Hello!
The following transformations are done automagically now:
(-x+y)*(x-y) -> -(x-y)^2
(3*x+y)/(6*x+2*y)^2 -> 1/4*(y+3*x)^(-1)
Please note: exam_series13() from check/exam_pseries.cpp fails due to
this patch, because the expression 1/x*(-(1+x)/(1-x)) + (1+x)/x/(1-x)
gets evaluated to zero.
---
ginac/mul.cpp | 55 ++++++++++++++++++++++++++++++++++++++++++++++++++++++-
ginac/power.cpp | 22 ++++++++++++++++++++++
2 files changed, 76 insertions(+), 1 deletions(-)
diff --git a/ginac/mul.cpp b/ginac/mul.cpp
index 9bbcd61..4902cf1 100644
--- a/ginac/mul.cpp
+++ b/ginac/mul.cpp
@@ -448,7 +448,60 @@ ex mul::eval(int level) const
ex_to<numeric>(addref.overall_coeff).
mul_dyn(ex_to<numeric>(overall_coeff))))
->setflag(status_flags::dynallocated | status_flags::evaluated);
- }
+ } else if (seq_size >= 2) {
+ // Strip the content and the unit part from the each term. Thus
+ // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)^2
+
+ epvector::const_iterator last = seq.end();
+ epvector::const_iterator i = seq.begin();
+ while (i!=last) {
+ if (! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1))) {
+ // power::eval has such a rule, no need to handle powers here
+ ++i;
+ continue;
+ }
+
+ // XXX: What is the best way to check if the polynomial is a primitive?
+ numeric c = i->rest.integer_content();
+ const numeric& lead_coeff =
+ ex_to<numeric>(ex_to<add>(i->rest).seq.begin()->coeff).div_dyn(c);
+ const bool canonicalizable = lead_coeff.is_integer();
+
+ // XXX: The main variable is chosen in a random way, so this code
+ // does NOT transform the term into the canonical form (thus, in some
+ // very unlucky event it can even loop forever). Hopefully the main
+ // variable will be the same for all terms in *this
+ const bool unit_normal = lead_coeff.is_pos_integer();
+ if ((c == *_num1_p) && ((! canonicalizable) || unit_normal)) {
+ ++i;
+ continue;
+ }
+
+ std::auto_ptr<epvector> s(new epvector);
+ s->reserve(seq.size());
+
+ epvector::const_iterator j=seq.begin();
+ while (j!=i) {
+ s->push_back(*j);
+ ++j;
+ }
+
+ if (! unit_normal)
+ c = c.mul(*_num_1_p);
+ const ex primitive = (i->rest)/c;
+ s->push_back(expair(primitive, _ex1));
+ ++j;
+
+ while (j!=last) {
+ s->push_back(*j);
+ ++j;
+ }
+ return (new mul(s,
+ ex_to<numeric>(overall_coeff).mul_dyn(c))
+ )->setflag(status_flags::dynallocated);
+ }
+ }
+
return this->hold();
}
diff --git a/ginac/power.cpp b/ginac/power.cpp
index fb5e351..2b8bfc5 100644
--- a/ginac/power.cpp
+++ b/ginac/power.cpp
@@ -477,6 +477,28 @@ ex power::eval(int level) const
return expand_mul(ex_to<mul>(ebasis), *num_exponent, 0);
}
+ // (2*x + 6*y)^(-4) -> 1/16*(x + 3*y)^(-4)
+ if (num_exponent->is_integer() && is_exactly_a<add>(ebasis)) {
+ const numeric icont = ebasis.integer_content();
+ const numeric& lead_coeff =
+ ex_to<numeric>(ex_to<add>(ebasis).seq.begin()->coeff).div_dyn(icont);
+
+ const bool canonicalizable = lead_coeff.is_integer();
+ const bool unit_normal = lead_coeff.is_pos_integer();
+
+ if (icont != *_num1_p)
+ return (new mul(power(ebasis/icont, *num_exponent),
+ power(icont, *num_exponent)))->setflag(status_flags::dynallocated);
+
+ if (canonicalizable && (! unit_normal)) {
+ if (num_exponent->is_even())
+ return power(-ebasis, *num_exponent);
+ else
+ return (new mul(power(-ebasis, *num_exponent),
+ *_num_1_p))->setflag(status_flags::dynallocated);
+ }
+ }
+
// ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
// ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0)
if (is_exactly_a<mul>(ebasis)) {
--
1.4.4.4
Best regards,
Alexei
--
All science is either physics or stamp collecting.