* functions. */
/*
- * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include "exams.h"
-
+#include <iostream>
#include <fstream>
+#include "ginac.h"
+using namespace std;
+using namespace GiNaC;
+
////////////////////////////////////////////////////////////////////////////////
}
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+// H/Li exam
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
+
+static unsigned inifcns_test_LiG()
+{
+ int digitsbuf = Digits;
+ Digits = 17;
+ ex prec = 5 * pow(10, -(int)Digits);
+ numeric almostone("0.99999999999999999999");
+ unsigned result = 0;
+
+ lst res;
+
+ res.append(Li(lst(4), lst(6)).hold() - Li(4, 6.0));
+ res.append(G(lst(0,0,5.0,0,2.0,0,0,0,3.0),0.5).hold()
+ + Li(lst(3,2,4), lst(numeric(1,10), numeric(5,2), numeric(2,3))));
+ res.append(Li(lst(2,1,1), lst(almostone, almostone, almostone)) - zeta(lst(2,1,1)));
+
+ // check Li_{1,1} against known expression
+ symbol x("x"), y("y");
+ ex eps = 1e-30*I;
+ ex s1 = Li(lst(1,1),lst(x,y));
+ ex s2 = log(1-1/x/y-eps)*log((1-1/x-eps)/(1/x/y-1/x)) + Li(2,(1-1/x/y-eps)/(1/x-1/x/y))
+ - log(-1/x/y-eps)*log((-1/x-eps)/(1/x/y-1/x)) - Li(2,(-1/x/y-eps)/(1/x-1/x/y))
+ - log(-1/x/y-eps)*log(1-1/x-eps) + log(-1/x/y-eps)*log(-1/x-eps);
+ res.append(s1.subs(lst(x==numeric(1)/2, y==3)) - s2.subs(lst(x==numeric(1)/2, y==3)));
+ res.append(s1.subs(lst(x==numeric(3)/2, y==numeric(1)/2)) - s2.subs(lst(x==numeric(3)/2, y==numeric(1)/2)));
+ res.append(s1.subs(lst(x==2, y==numeric(4)/5)) - s2.subs(lst(x==2, y==numeric(4)/5)));
+
+ // shuffle and quasi-shuffle identities
+ res.append(G(lst(0,0.2),1).hold() * G(lst(0.5),1).hold() - G(lst(0.5,0,0.2),1).hold()
+ - G(lst(0,0.5,0.2),1).hold() - G(lst(0,0.2,0.5),1).hold());
+ res.append(G(lst(0,0.5),1).hold() * G(lst(0.6),1).hold() - G(lst(0,0.5,0.5*0.6),1).hold()
+ - G(lst(0.6,0,0.5*0.6),1).hold() + G(lst(0,0,0.5*0.6),1).hold());
+ res.append(Li(lst(2),lst(numeric(1,5))).hold() * Li(lst(3),lst(7)).hold() - Li(lst(2,3),lst(numeric(1,5),7)).hold()
+ - Li(lst(3,2),lst(7,numeric(1,5))).hold() - Li(lst(5),lst(numeric(7,5))).hold());
+ symbol a1, a2, a3, a4;
+ res.append((G(lst(a1,a2),1) * G(lst(a3,a4),1) - G(lst(a1,a2,a3,a4),1)
+ - G(lst(a1,a3,a2,a4),1) - G(lst(a3,a1,a2,a4),1)
+ - G(lst(a1,a3,a4,a2),1) - G(lst(a3,a1,a4,a2),1) - G(lst(a3,a4,a1,a2),1))
+ .subs(lst(a1==numeric(1)/10, a2==numeric(3)/10, a3==numeric(7)/10, a4==5)));
+ res.append(G(lst(-0.009),1).hold() * G(lst(-8,1.4999),1).hold() - G(lst(-0.009,-8,1.4999),1).hold()
+ - G(lst(-8,-0.009,1.4999),1).hold() - G(lst(-8,1.4999,-0.009),1).hold());
+ res.append(G(lst(sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)),1).hold() * G(lst(1.51,-0.999),1).hold()
+ - G(lst(sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),1.51,-0.999),1).hold()
+ - G(lst(1.51,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),-0.999),1).hold()
+ - G(lst(1.51,-0.999,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)),1).hold());
+ // checks for hoelder convolution which is used if one argument has a distance to one smaller than 0.01
+ res.append(G(lst(0, 1.2, 1, 1.01), 1).hold() - G(lst(0, 1.2, 1, numeric("1.009999999999999999")), 1).hold());
+
+ for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
+ ex diff = abs((*it).evalf());
+ if (diff > prec) {
+ clog << *it << " seems to be wrong: " << diff << endl;
+ result++;
+ }
+ cout << "." << flush;
+ }
+
+ return result;
+}
+
+
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+// legacy exam - checking for historical bugs
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
+
+static unsigned inifcns_test_legacy()
+{
+ Digits = 17;
+ ex prec = 5 * pow(10, -(int)Digits);
+
+ unsigned result = 0;
+
+ ex r1 = zeta(lst(1,1,1,1,1,1),lst(-1,-1,-1,1,1,1));
+ if ((r1.evalf() - numeric("-0.0012588769028204890704")) > prec) {
+ clog << "zeta({1,1,1,1,1,1},{-1,-1,-1,1,1,1}) seems to be wrong." << endl;
+ result++;
+ }
+
+ ex x1 = exp(2*Pi*I/13).evalf();
+ ex x2 = exp(24*Pi*I/13).evalf();
+ ex r2 = Li(lst(2),lst(x1)).hold().evalf();
+ ex r3 = Li(lst(2),lst(x2)).hold().evalf();
+ if ( abs(r2-conjugate(r3)) > prec ) {
+ clog << "Legacy test 2 seems to be wrong." << endl;
+ result++;
+ }
+
+ ex x3 = exp(5*Pi*I/3).evalf();
+ ex r4 = Li(lst(3),lst(x3)).hold().evalf();
+ if ( abs(r4 - numeric("0.40068563438653142847-0.95698384815740185713*I")) > prec ) {
+ clog << "Legacy test 3 seems to be wrong." << endl;
+ result++;
+ }
+
+ Digits = 100;
+ prec = 5 * pow(10, -(int)Digits);
+ ex x0 = 1.;
+ x1 = exp(Pi*I/3).evalf();
+ x2 = exp(2*Pi*I/3).evalf();
+ x3 = -1.;
+ ex x4 = exp(4*Pi*I/3).evalf();
+ ex x5 = exp(5*Pi*I/3).evalf();
+
+ ex r5 = Li(lst(1,1,1,1),lst(x2,x4,x3,x0)).hold().evalf();
+ ex r6 = Li(lst(1,1,1,1),lst(x4,x2,x3,x0)).hold().evalf();
+ if ( abs(r5-conjugate(r6)) > prec ) {
+ clog << "Legacy test 4 seems to be wrong." << endl;
+ result++;
+ }
+
+ ex r7 = Li(lst(1,2,1),lst(x3,x2,x4)).hold().evalf()
+ +Li(lst(1,1,2),lst(x3,x2,x4)).hold().evalf()
+ +Li(lst(1,1,1,1),lst(x3,x0,x2,x4)).hold().evalf()
+ +Li(lst(1,1,1,1),lst(x3,x2,x0,x4)).hold().evalf()
+ +Li(lst(1,1,1,1),lst(x3,x2,x4,x0)).hold().evalf()
+ +Li(lst(1,2,1),lst(x2,x1,x0)).hold().evalf()
+ +Li(lst(1,1,2),lst(x2,x3,x4)).hold().evalf()
+ +Li(lst(1,1,1,1),lst(x2,x4,x3,x0)).hold().evalf()
+ +Li(lst(1,1,1,1),lst(x2,x3,x4,x0)).hold().evalf()
+ +Li(lst(1,1,1,1),lst(x2,x3,x0,x4)).hold().evalf()
+ +Li(lst(2,2),lst(x5,x4)).hold().evalf()
+ +Li(lst(2,1,1),lst(x5,x0,x4)).hold().evalf()
+ +Li(lst(2,1,1),lst(x5,x4,x0)).hold().evalf()
+ -Li(lst(1,1),lst(x3,x0)).hold().evalf()*Li(lst(1,1),lst(x2,x4)).hold().evalf();
+ if ( abs(r7) > prec ) {
+ clog << "Legacy test 5 seems to be wrong." << endl;
+ result++;
+ }
+
+ return result;
+}
+
+
unsigned exam_inifcns_nstdsums(void)
{
unsigned result = 0;
cout << "examining consistency of nestedsums functions" << flush;
- clog << "----------consistency of nestedsums functions:" << endl;
result += inifcns_test_zeta();
result += inifcns_test_S();
result += inifcns_test_HLi();
-
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
+ result += inifcns_test_LiG();
+ result += inifcns_test_legacy();
return result;
}
+
+int main(int argc, char** argv)
+{
+ return exam_inifcns_nstdsums();
+}
git://www.ginac.de / ginac.git / blobdiff