--- /dev/null
+// check/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. */
+
+#include "ginac.h"
+
+static unsigned powerlaws1(void)
+{
+ // (x^a)^b = x^(a*b)
+
+ symbol x("x");
+ symbol a("a");
+ symbol b("b");
+
+ ex e1=power(power(x,a),b);
+ if (!(is_ex_exactly_of_type(e1,power) &&
+ is_ex_exactly_of_type(e1.op(0),power) &&
+ is_ex_exactly_of_type(e1.op(0).op(0),symbol) &&
+ is_ex_exactly_of_type(e1.op(0).op(1),symbol) &&
+ is_ex_exactly_of_type(e1.op(1),symbol) &&
+ 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_ex_exactly_of_type(e2,power) &&
+ is_ex_exactly_of_type(e2.op(0),symbol) &&
+ is_ex_exactly_of_type(e2.op(1),symbol) &&
+ 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_ex_exactly_of_type(e3,power) &&
+ is_ex_exactly_of_type(e3.op(0),power) &&
+ is_ex_exactly_of_type(e3.op(0).op(0),symbol) &&
+ is_ex_exactly_of_type(e3.op(0).op(1),numeric) &&
+ is_ex_exactly_of_type(e3.op(1),symbol) &&
+ 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_ex_exactly_of_type(e4,power) &&
+ is_ex_exactly_of_type(e4.op(0),power) &&
+ is_ex_exactly_of_type(e4.op(0).op(0),symbol) &&
+ is_ex_exactly_of_type(e4.op(0).op(1),numeric) &&
+ is_ex_exactly_of_type(e4.op(1),numeric) &&
+ 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_ex_exactly_of_type(e5,power) &&
+ is_ex_exactly_of_type(e5.op(0),symbol) &&
+ is_ex_exactly_of_type(e5.op(1),numeric) &&
+ 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_ex_exactly_of_type(e6,power) &&
+ is_ex_exactly_of_type(e6.op(0),symbol) &&
+ is_ex_exactly_of_type(e6.op(1),numeric) &&
+ 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 powerlaws2(void)
+{
+ // (a*x)^b = a^b * x^b
+
+ symbol x("x");
+ symbol a("a");
+ symbol b("b");
+
+ ex e1=power(a*x,b);
+ if (!(is_ex_exactly_of_type(e1,power) &&
+ is_ex_exactly_of_type(e1.op(0),mul) &&
+ (e1.op(0).nops()==2) &&
+ is_ex_exactly_of_type(e1.op(0).op(0),symbol) &&
+ is_ex_exactly_of_type(e1.op(0).op(1),symbol) &&
+ is_ex_exactly_of_type(e1.op(1),symbol) &&
+ 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_ex_exactly_of_type(e2,power) &&
+ is_ex_exactly_of_type(e2.op(0),mul) &&
+ (e2.op(0).nops()==2) &&
+ is_ex_exactly_of_type(e2.op(0).op(0),symbol) &&
+ is_ex_exactly_of_type(e2.op(0).op(1),numeric) &&
+ is_ex_exactly_of_type(e2.op(1),symbol) &&
+ 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_ex_exactly_of_type(e3,mul) &&
+ (e3.nops()==2) &&
+ is_ex_exactly_of_type(e3.op(0),power) &&
+ is_ex_exactly_of_type(e3.op(1),power) &&
+ 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_ex_exactly_of_type(e4,power) &&
+ is_ex_exactly_of_type(e4.op(0),mul) &&
+ (e4.op(0).nops()==2) &&
+ is_ex_exactly_of_type(e4.op(0).op(0),symbol) &&
+ is_ex_exactly_of_type(e4.op(0).op(1),symbol) &&
+ is_ex_exactly_of_type(e4.op(1),numeric) &&
+ 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_ex_exactly_of_type(e5,mul) &&
+ (e5.nops()==2) &&
+ is_ex_exactly_of_type(e5.op(0),power) &&
+ is_ex_exactly_of_type(e5.op(1),numeric) &&
+ 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_ex_exactly_of_type(e6,mul) &&
+ (e6.nops()==2) &&
+ is_ex_exactly_of_type(e6.op(0),power) &&
+ is_ex_exactly_of_type(e6.op(1),numeric) &&
+ 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_ex_exactly_of_type(e7,power) &&
+ is_ex_exactly_of_type(e7.op(0),mul) &&
+ (e7.op(0).nops()==2) &&
+ is_ex_exactly_of_type(e7.op(0).op(0),symbol) &&
+ is_ex_exactly_of_type(e7.op(0).op(1),numeric) &&
+ is_ex_exactly_of_type(e7.op(1),numeric) &&
+ 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 powerlaws3(void)
+{
+ // numeric evaluation
+
+ ex e1=power(numeric(4),numeric(1)/numeric(2));
+ if (e1 != 2) {
+ clog << "4^(1/2) wrongly returned " << e1 << endl;
+ return 1;
+ }
+
+ ex e2=power(numeric(27),numeric(2)/numeric(3));
+ if (e2 != 9) {
+ clog << "27^(2/3) wrongly returned " << e2 << endl;
+ return 1;
+ }
+
+ ex e3=power(numeric(5),numeric(1)/numeric(2));
+ if (!(is_ex_exactly_of_type(e3,power) &&
+ e3.op(0).is_equal(numeric(5)) &&
+ e3.op(1).is_equal(numeric(1)/numeric(2)) )) {
+ clog << "5^(1/2) wrongly returned " << e3 << endl;
+ return 1;
+ }
+
+ ex e4=power(numeric(5),evalf(numeric(1)/numeric(2)));
+ if (!(is_ex_exactly_of_type(e4,numeric))) {
+ clog << "5^(0.5) wrongly returned " << e4 << endl;
+ return 1;
+ }
+
+ ex e5=power(evalf(numeric(5)),numeric(1)/numeric(2));
+ if (!(is_ex_exactly_of_type(e5,numeric))) {
+ clog << "5.0^(1/2) wrongly returned " << e5 << endl;
+ return 1;
+ }
+
+ return 0;
+}
+
+static unsigned powerlaws4(void)
+{
+ // 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;
+}
+
+unsigned powerlaws(void)
+{
+ unsigned result = 0;
+
+ cout << "checking power laws..." << flush;
+ clog << "---------power laws:" << endl;
+
+ result += powerlaws1();
+ result += powerlaws2();
+ result += powerlaws3();
+ result += powerlaws4();
+
+ if (!result) {
+ cout << " passed ";
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed ";
+ }
+ return result;
+}
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