if (e.info(info_flags::rational))
return lcm(ex_to<numeric>(e).denom(), l);
else if (is_ex_exactly_of_type(e, add)) {
- numeric c = _num1();
+ numeric c = _num1;
for (unsigned i=0; i<e.nops(); i++)
c = lcmcoeff(e.op(i), c);
return lcm(c, l);
} else if (is_ex_exactly_of_type(e, mul)) {
- numeric c = _num1();
+ numeric c = _num1;
for (unsigned i=0; i<e.nops(); i++)
- c *= lcmcoeff(e.op(i), _num1());
+ c *= lcmcoeff(e.op(i), _num1);
return lcm(c, l);
} else if (is_ex_exactly_of_type(e, power)) {
if (is_ex_exactly_of_type(e.op(0), symbol))
* @return LCM of denominators of coefficients */
static numeric lcm_of_coefficients_denominators(const ex &e)
{
- return lcmcoeff(e, _num1());
+ return lcmcoeff(e, _num1);
}
/** Bring polynomial from Q[X] to Z[X] by multiplying in the previously
if (is_ex_exactly_of_type(e, mul)) {
unsigned num = e.nops();
exvector v; v.reserve(num + 1);
- numeric lcm_accum = _num1();
+ numeric lcm_accum = _num1;
for (unsigned i=0; i<e.nops(); i++) {
- numeric op_lcm = lcmcoeff(e.op(i), _num1());
+ numeric op_lcm = lcmcoeff(e.op(i), _num1);
v.push_back(multiply_lcm(e.op(i), op_lcm));
lcm_accum *= op_lcm;
}
numeric basic::integer_content(void) const
{
- return _num1();
+ return _num1;
}
numeric numeric::integer_content(void) const
{
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
- numeric c = _num0();
+ numeric c = _num0;
while (it != itend) {
- GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
- GINAC_ASSERT(is_ex_exactly_of_type(it->coeff,numeric));
+ GINAC_ASSERT(!is_exactly_a<numeric>(it->rest));
+ GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
c = gcd(ex_to<numeric>(it->coeff), c);
it++;
}
- GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
c = gcd(ex_to<numeric>(overall_coeff),c);
return c;
}
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
while (it != itend) {
- GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
+ GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*it)));
++it;
}
#endif // def DO_GINAC_ASSERT
- GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
return abs(ex_to<numeric>(overall_coeff));
}
return a / b;
#if FAST_COMPARE
if (a.is_equal(b))
- return _ex1();
+ return _ex1;
#endif
if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)))
throw(std::invalid_argument("quo: arguments must be polynomials over the rationals"));
throw(std::overflow_error("rem: division by zero"));
if (is_ex_exactly_of_type(a, numeric)) {
if (is_ex_exactly_of_type(b, numeric))
- return _ex0();
+ return _ex0;
else
return a;
}
#if FAST_COMPARE
if (a.is_equal(b))
- return _ex0();
+ return _ex0;
#endif
if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)))
throw(std::invalid_argument("rem: arguments must be polynomials over the rationals"));
throw(std::overflow_error("prem: division by zero"));
if (is_ex_exactly_of_type(a, numeric)) {
if (is_ex_exactly_of_type(b, numeric))
- return _ex0();
+ return _ex0;
else
return b;
}
if (bdeg <= rdeg) {
blcoeff = eb.coeff(x, bdeg);
if (bdeg == 0)
- eb = _ex0();
+ eb = _ex0;
else
eb -= blcoeff * power(x, bdeg);
} else
- blcoeff = _ex1();
+ blcoeff = _ex1;
int delta = rdeg - bdeg + 1, i = 0;
while (rdeg >= bdeg && !r.is_zero()) {
ex rlcoeff = r.coeff(x, rdeg);
ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
if (rdeg == 0)
- r = _ex0();
+ r = _ex0;
else
r -= rlcoeff * power(x, rdeg);
r = (blcoeff * r).expand() - term;
throw(std::overflow_error("prem: division by zero"));
if (is_ex_exactly_of_type(a, numeric)) {
if (is_ex_exactly_of_type(b, numeric))
- return _ex0();
+ return _ex0;
else
return b;
}
if (bdeg <= rdeg) {
blcoeff = eb.coeff(x, bdeg);
if (bdeg == 0)
- eb = _ex0();
+ eb = _ex0;
else
eb -= blcoeff * power(x, bdeg);
} else
- blcoeff = _ex1();
+ blcoeff = _ex1;
while (rdeg >= bdeg && !r.is_zero()) {
ex rlcoeff = r.coeff(x, rdeg);
ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
if (rdeg == 0)
- r = _ex0();
+ r = _ex0;
else
r -= rlcoeff * power(x, rdeg);
r = (blcoeff * r).expand() - term;
* "false" otherwise */
bool divide(const ex &a, const ex &b, ex &q, bool check_args)
{
- q = _ex0();
+ q = _ex0;
if (b.is_zero())
throw(std::overflow_error("divide: division by zero"));
if (a.is_zero())
return false;
#if FAST_COMPARE
if (a.is_equal(b)) {
- q = _ex1();
+ q = _ex1;
return true;
}
#endif
* @see get_symbol_stats, heur_gcd */
static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_iterator var)
{
- q = _ex0();
+ q = _ex0;
if (b.is_zero())
throw(std::overflow_error("divide_in_z: division by zero"));
- if (b.is_equal(_ex1())) {
+ if (b.is_equal(_ex1)) {
q = a;
return true;
}
}
#if FAST_COMPARE
if (a.is_equal(b)) {
- q = _ex1();
+ q = _ex1;
return true;
}
#endif
// Compute values at evaluation points 0..adeg
vector<numeric> alpha; alpha.reserve(adeg + 1);
exvector u; u.reserve(adeg + 1);
- numeric point = _num0();
+ numeric point = _num0;
ex c;
for (i=0; i<=adeg; i++) {
ex bs = b.subs(*x == point);
while (bs.is_zero()) {
- point += _num1();
+ point += _num1;
bs = b.subs(*x == point);
}
if (!divide_in_z(a.subs(*x == point), bs, c, var+1))
return false;
alpha.push_back(point);
u.push_back(c);
- point += _num1();
+ point += _num1;
}
// Compute inverses
vector<numeric> rcp; rcp.reserve(adeg + 1);
- rcp.push_back(_num0());
+ rcp.push_back(_num0);
for (k=1; k<=adeg; k++) {
numeric product = alpha[k] - alpha[0];
for (i=1; i<k; i++)
{
ex c = expand().lcoeff(x);
if (is_ex_exactly_of_type(c, numeric))
- return c < _ex0() ? _ex_1() : _ex1();
+ return c < _ex0 ? _ex_1 : _ex1;
else {
const symbol *y;
if (get_first_symbol(c, y))
ex ex::content(const symbol &x) const
{
if (is_zero())
- return _ex0();
+ return _ex0;
if (is_ex_exactly_of_type(*this, numeric))
return info(info_flags::negative) ? -*this : *this;
ex e = expand();
if (e.is_zero())
- return _ex0();
+ return _ex0;
// First, try the integer content
ex c = e.integer_content();
int ldeg = e.ldegree(x);
if (deg == ldeg)
return e.lcoeff(x) / e.unit(x);
- c = _ex0();
+ c = _ex0;
for (int i=ldeg; i<=deg; i++)
c = gcd(e.coeff(x, i), c, NULL, NULL, false);
return c;
ex ex::primpart(const symbol &x) const
{
if (is_zero())
- return _ex0();
+ return _ex0;
if (is_ex_exactly_of_type(*this, numeric))
- return _ex1();
+ return _ex1;
ex c = content(x);
if (c.is_zero())
- return _ex0();
+ return _ex0;
ex u = unit(x);
if (is_ex_exactly_of_type(c, numeric))
return *this / (c * u);
ex ex::primpart(const symbol &x, const ex &c) const
{
if (is_zero())
- return _ex0();
+ return _ex0;
if (c.is_zero())
- return _ex0();
+ return _ex0;
if (is_ex_exactly_of_type(*this, numeric))
- return _ex1();
+ return _ex1;
ex u = unit(x);
if (is_ex_exactly_of_type(c, numeric))
d = d.primpart(*x, cont_d);
// First element of divisor sequence
- ex r, ri = _ex1();
+ ex r, ri = _ex1;
int delta = cdeg - ddeg;
for (;;) {
//std::clog << " content " << gamma << " removed, continuing with sr_gcd(" << c << "," << d << ")\n";
// First element of subresultant sequence
- ex r = _ex0(), ri = _ex1(), psi = _ex1();
+ ex r = _ex0, ri = _ex1, psi = _ex1;
int delta = cdeg - ddeg;
for (;;) {
* @see heur_gcd */
numeric basic::max_coefficient(void) const
{
- return _num1();
+ return _num1;
}
numeric numeric::max_coefficient(void) const
{
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
- GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
numeric cur_max = abs(ex_to<numeric>(overall_coeff));
while (it != itend) {
numeric a;
- GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
+ GINAC_ASSERT(!is_exactly_a<numeric>(it->rest));
a = abs(ex_to<numeric>(it->coeff));
if (a > cur_max)
cur_max = a;
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
while (it != itend) {
- GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
+ GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*it)));
it++;
}
#endif // def DO_GINAC_ASSERT
- GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
return abs(ex_to<numeric>(overall_coeff));
}
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
while (it != itend) {
- GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
+ GINAC_ASSERT(!is_exactly_a<numeric>(it->rest));
numeric coeff = GiNaC::smod(ex_to<numeric>(it->coeff), xi);
if (!coeff.is_zero())
newseq.push_back(expair(it->rest, coeff));
it++;
}
- GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
numeric coeff = GiNaC::smod(ex_to<numeric>(overall_coeff), xi);
return (new add(newseq,coeff))->setflag(status_flags::dynallocated);
}
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
while (it != itend) {
- GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
+ GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*it)));
it++;
}
#endif // def DO_GINAC_ASSERT
mul * mulcopyp = new mul(*this);
- GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
mulcopyp->overall_coeff = GiNaC::smod(ex_to<numeric>(overall_coeff),xi);
mulcopyp->clearflag(status_flags::evaluated);
mulcopyp->clearflag(status_flags::hash_calculated);
numeric mq = q.max_coefficient();
numeric xi;
if (mp > mq)
- xi = mq * _num2() + _num2();
+ xi = mq * _num2 + _num2;
else
- xi = mp * _num2() + _num2();
+ xi = mp * _num2 + _num2;
// 6 tries maximum
for (int t=0; t<6; t++) {
if (ca || cb) {
if (g.is_zero()) {
if (ca)
- *ca = _ex0();
+ *ca = _ex0;
if (cb)
- *cb = _ex0();
+ *cb = _ex0;
} else {
if (ca)
*ca = ex_to<numeric>(a) / g;
ex exp_a = a.op(1), exp_b = b.op(1);
if (exp_a < exp_b) {
if (ca)
- *ca = _ex1();
+ *ca = _ex1;
if (cb)
*cb = power(p, exp_b - exp_a);
return power(p, exp_a);
if (ca)
*ca = power(p, exp_a - exp_b);
if (cb)
- *cb = _ex1();
+ *cb = _ex1;
return power(p, exp_b);
}
}
if (ca)
*ca = power(p, a.op(1) - 1);
if (cb)
- *cb = _ex1();
+ *cb = _ex1;
return p;
}
}
if (p.is_equal(a)) {
// a = p, b = p^n, gcd = p
if (ca)
- *ca = _ex1();
+ *ca = _ex1;
if (cb)
*cb = power(p, b.op(1) - 1);
return p;
ex aex = a.expand(), bex = b.expand();
if (aex.is_zero()) {
if (ca)
- *ca = _ex0();
+ *ca = _ex0;
if (cb)
- *cb = _ex1();
+ *cb = _ex1;
return b;
}
if (bex.is_zero()) {
if (ca)
- *ca = _ex1();
+ *ca = _ex1;
if (cb)
- *cb = _ex0();
+ *cb = _ex0;
return a;
}
- if (aex.is_equal(_ex1()) || bex.is_equal(_ex1())) {
+ if (aex.is_equal(_ex1) || bex.is_equal(_ex1)) {
if (ca)
*ca = a;
if (cb)
*cb = b;
- return _ex1();
+ return _ex1;
}
#if FAST_COMPARE
if (a.is_equal(b)) {
if (ca)
- *ca = _ex1();
+ *ca = _ex1;
if (cb)
- *cb = _ex1();
+ *cb = _ex1;
return a;
}
#endif
// g = peu_gcd(aex, bex, &x);
// g = red_gcd(aex, bex, &x);
g = sr_gcd(aex, bex, var);
- if (g.is_equal(_ex1())) {
+ if (g.is_equal(_ex1)) {
// Keep cofactors factored if possible
if (ca)
*ca = a;
}
#if 1
} else {
- if (g.is_equal(_ex1())) {
+ if (g.is_equal(_ex1)) {
// Keep cofactors factored if possible
if (ca)
*ca = a;
ex w = a;
ex z = w.diff(x);
ex g = gcd(w, z);
- if (g.is_equal(_ex1())) {
+ if (g.is_equal(_ex1)) {
res.push_back(a);
return res;
}
lst args;
if (l.nops()==0) {
sym_desc_vec sdv;
- get_symbol_stats(a, _ex0(), sdv);
+ get_symbol_stats(a, _ex0, sdv);
sym_desc_vec::const_iterator it = sdv.begin(), itend = sdv.end();
while (it != itend) {
args.append(*it->sym);
}
// Done with recursion, now construct the final result
- ex result = _ex1();
+ ex result = _ex1;
exvector::const_iterator it = factors.begin(), itend = factors.end();
for (int p = 1; it!=itend; ++it, ++p)
result *= power(*it, p);
exvector factor; factor.reserve(num_yun);
exvector cofac; cofac.reserve(num_yun);
for (unsigned i=0; i<num_yun; i++) {
- if (!yun[i].is_equal(_ex1())) {
+ if (!yun[i].is_equal(_ex1)) {
for (unsigned j=0; j<=i; j++) {
factor.push_back(pow(yun[i], j+1));
- ex prod = _ex1();
+ ex prod = _ex1;
for (unsigned k=0; k<num_yun; k++) {
if (k == i)
prod *= pow(yun[k], i-j);
ex basic::normal(lst &sym_lst, lst &repl_lst, 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, sym_lst, repl_lst), _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, sym_lst, repl_lst), _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), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
}
}
}
* @see ex::normal */
ex symbol::normal(lst &sym_lst, lst &repl_lst, int level) const
{
- return (new lst(*this, _ex1()))->setflag(status_flags::dynallocated);
+ return (new lst(*this, _ex1))->setflag(status_flags::dynallocated);
}
{
ex num = n;
ex den = d;
- numeric pre_factor = _num1();
+ numeric pre_factor = _num1;
//std::clog << "frac_cancel num = " << num << ", den = " << den << std::endl;
// Handle trivial case where denominator is 1
- if (den.is_equal(_ex1()))
+ if (den.is_equal(_ex1))
return (new lst(num, den))->setflag(status_flags::dynallocated);
// Handle special cases where numerator or denominator is 0
if (num.is_zero())
- return (new lst(num, _ex1()))->setflag(status_flags::dynallocated);
+ return (new lst(num, _ex1))->setflag(status_flags::dynallocated);
if (den.expand().is_zero())
throw(std::overflow_error("frac_cancel: division by zero in frac_cancel"));
// Cancel GCD from numerator and denominator
ex cnum, cden;
- if (gcd(num, den, &cnum, &cden, false) != _ex1()) {
+ if (gcd(num, den, &cnum, &cden, false) != _ex1) {
num = cnum;
den = cden;
}
// as defined by get_first_symbol() is made positive)
const symbol *x;
if (get_first_symbol(den, x)) {
- GINAC_ASSERT(is_ex_exactly_of_type(den.unit(*x),numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(den.unit(*x)));
if (ex_to<numeric>(den.unit(*x)).is_negative()) {
- num *= _ex_1();
- den *= _ex_1();
+ num *= _ex_1;
+ den *= _ex_1;
}
}
ex add::normal(lst &sym_lst, lst &repl_lst, 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, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
ex mul::normal(lst &sym_lst, lst &repl_lst, 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, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
ex power::normal(lst &sym_lst, lst &repl_lst, 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, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
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), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
} else if (n_exponent.info(info_flags::negative)) {
- if (n_basis.op(1).is_equal(_ex1())) {
+ 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), sym_lst, repl_lst)))->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), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
}
} else { // n_exponent not numeric
// (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), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
}
}
}
++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, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated);
}
lst sym_lst, repl_lst;
ex e = bp->normal(sym_lst, repl_lst, level);
- GINAC_ASSERT(is_ex_of_type(e, lst));
+ GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
if (sym_lst.nops() > 0)
lst sym_lst, repl_lst;
ex e = bp->normal(sym_lst, repl_lst, 0);
- GINAC_ASSERT(is_ex_of_type(e, lst));
+ GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
if (sym_lst.nops() > 0)
lst sym_lst, repl_lst;
ex e = bp->normal(sym_lst, repl_lst, 0);
- GINAC_ASSERT(is_ex_of_type(e, lst));
+ GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
if (sym_lst.nops() > 0)
lst sym_lst, repl_lst;
ex e = bp->normal(sym_lst, repl_lst, 0);
- GINAC_ASSERT(is_ex_of_type(e, lst));
+ GINAC_ASSERT(is_a<lst>(e));
// Re-insert replaced symbols
if (sym_lst.nops() > 0)
if (oc.info(info_flags::numeric))
return thisexpairseq(s, overall_coeff);
else
- s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1()));
+ s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1));
return thisexpairseq(s, default_overall_coeff());
}