Make power::expand() (x*p)^c -> x^c * p^c, if p>0.
authorVladimir Kisil <kisilv@maths.leeds.ac.uk>
Tue, 14 Apr 2015 21:14:09 +0000 (23:14 +0200)
committerRichard Kreckel <kreckel@ginac.de>
Tue, 14 Apr 2015 21:14:09 +0000 (23:14 +0200)
This expansion seems to be helpful in many cases.

check/exam_powerlaws.cpp
ginac/power.cpp

index 0903c4e..b817603 100644 (file)
@@ -288,6 +288,37 @@ static unsigned exam_powerlaws5()
        return 0;
 }
 
+static unsigned exam_powerlaws6()
+{
+       // check expansion rules for positive symbols
+
+       symbol a("a");
+       symbol b("b");
+       symbol c("c");
+       realsymbol x("x");
+       realsymbol y("y");
+       possymbol p("p");
+       possymbol q("q");
+       numeric half=numeric(1,2);
+
+       ex e1 = pow(5*pow(3*a*b*x*y*p*q,2),7*half*c).expand();
+       ex e2 = pow(p,7*c)*pow(q,7*c)*pow(pow(a*b*x*y,2),numeric(7,2)*c)*pow(45,numeric(7,2)*c);
+       if (!e1.is_equal(e2)) {
+               clog << "Could not expand exponents with positive bases in " << e1 << endl;
+               return 1;
+       }
+
+       ex e3 = pow(-pow(-a*x*p,3)*pow(b*y*p,3),half*c).expand().normal();
+       ex e4 = pow(p,3*c)*pow(pow(a*b*x*y,3),half*c);
+
+       if (!e3.is_equal(e4)) {
+               clog << "Could not expand exponents with positive bases in " << e3 << endl;
+               return 1;
+       }
+
+       return 0;
+}
+
 unsigned exam_powerlaws()
 {
        unsigned result = 0;
@@ -299,6 +330,7 @@ unsigned exam_powerlaws()
        result += exam_powerlaws3();  cout << '.' << flush;
        result += exam_powerlaws4();  cout << '.' << flush;
        result += exam_powerlaws5();  cout << '.' << flush;
+       result += exam_powerlaws6();  cout << '.' << flush;
        
        return result;
 }
index 6d6f81d..82200d7 100644 (file)
@@ -799,6 +799,51 @@ ex power::expand(unsigned options) const
                return *this;
        }
 
+       // (x*p)^c -> x^c * p^c, if p>0
+       // makes sense before expanding the basis
+       if (is_exactly_a<mul>(basis) && !basis.info(info_flags::indefinite)) {
+               const mul &m = ex_to<mul>(basis);
+               exvector prodseq;
+               epvector powseq;
+               prodseq.reserve(m.seq.size() + 1);
+               powseq.reserve(m.seq.size() + 1);
+               epvector::const_iterator last = m.seq.end();
+               epvector::const_iterator cit = m.seq.begin();
+               bool possign = true;
+
+               // search for positive/negative factors
+               while (cit!=last) {
+                       ex e=m.recombine_pair_to_ex(*cit);
+                       if (e.info(info_flags::positive))
+                               prodseq.push_back(pow(e, exponent).expand(options));
+                       else if (e.info(info_flags::negative)) {
+                               prodseq.push_back(pow(-e, exponent).expand(options));
+                               possign = !possign;
+                       } else
+                               powseq.push_back(*cit);
+                       ++cit;
+               }
+
+               // take care on the numeric coefficient
+               ex coeff=(possign? _ex1 : _ex_1);
+               if (m.overall_coeff.info(info_flags::positive) && m.overall_coeff != _ex1)
+                       prodseq.push_back(power(m.overall_coeff, exponent));
+               else if (m.overall_coeff.info(info_flags::negative) && m.overall_coeff != _ex_1)
+                       prodseq.push_back(power(-m.overall_coeff, exponent));
+               else
+                       coeff *= m.overall_coeff;
+
+               // If positive/negative factors are found, then extract them.
+               // In either case we set a flag to avoid the second run on a part
+               // which does not have positive/negative terms.
+               if (prodseq.size() > 0) {
+                       ex newbasis = coeff*mul(powseq);
+                       ex_to<basic>(newbasis).setflag(status_flags::purely_indefinite);
+                       return ((new mul(prodseq))->setflag(status_flags::dynallocated)*(new power(newbasis, exponent))->setflag(status_flags::dynallocated).expand(options)).expand(options);
+               } else
+                       ex_to<basic>(basis).setflag(status_flags::purely_indefinite);
+       }
+
        const ex expanded_basis = basis.expand(options);
        const ex expanded_exponent = exponent.expand(options);