/** @file exam_powerlaws.cpp
*
* Tests for power laws. You shouldn't try to draw much inspiration from
* this code, it is a sanity check rather deeply rooted in GiNaC's classes. */
/*
* GiNaC Copyright (C) 1999-2007 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
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include "exams.h"
static unsigned exam_powerlaws1()
{
// (x^a)^b = x^(a*b)
symbol x("x");
symbol a("a");
symbol b("b");
ex e1 = power(power(x,a), b);
if (!(is_exactly_a<power>(e1) &&
is_exactly_a<power>(e1.op(0)) &&
is_exactly_a<symbol>(e1.op(0).op(0)) &&
is_exactly_a<symbol>(e1.op(0).op(1)) &&
is_exactly_a<symbol>(e1.op(1)) &&
e1.is_equal(power(power(x,a),b)) )) {
clog << "(x^a)^b, x,a,b symbolic wrong" << endl;
clog << "returned: " << e1 << endl;
return 1;
}
ex e2 = e1.subs(a==1);
if (!(is_exactly_a<power>(e2) &&
is_exactly_a<symbol>(e2.op(0)) &&
is_exactly_a<symbol>(e2.op(1)) &&
e2.is_equal(power(x,b)) )) {
clog << "(x^a)^b, x,b symbolic, a==1 wrong" << endl;
clog << "returned: " << e2 << endl;
return 1;
}
ex e3 = e1.subs(a==-1);
if (!(is_exactly_a<power>(e3) &&
is_exactly_a<power>(e3.op(0)) &&
is_exactly_a<symbol>(e3.op(0).op(0)) &&
is_exactly_a<numeric>(e3.op(0).op(1)) &&
is_exactly_a<symbol>(e3.op(1)) &&
e3.is_equal(power(power(x,-1),b)) )) {
clog << "(x^a)^b, x,b symbolic, a==-1 wrong" << endl;
clog << "returned: " << e3 << endl;
return 1;
}
ex e4 = e1.subs(lst(a==-1, b==2.5));
if (!(is_exactly_a<power>(e4) &&
is_exactly_a<power>(e4.op(0)) &&
is_exactly_a<symbol>(e4.op(0).op(0)) &&
is_exactly_a<numeric>(e4.op(0).op(1)) &&
is_exactly_a<numeric>(e4.op(1)) &&
e4.is_equal(power(power(x,-1),2.5)) )) {
clog << "(x^a)^b, x symbolic, a==-1, b==2.5 wrong" << endl;
clog << "returned: " << e4 << endl;
return 1;
}
ex e5 = e1.subs(lst(a==-0.9, b==2.5));
if (!(is_exactly_a<power>(e5) &&
is_exactly_a<symbol>(e5.op(0)) &&
is_exactly_a<numeric>(e5.op(1)) &&
e5.is_equal(power(x,numeric(-0.9)*numeric(2.5))) )) {
clog << "(x^a)^b, x symbolic, a==-0.9, b==2.5 wrong" << endl;
clog << "returned: " << e5 << endl;
return 1;
}
ex e6 = e1.subs(lst(a==numeric(3)+numeric(5.3)*I, b==-5));
if (!(is_exactly_a<power>(e6) &&
is_exactly_a<symbol>(e6.op(0)) &&
is_exactly_a<numeric>(e6.op(1)) &&
e6.is_equal(power(x,numeric(-15)+numeric(5.3)*numeric(-5)*I)) )) {
clog << "(x^a)^b, x symbolic, a==3+5.3*I, b==-5 wrong" << endl;
clog << "returned: " << e6 << endl;
return 1;
}
return 0;
}
static unsigned exam_powerlaws2()
{
// (a*x)^b = a^b * x^b
symbol x("x");
symbol a("a");
symbol b("b");
ex e1 = power(a*x,b);
if (!(is_exactly_a<power>(e1) &&
is_exactly_a<mul>(e1.op(0)) &&
(e1.op(0).nops()==2) &&
is_exactly_a<symbol>(e1.op(0).op(0)) &&
is_exactly_a<symbol>(e1.op(0).op(1)) &&
is_exactly_a<symbol>(e1.op(1)) &&
e1.is_equal(power(a*x,b)) )) {
clog << "(a*x)^b, x,a,b symbolic wrong" << endl;
clog << "returned: " << e1 << endl;
return 1;
}
ex e2 = e1.subs(a==3);
if (!(is_exactly_a<power>(e2) &&
is_exactly_a<mul>(e2.op(0)) &&
(e2.op(0).nops()==2) &&
is_exactly_a<symbol>(e2.op(0).op(0)) &&
is_exactly_a<numeric>(e2.op(0).op(1)) &&
is_exactly_a<symbol>(e2.op(1)) &&
e2.is_equal(power(3*x,b)) )) {
clog << "(a*x)^b, x,b symbolic, a==3 wrong" << endl;
clog << "returned: " << e2 << endl;
return 1;
}
ex e3 = e1.subs(b==-3);
if (!(is_exactly_a<mul>(e3) &&
(e3.nops()==2) &&
is_exactly_a<power>(e3.op(0)) &&
is_exactly_a<power>(e3.op(1)) &&
e3.is_equal(power(a,-3)*power(x,-3)) )) {
clog << "(a*x)^b, x,a symbolic, b==-3 wrong" << endl;
clog << "returned: " << e3 << endl;
return 1;
}
ex e4 = e1.subs(b==4.5);
if (!(is_exactly_a<power>(e4) &&
is_exactly_a<mul>(e4.op(0)) &&
(e4.op(0).nops()==2) &&
is_exactly_a<symbol>(e4.op(0).op(0)) &&
is_exactly_a<symbol>(e4.op(0).op(1)) &&
is_exactly_a<numeric>(e4.op(1)) &&
e4.is_equal(power(a*x,4.5)) )) {
clog << "(a*x)^b, x,a symbolic, b==4.5 wrong" << endl;
clog << "returned: " << e4 << endl;
return 1;
}
ex e5 = e1.subs(lst(a==3.2, b==3+numeric(5)*I));
if (!(is_exactly_a<mul>(e5) &&
(e5.nops()==2) &&
is_exactly_a<power>(e5.op(0)) &&
is_exactly_a<numeric>(e5.op(1)) &&
e5.is_equal(power(x,3+numeric(5)*I)*
power(numeric(3.2),3+numeric(5)*I)) )) {
clog << "(a*x)^b, x symbolic, a==3.2, b==3+5*I wrong" << endl;
clog << "returned: " << e5 << endl;
return 1;
}
ex e6 = e1.subs(lst(a==-3.2, b==3+numeric(5)*I));
if (!(is_exactly_a<mul>(e6) &&
(e6.nops()==2) &&
is_exactly_a<power>(e6.op(0)) &&
is_exactly_a<numeric>(e6.op(1)) &&
e6.is_equal(power(-x,3+numeric(5)*I)*
power(numeric(3.2),3+numeric(5)*I)) )) {
clog << "(a*x)^b, x symbolic, a==-3.2, b==3+5*I wrong" << endl;
clog << "returned: " << e6 << endl;
return 1;
}
ex e7 = e1.subs(lst(a==3+numeric(5)*I, b==3.2));
if (!(is_exactly_a<power>(e7) &&
is_exactly_a<mul>(e7.op(0)) &&
(e7.op(0).nops()==2) &&
is_exactly_a<symbol>(e7.op(0).op(0)) &&
is_exactly_a<numeric>(e7.op(0).op(1)) &&
is_exactly_a<numeric>(e7.op(1)) &&
e7.is_equal(power((3+numeric(5)*I)*x,3.2)) )) {
clog << "(a*x)^b, x symbolic, a==3+5*I, b==3.2 wrong" << endl;
clog << "returned: " << e7 << endl;
return 1;
}
return 0;
}
static unsigned exam_powerlaws3()
{
// numeric evaluation
ex e1 = power(numeric(4),numeric(1,2));
if (e1 != 2) {
clog << "4^(1/2) wrongly returned " << e1 << endl;
return 1;
}
ex e2 = power(numeric(27),numeric(2,3));
if (e2 != 9) {
clog << "27^(2/3) wrongly returned " << e2 << endl;
return 1;
}
ex e3 = power(numeric(5),numeric(1,2));
if (!(is_exactly_a<power>(e3) &&
e3.op(0).is_equal(numeric(5)) &&
e3.op(1).is_equal(numeric(1,2)))) {
clog << "5^(1/2) wrongly returned " << e3 << endl;
return 1;
}
ex e4 = power(numeric(5),evalf(numeric(1,2)));
if (!(is_exactly_a<numeric>(e4))) {
clog << "5^(0.5) wrongly returned " << e4 << endl;
return 1;
}
ex e5 = power(evalf(numeric(5)),numeric(1,2));
if (!(is_exactly_a<numeric>(e5))) {
clog << "5.0^(1/2) wrongly returned " << e5 << endl;
return 1;
}
return 0;
}
static unsigned exam_powerlaws4()
{
// test for mul::eval()
symbol a("a");
symbol b("b");
symbol c("c");
ex f1 = power(a*b,ex(1)/ex(2));
ex f2 = power(a*b,ex(3)/ex(2));
ex f3 = c;
exvector v;
v.push_back(f1);
v.push_back(f2);
v.push_back(f3);
ex e1 = mul(v);
if (e1!=a*a*b*b*c) {
clog << "(a*b)^(1/2)*(a*b)^(3/2)*c wrongly returned " << e1 << endl;
return 1;
}
return 0;
}
static unsigned exam_powerlaws5()
{
// cabinet of slightly pathological cases
symbol a("a");
ex e1 = pow(1,a);
if (e1 != 1) {
clog << "1^a wrongly returned " << e1 << endl;
return 1;
}
ex e2 = pow(0,a);
if (!(is_exactly_a<power>(e2))) {
clog << "0^a was evaluated to " << e2
<< " though nothing is known about a." << endl;
return 1;
}
return 0;
}
unsigned exam_powerlaws()
{
unsigned result = 0;
cout << "examining power laws" << flush;
clog << "----------power laws:" << endl;
result += exam_powerlaws1(); cout << '.' << flush;
result += exam_powerlaws2(); cout << '.' << flush;
result += exam_powerlaws3(); cout << '.' << flush;
result += exam_powerlaws4(); cout << '.' << flush;
result += exam_powerlaws5(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;
clog << "(no output)" << endl;
} else {
cout << " failed " << endl;
}
return result;
}
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