_factors = factor.size();
+ size_t num_factors = factor.size();
//clog << "factors : " << exprseq(factor) << endl;
//clog << "cofactors: " << exprseq(cofac) << endl;
matrix sys(max_denom_deg + 1, num_factors);
matrix rhs(max_denom_deg + 1, 1);
for (int i=0; i<=max_denom_deg; i++) {
- for (unsigned j=0; j<num_factors; j++)
+ for (size_t j=0; j<num_factors; j++)
sys(i, j) = cofac[j].coeff(x, i);
rhs(i, 0) = red_numer.coeff(x, i);
}
// Solve resulting linear system
matrix vars(num_factors, 1);
- for (unsigned i=0; i<num_factors; i++)
+ for (size_t i=0; i<num_factors; i++)
vars(i, 0) = symbol();
matrix sol = sys.solve(vars, rhs);
// Sum up decomposed fractions
ex sum = 0;
- for (unsigned i=0; i<num_factors; i++)
+ for (size_t i=0; i<num_factors; i++)
sum += sol(i, 0) / factor[i];
return red_poly + sum;
/** 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, exmap & rev_lookup)
{
- // Expression already in repl_lst? Then return the assigned symbol
- for (unsigned i=0; i<repl_lst.nops(); i++)
- if (repl_lst.op(i).is_equal(e))
- return sym_lst.op(i);
+ // Expression already replaced? Then return the assigned symbol
+ exmap::const_iterator it = rev_lookup.find(e);
+ if (it != rev_lookup.end())
+ return it->second;
// 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, subs_options::no_pattern);
+ repl[es] = e_replaced;
+ rev_lookup[e_replaced] = es;
return es;
}
/** Create a symbol for replacing the expression "e" (or return a previously
* assigned symbol). An expression of the form "symbol == expression" is added
* to repl_lst and the symbol is returned.
- * @see basic::to_rational */
-static ex replace_with_symbol(const ex &e, lst &repl_lst)
+ * @see basic::to_rational
+ * @see basic::to_polynomial */
+static ex replace_with_symbol(const ex & e, lst & repl_lst)
{
// Expression already in repl_lst? Then return the assigned symbol
- for (unsigned i=0; i<repl_lst.nops(); i++)
- if (repl_lst.op(i).op(1).is_equal(e))
- return repl_lst.op(i).op(0);
+ for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it)
+ if (it->op(1).is_equal(e))
+ 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 e_replaced = e.subs(repl_lst);
+ ex es = (new symbol)->setflag(status_flags::dynallocated);
+ ex e_replaced = e.subs(repl_lst, subs_options::no_pattern);
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, exmap & rev_lookup, 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, rev_lookup), _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, rev_lookup), _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, rev_lookup), _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, exmap & rev_lookup, 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, exmap & rev_lookup, 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, rev_lookup);
} 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, rev_lookup);
+ ex im_ex = im.is_rational() ? im : replace_with_symbol(im, repl, rev_lookup);
+ numex = re_ex + im_ex * replace_with_symbol(I, repl, rev_lookup);
}
// 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, exmap & rev_lookup, 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, rev_lookup), _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, rev_lookup, 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, rev_lookup, 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, exmap & rev_lookup, 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, rev_lookup), _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, rev_lookup, 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, rev_lookup, level-1);
num.push_back(n.op(0));
den.push_back(n.op(1));
}
-/** Implementation of ex::normal() for powers. It normalizes the basis,
+/** Implementation of ex::normal([B) for powers. It normalizes the basis,
* 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, exmap & rev_lookup, 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, rev_lookup), _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, rev_lookup, level-1);
+ ex n_exponent = ex_to<basic>(exponent).normal(repl, rev_lookup, 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, rev_lookup), _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, rev_lookup)))->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, rev_lookup), _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, rev_lookup), _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, exmap & rev_lookup, 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, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
}
* @return normalized expression */
ex ex::normal(int level) const
{
- lst sym_lst, repl_lst;
+ exmap repl, rev_lookup;
- ex e = bp->normal(sym_lst, repl_lst, level);
+ ex e = bp->normal(repl, rev_lookup, 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, subs_options::no_pattern);
// Convert {numerator, denominator} form back to fraction
return e.op(0) / e.op(1);
*
* @see ex::normal
* @return numerator */
-ex ex::numer(void) const
+ex ex::numer() const
{
- lst sym_lst, repl_lst;
+ exmap repl, rev_lookup;
- ex e = bp->normal(sym_lst, repl_lst, 0);
+ ex e = bp->normal(repl, rev_lookup, 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, subs_options::no_pattern);
}
/** Get denominator of an expression. If the expression is not of the normal
*
* @see ex::normal
* @return denominator */
-ex ex::denom(void) const
+ex ex::denom() const
{
- lst sym_lst, repl_lst;
+ exmap repl, rev_lookup;
- ex e = bp->normal(sym_lst, repl_lst, 0);
+ ex e = bp->normal(repl, rev_lookup, 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, subs_options::no_pattern);
}
/** Get numerator and denominator of an expression. If the expresison is not
*
* @see ex::normal
* @return a list [numerator, denominator] */
-ex ex::numer_denom(void) const
+ex ex::numer_denom() const
{
- lst sym_lst, repl_lst;
+ exmap repl, rev_lookup;
- ex e = bp->normal(sym_lst, repl_lst, 0);
+ ex e = bp->normal(repl, rev_lookup, 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, subs_options::no_pattern);
}
/** Rationalization of non-rational functions.
- * This function converts a general expression to a rational polynomial
+ * This function converts a general expression to a rational function
* by replacing all non-rational subexpressions (like non-rational numbers,
* non-integer powers or functions like sin(), cos() etc.) to temporary
* symbols. This makes it possible to use functions like gcd() and divide()
*
* @param repl_lst collects a list of all temporary symbols and their replacements
* @return rationalized expression */
+ex ex::to_rational(lst &repl_lst) const
+{
+ return bp->to_rational(repl_lst);
+}
+
+ex ex::to_polynomial(lst &repl_lst) const
+{
+ return bp->to_polynomial(repl_lst);
+}
+
+
+/** Default implementation of ex::to_rational(). This replaces the object with
+ * a temporary symbol. */
ex basic::to_rational(lst &repl_lst) const
{
return replace_with_symbol(*this, repl_lst);
}
+ex basic::to_polynomial(lst &repl_lst) const
+{
+ return replace_with_symbol(*this, repl_lst);
+}
+
/** Implementation of ex::to_rational() for symbols. This returns the
* unmodified symbol. */
return *this;
}
+/** Implementation of ex::to_polynomial() for symbols. This returns the
+ * unmodified symbol. */
+ex symbol::to_polynomial(lst &repl_lst) const
+{
+ return *this;
+}
+
/** Implementation of ex::to_rational() for a numeric. It splits complex
* numbers into re+I*im and replaces I and non-rational real numbers with a
return *this;
}
+/** Implementation of ex::to_polynomial() for a numeric. It splits complex
+ * numbers into re+I*im and replaces I and non-integer real numbers with a
+ * temporary symbol. */
+ex numeric::to_polynomial(lst &repl_lst) const
+{
+ if (is_real()) {
+ if (!is_integer())
+ return replace_with_symbol(*this, repl_lst);
+ } else { // complex
+ numeric re = real();
+ numeric im = imag();
+ ex re_ex = re.is_integer() ? re : replace_with_symbol(re, repl_lst);
+ ex im_ex = im.is_integer() ? im : replace_with_symbol(im, repl_lst);
+ return re_ex + im_ex * replace_with_symbol(I, repl_lst);
+ }
+ return *this;
+}
+
/** Implementation of ex::to_rational() for powers. It replaces non-integer
* powers by temporary symbols. */
return replace_with_symbol(*this, repl_lst);
}
+/** Implementation of ex::to_polynomial() for powers. It replaces non-posint
+ * powers by temporary symbols. */
+ex power::to_polynomial(lst &repl_lst) const
+{
+ if (exponent.info(info_flags::posint))
+ return power(basis.to_rational(repl_lst), exponent);
+ else
+ return replace_with_symbol(*this, repl_lst);
+}
+
/** Implementation of ex::to_rational() for expairseqs. */
ex expairseq::to_rational(lst &repl_lst) const
return thisexpairseq(s, default_overall_coeff());
}
+/** Implementation of ex::to_polynomial() for expairseqs. */
+ex expairseq::to_polynomial(lst &repl_lst) const
+{
+ epvector s;
+ s.reserve(seq.size());
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ s.push_back(split_ex_to_pair(recombine_pair_to_ex(*i).to_polynomial(repl_lst)));
+ ++i;
+ }
+ ex oc = overall_coeff.to_polynomial(repl_lst);
+ if (oc.info(info_flags::numeric))
+ return thisexpairseq(s, overall_coeff);
+ else
+ s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1));
+ return thisexpairseq(s, default_overall_coeff());
+}
+
/** Remove the common factor in the terms of a sum 'e' by calculating the GCD,
* and multiply it into the expression 'factor' (which needs to be initialized
{
if (is_exactly_a<add>(e)) {
- unsigned num = e.nops();
+ size_t num = e.nops();
exvector terms; terms.reserve(num);
ex gc;
// Find the common GCD
- for (unsigned i=0; i<num; i++) {
- ex x = e.op(i).to_rational(repl);
+ for (size_t i=0; i<num; i++) {
+ ex x = e.op(i).to_polynomial(repl);
if (is_exactly_a<add>(x) || is_exactly_a<mul>(x)) {
ex f = 1;
factor *= gc;
// Now divide all terms by the GCD
- for (unsigned i=0; i<num; i++) {
+ for (size_t i=0; i<num; i++) {
ex x;
// Try to avoid divide() because it expands the polynomial
ex &t = terms[i];
if (is_exactly_a<mul>(t)) {
- for (unsigned j=0; j<t.nops(); j++) {
+ for (size_t j=0; j<t.nops(); j++) {
if (t.op(j).is_equal(gc)) {
exvector v; v.reserve(t.nops());
- for (unsigned k=0; k<t.nops(); k++) {
+ for (size_t k=0; k<t.nops(); k++) {
if (k == j)
v.push_back(_ex1);
else
} else if (is_exactly_a<mul>(e)) {
- unsigned num = e.nops();
+ size_t num = e.nops();
exvector v; v.reserve(num);
- for (unsigned i=0; i<num; i++)
+ for (size_t i=0; i<num; i++)
v.push_back(find_common_factor(e.op(i), factor, repl));
return (new mul(v))->setflag(status_flags::dynallocated);
} else if (is_exactly_a<power>(e)) {
- ex x = e.to_rational(repl);
- if (is_exactly_a<power>(x) && x.op(1).info(info_flags::negative))
- return replace_with_symbol(x, repl);
- else
- return x;
+ return e.to_polynomial(repl);
} else
return e;
lst repl;
ex factor = 1;
ex r = find_common_factor(e, factor, repl);
- return factor.subs(repl) * r.subs(repl);
+ return factor.subs(repl, subs_options::no_pattern) * r.subs(repl, subs_options::no_pattern);
} else
return e;
git://www.ginac.de / ginac.git / blobdiff