* this code, it is a sanity check rather deeply rooted in GiNaC's classes. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
#include "exams.h"
-static unsigned exam_powerlaws1(void)
+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_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;
+ // (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(void)
+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_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;
+ // (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(void)
+static unsigned exam_powerlaws3()
{
- // numeric evaluation
+ // 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;
+ 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(void)
+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;
+ // 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;
+}
- 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(void)
+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;
-
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
-
- return result;
+ 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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