}
// Check arguments
- if (check_args && !a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)) {
+ if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial))) {
throw(std::invalid_argument("gcd: arguments must be polynomials over the rationals"));
}
{
if (is_ex_exactly_of_type(a, numeric) && is_ex_exactly_of_type(b, numeric))
return lcm(ex_to_numeric(a), ex_to_numeric(b));
- if (check_args && !a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial))
+ if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)))
throw(std::invalid_argument("lcm: arguments must be polynomials over the rationals"));
ex ca, cb;
//std::clog << "frac_cancel num = " << num << ", den = " << den << endl;
+ // Handle trivial case where denominator is 1
+ 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(_ex0(), _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"));
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
- // Normalize and expand children, chop into summands and split each
- // one into numerator and denominator
+ // Normalize children and split each one into numerator and denominator
exvector nums, dens;
nums.reserve(seq.size()+1);
dens.reserve(seq.size()+1);
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
-
- // Normalize and expand child
- ex n = recombine_pair_to_ex(*it).bp->normal(sym_lst, repl_lst, level-1).expand();
-
- // If numerator is a sum, chop into summands
- if (is_ex_exactly_of_type(n.op(0), add)) {
- epvector::const_iterator bit = ex_to_add(n.op(0)).seq.begin(), bitend = ex_to_add(n.op(0)).seq.end();
- while (bit != bitend) {
- nums.push_back(recombine_pair_to_ex(*bit));
- dens.push_back(n.op(1));
- bit++;
- }
-
- // The overall_coeff is already normalized (== rational), we just
- // split it into numerator and denominator
- GINAC_ASSERT(ex_to_numeric(ex_to_add(n.op(0)).overall_coeff).is_rational());
- numeric overall = ex_to_numeric(ex_to_add(n.op(0)).overall_coeff);
- nums.push_back(overall.numer());
- dens.push_back(overall.denom() * n.op(1));
- } else {
- nums.push_back(n.op(0));
- dens.push_back(n.op(1));
- }
+ ex n = recombine_pair_to_ex(*it).bp->normal(sym_lst, repl_lst, level-1);
+ nums.push_back(n.op(0));
+ dens.push_back(n.op(1));
it++;
}
ex n = overall_coeff.bp->normal(sym_lst, repl_lst, level-1);
// Now, nums is a vector of all numerators and dens is a vector of
// all denominators
+//std::clog << "add::normal uses " << nums.size() << " summands:\n";
// Add fractions sequentially
exvector::const_iterator num_it = nums.begin(), num_itend = nums.end();
exvector::const_iterator den_it = dens.begin(), den_itend = dens.end();
-//std::clog << "add::normal uses the following summands:\n";
//std::clog << " num = " << *num_it << ", den = " << *den_it << endl;
ex num = *num_it++, den = *den_it++;
while (num_it != num_itend) {
//std::clog << " num = " << *num_it << ", den = " << *den_it << endl;
+ ex next_num = *num_it++, next_den = *den_it++;
+
+ // Trivially add sequences of fractions with identical denominators
+ while ((den_it != den_itend) && next_den.is_equal(*den_it)) {
+ next_num += *num_it;
+ num_it++; den_it++;
+ }
+
+ // Additiion of two fractions, taking advantage of the fact that
+ // the heuristic GCD algorithm computes the cofactors at no extra cost
ex co_den1, co_den2;
- ex g = gcd(den, *den_it, &co_den1, &co_den2, false);
- num = (num * co_den2) + (*num_it * co_den1);
- den *= co_den2; // this is the lcm(den, *den_it)
- num_it++; den_it++;
+ ex g = gcd(den, next_den, &co_den1, &co_den2, false);
+ num = ((num * co_den2) + (next_num * co_den1)).expand();
+ den *= co_den2; // this is the lcm(den, next_den)
}
//std::clog << " common denominator = " << den << endl;