Thanks very much, I0m sorry it was my mistake :) (1/2 ->> numeric(1,2)) Javier On Mon, 2007-05-28 at 12:27 +0400, Sheplyakov Alexei wrote:
Hello!
On Mon, May 28, 2007 at 09:44:44AM +0200, Javier Ros Ganuza wrote:
cout << "subs Rotation R * e00 * R^\\dag = " << canonicalize_clifford((R * e00 * clifford_star(R)).expand()) << endl;
cout << "subs Rotation R * e00 * R^\\dag = " << canonicalize_clifford((R * e00 * clifford_star(R)).expand()).subs(sin(wild())*cos(wild())==sin(2*wild())/2) << endl;
cout << "subs Rotation R * e00 * R^\\dag = " << canonicalize_clifford((R * e00 * clifford_star(R)).expand()).subs(sin(wild())*cos(wild())==sin(2*wild())/2,subs_options::algebraic) << endl;
Gives no subs at all
subs Rotation R * e00 * R^\dag = e~0*cos(1/2*theta)^2 +2*e~1*sin(1/2*theta)*cos(1/2*theta)-e~0*sin(1/2*theta)^2 subs Rotation R * e00 * R^\dag = e~0*cos(1/2*theta)^2 +2*e~1*sin(1/2*theta)*cos(1/2*theta)-e~0*sin(1/2*theta)^2 subs Rotation R * e00 * R^\dag = e~0*cos(1/2*theta)^2 +2*e~1*sin(1/2*theta)*cos(1/2*theta)-e~0*sin(1/2*theta)^2
Interesting. This program works for me:
$ cat substest.cpp #include <iostream> #include <stdexcept> #include <ginac/ginac.h> using namespace std; using namespace GiNaC;
int main(int argc, char** argv) { symbol x("x"), p("p"), eps("eps"); varidx mu(symbol("mu"), 4-2*eps), nu(symbol("nu"), 4-2*eps);
ex test = dirac_gamma(mu)*dirac_gamma(nu)*sin(x/2)*cos(x/2) + lorentz_g(mu, nu)*pow(sin(x), 2); cout << test << " ==> " << endl; cout << test.subs(sin(wild())*cos(wild())==sin(2*wild())/2, subs_options::algebraic) << endl; return 0; } $ g++ substest.cpp -lginac $ ./a.out (gamma~mu*gamma~nu)*cos(1/2*x)*sin(1/2*x)+eta~mu~nu*sin(x)^2 ==> eta~mu~nu*sin(x)^2+1/2*(gamma~mu*gamma~nu)*sin(x) $ pkg-config --modversion ginac 1.3.7
I understand that
cout << "subs Rotation R * e00 * R^\\dag = " << canonicalize_clifford((R * e00 * clifford_star(R)).expand()) << endl;
cout << "subs Rotation R * e00 * R^\\dag = " << canonicalize_clifford((R * e00 * clifford_star(R)).expand()).subs(2*sin(1/2*theta)*cos(1/2*theta)==sin(theta)) << endl;
In C[++] 1/2 means integer division, so 1/2*theta is zero. So your rule is subs(0==sin(theta))...
cout << "subs Rotation R * e00 * R^\\dag = " << canonicalize_clifford((R * e00 * clifford_star(R)).expand()).subs(2*sin(1/2*theta)*cos(1/2*theta)==sin(theta),subs_options::algebraic) << endl;
Produces nonsense substitutions:
subs Rotation R * e00 * R^\dag = -e~0*sin(1/2*theta)^2 +cos(1/2*theta)^2*e~0+2*cos(1/2*theta)*e~1*sin(1/2*theta) subs Rotation R * e00 * R^\dag = -e~(sin(theta))*sin(1/2*theta)^2 +2*cos(1/2*theta)*e~1*sin(1/2*theta)+cos(1/2*theta)^2*e~(sin(theta)) subs Rotation R * e00 * R^\dag = -e~(sin(theta))*sin(1/2*theta)^2 +2*cos(1/2*theta)*e~1*sin(1/2*theta)+cos(1/2*theta)^2*e~(sin(theta))
... and you got exactly what you asked for: e~0 turned into e~(sin(theta)
For example: what does mean: -e~(sin(theta)) ?
Something like \gamma~(4-2*eps) in dimensional regularisation? :)
Also in this simple expresion, even expand() is giving a bad result
cout << "out: " << ((2*sin(1/2*theta)*cos(1/2*theta) + 1).expand()) << endl;
Again, 1/2 is 0, so the expression is 1, ...
cout << "out: " << ((2*sin(1/2*theta)*cos(1/2*theta) + 1).expand()).subs(2*sin(1/2*theta)*cos(1/2*theta)==sin(theta)) << endl;
... and the rule is to replace zero with sin(theta) ...
cout << "out: " << ((2*sin(1/2*theta)*cos(1/2*theta) + 1).expand()).subs(2*sin(1/2*theta)*cos(1/2*theta)==sin(theta),subs_options::algebraic) << endl;
cout << "out: " << ((2*sin(1/2*theta)*cos(1/2*theta) + 1).expand()).subs(sin(wild())*cos(wild())==sin(2*wild())/2) << endl;
cout << "out: " << ((2*sin(1/2*theta)*cos(1/2*theta) + 1).expand()).subs(sin(wild())*cos(wild())==sin(2*wild())/2,subs_options::algebraic) << endl;
out: 1 out: 1 out: 1 out: 1 out: 1
... and (obviously) there are no matches.
Best regards, Alexei
-- All science is either physics or stamp collecting.
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