[GiNaC-devel] [PATCH] {add, power}::eval(): convert terms into primitive polynomials when possible.

[Alexei Sheplyakov]

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.

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