X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_paranoia.cpp;h=b5f1260816be3cd2c2249d919a56d56d8ebf5126;hp=2c6fe6ae627557f450fe8ea4dfd680bbc7fae628;hb=452e51c8a3b84c368ae3ba2e60dacbc1985e7b5c;hpb=db5765dc91202851739e196ba11bfccb0b3fe7bc

diff --git a/check/exam_paranoia.cpp b/check/exam_paranoia.cpp
index 2c6fe6ae..b5f12608 100644
--- a/check/exam_paranoia.cpp
+++ b/check/exam_paranoia.cpp
@@ -1,12 +1,12 @@
 /** @file exam_paranoia.cpp
  *
  *  This set of tests checks for some of GiNaC's oopses which showed up during
- *  development.  Things were evaluated wrongly and so.  Such a sick behaviour
+ *  development.  Things were evaluated wrongly and so.  Such a sick behavior
  *  shouldn't occur any more.  But we are paranoic and we want to exclude these
  *  these oopses for good, so we run those stupid tests... */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2019 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
@@ -20,211 +20,187 @@
  *
  *  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 "ginac.h"
+using namespace GiNaC;
+
+#include <iostream>
+using namespace std;
 
 // The very first pair of historic problems had its roots in power.cpp and was
 // finally resolved on April 27th 1999. (Fixing the first on April 23rd
 // actually introduced the second.)
-static unsigned exam_paranoia1(void)
+static unsigned exam_paranoia1()
 {
-    unsigned result = 0;
-    symbol x("x"), y("y"), z("z");
-    ex e, f, g;
-
-    e = x * y * z;
-    f = y * z;
-    g = e / f;
-
-    // In the first one expand did not do any job at all:
-    if (!g.expand().is_equal(x)) {
-        clog << "e = x*y*z; f = y*z; expand(e/f) erroneously returned "
-             << g.expand() << endl;
-        ++result;
-    }
-
-    // This one somehow used to return 0:
-    e = pow(x + 1, -1);
-    if (!e.expand().is_equal(e)) {
-        clog << "expand(pow(x + 1, -1)) erroneously returned "
-             << e.expand() << endl;
-        ++result;
-    }
-
-    return result;
+	unsigned result = 0;
+	symbol x("x"), y("y"), z("z");
+	ex e, f, g;
+
+	e = x * y * z;
+	f = y * z;
+	g = e / f;
+
+	// In the first one expand did not do any job at all:
+	if (!g.expand().is_equal(x)) {
+		clog << "e = x*y*z; f = y*z; expand(e/f) erroneously returned "
+		     << g.expand() << endl;
+		++result;
+	}
+
+	// This one somehow used to return 0:
+	e = pow(x + 1, -1);
+	if (!e.expand().is_equal(e)) {
+		clog << "expand(pow(x + 1, -1)) erroneously returned "
+		     << e.expand() << endl;
+		++result;
+	}
+
+	return result;
 }
 
 // And here the second oops which showed up until May 17th 1999.  It had to do
 // with lexicographic canonicalization and thus showed up only if the variables
 // had the names as given here:
-static unsigned exam_paranoia2(void)
+static unsigned exam_paranoia2()
 {
-    unsigned result = 0;
-    symbol x("x"), y("y"), z("z");
-    ex e, f, g;
-
-    e = x + z*x;
-    f = e*y;
-    g = f - e*y;
-
-    // After .expand(), g should be zero:
-    if (!g.expand().is_zero()) {
-        clog << "e = (x + z*x); f = e*y; expand(f - e*y) erroneously returned "
-             << g.expand() << endl;
-        ++result;
-    }
-    // After .eval(), g should be zero:
-    if (!g.eval().is_zero()) {
-        clog << "e = (x + z*x); f = e*y; eval(f - e*y) erroneously returned "
-             << g.eval() << endl;
-        ++result;
-    }
-    // This actually worked already back in April 1999.
-    // But we are *very* paranoic!
-    if (!g.expand().eval().is_zero()) {
-        clog << "e = (x + z*x); f = e*y; eval(expand(f - e*y)) erroneously returned "
-             << g.expand().eval() << endl;
-        ++result;
-    }
-
-    return result;
+	unsigned result = 0;
+	symbol x("x"), y("y"), z("z");
+	ex e, f, g;
+
+	e = x + z*x;
+	f = e*y;
+	g = f - e*y;
+
+	// After .eval(), g should be zero:
+	if (!g.is_zero()) {
+		clog << "e = (x + z*x); f = e*y; g = (f - e*y) erroneously returned g == "
+		     << g << endl;
+		++result;
+	}
+
+	return result;
 }
 
 // The third bug was introduced on May 18th 1999, discovered on May 19 and
 // fixed that same day.  It worked when x was substituted by 1 but not with
 // other numbers:
-static unsigned exam_paranoia3(void)
+static unsigned exam_paranoia3()
 {
-    unsigned result = 0;
-    symbol x("x"), y("y");
-    ex e, f;
-
-    e = x*y - y;
-    f = e.subs(x == 2);
-
-    if (!f.is_equal(y)) {
-        clog << "e = x*y - y; f = e.subs(x == 2) erroneously returned "
-             << f << endl;
-        ++result;
-    }
-    if (!f.eval().is_equal(y)) {
-        clog << "e = x*y - y; eval(e.subs(x == 2)) erroneously returned "
-             << f.eval() << endl;
-        ++result;
-    }
-    if (!f.expand().is_equal(y)) {
-        clog << "e = x*y - y; expand(e.subs(x == 2)) erroneously returned "
-             << f.expand() << endl;
-        ++result;
-    }
-
-    return result;
+	unsigned result = 0;
+	symbol x("x"), y("y");
+	ex e, f;
+
+	e = x*y - y;
+	f = e.subs(x == 2);
+
+	if (!f.is_equal(y)) {
+		clog << "e = x*y - y; f = e.subs(x == 2) erroneously returned "
+		     << f << endl;
+		++result;
+	}
+
+	return result;
 }
 
 // The fourth bug was also discovered on May 19th 1999 and fixed immediately:
-static unsigned exam_paranoia4(void)
+static unsigned exam_paranoia4()
 {
-    unsigned result = 0;
-    symbol x("x");
-    ex e, f, g;
-
-    e = pow(x, 2) + x + 1;
-    f = pow(x, 2) + x + 1;
-    g = e - f;
-
-    if (!g.is_zero()) {
-        clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g erroneously returned "
-             << g << endl;
-        ++result;
-    }
-    if (!g.is_zero()) {
-        clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g.eval() erroneously returned "
-             << g.eval() << endl;
-        ++result;
-    }
-
-    return result;
+	unsigned result = 0;
+	symbol x("x");
+	ex e, f, g;
+
+	e = pow(x, 2) + x + 1;
+	f = pow(x, 2) + x + 1;
+	g = e - f;
+
+	if (!g.is_zero()) {
+		clog << "e = pow(x,2) + x + 1; f = pow(x,2) + x + 1; g = e-f; g erroneously returned "
+		     << g << endl;
+		++result;
+	}
+
+	return result;
 }
 
 // The fifth oops was discovered on May 20th 1999 and fixed a day later:
-static unsigned exam_paranoia5(void)
+static unsigned exam_paranoia5()
 {
-    unsigned result = 0;
-    symbol x("x"), y("y");
+	unsigned result = 0;
+	symbol x("x"), y("y");
 
-    ex e, f;
-    e = pow(x*y + 1, 2);
-    f = pow(x, 2) * pow(y, 2) + 2*x*y + 1;
+	ex e, f;
+	e = pow(x*y + 1, 2);
+	f = pow(x, 2) * pow(y, 2) + 2*x*y + 1;
 
-    if (!(e-f).expand().is_zero()) {
-        clog << "e = pow(x*y+1,2); f = pow(x,2)*pow(y,2) + 2*x*y + 1; (e-f).expand() erroneously returned "
-             << (e-f).expand() << endl;
-        ++result;
-    }
+	if (!(e-f).expand().is_zero()) {
+		clog << "e = pow(x*y+1,2); f = pow(x,2)*pow(y,2) + 2*x*y + 1; (e-f).expand() erroneously returned "
+		     << (e-f).expand() << endl;
+		++result;
+	}
 
-    return result;
+	return result;
 }
 
 // This one was discovered on Jun 1st 1999 and fixed the same day:
-static unsigned exam_paranoia6(void)
+static unsigned exam_paranoia6()
 {
-    unsigned result = 0;
-    symbol x("x");
-
-    ex e, f;
-    e = pow(x, -5);
-    f = e.denom();
-
-    if (!f.is_equal(pow(x, 5))) {
-        clog << "e = pow(x, -5); f = e.denom(); f was " << f << " (should be x^5)" << endl;
-        ++result;
-    }
-    return result;
+	unsigned result = 0;
+	symbol x("x");
+
+	ex e, f;
+	e = pow(x, -5);
+	f = e.denom();
+
+	if (!f.is_equal(pow(x, 5))) {
+		clog << "e = pow(x, -5); f = e.denom(); f was " << f << " (should be x^5)" << endl;
+		++result;
+	}
+	return result;
 }
 
 // This one was introduced on June 1st 1999 by some aggressive manual
 // optimization. Discovered and fixed on June 2nd.
-static unsigned exam_paranoia7(void)
+static unsigned exam_paranoia7()
 {
-    unsigned result = 0;
-    symbol x("x"), y("y");
-
-    ex e = y + y*x + 2;
-    ex f = expand(pow(e, 2) - (e*y*(x + 1)));
-
-    if (f.nops() > 3) {
-        clog << "e=y+y*x+2; f=expand(pow(e,2)-(e*y*(x+1))) has "
-             << f.nops() << " arguments instead of 3 ( f=="
-             << f << " )" << endl;
-        ++result;
-    }
-    return result;
+	unsigned result = 0;
+	symbol x("x"), y("y");
+
+	ex e = y + y*x + 2;
+	ex f = expand(pow(e, 2) - (e*y*(x + 1)));
+
+	if (f.nops() > 3) {
+		clog << "e=y+y*x+2; f=expand(pow(e,2)-(e*y*(x+1))) has "
+		     << f.nops() << " arguments instead of 3 ( f=="
+		     << f << " )" << endl;
+		++result;
+	}
+	return result;
 }
 
 // This one was a result of the rewrite of mul::max_coefficient when we
 // introduced the overall_coefficient field in expairseq objects on Oct 1st
 // 1999. Fixed on Oct 4th.
-static unsigned exam_paranoia8(void)
+static unsigned exam_paranoia8()
 {
-    unsigned result = 0;
-    symbol x("x");
-
-    ex e = -x / (x+1);
-    ex f;
-    
-    try {
-        f = e.normal();
-        if (!f.is_equal(e)) {
-            clog << "normal(-x/(x+1)) returns " << f << " instead of -x/(x+1)\n";
-            ++result;
-        }
-    } catch (const exception &err) {
-        clog << "normal(-x/(x+1) throws " << err.what() << endl;
-        ++result;
-    }
-    return result;
+	unsigned result = 0;
+	symbol x("x");
+
+	ex e = -x / (x+1);
+	ex f;
+	
+	try {
+		f = e.normal();
+		if (!f.is_equal(e)) {
+			clog << "normal(-x/(x+1)) returns " << f << " instead of -x/(x+1)\n";
+			++result;
+		}
+	} catch (const exception &err) {
+		clog << "normal(-x/(x+1) throws " << err.what() << endl;
+		++result;
+	}
+	return result;
 }
 
 // This one was a result of a modification to frac_cancel() & Co. to avoid
@@ -232,81 +208,81 @@ static unsigned exam_paranoia8(void)
 // Z[X]. multiply_lcm() forgot to multiply the x-linear term with the LCM of
 // the coefficient's denominators (2 in this case).  Introduced on Jan 25th
 // 2000 and fixed on Jan 31th.
-static unsigned exam_paranoia9(void)
+static unsigned exam_paranoia9()
 {
-    unsigned result = 0;
-    symbol x("x");
+	unsigned result = 0;
+	symbol x("x");
 
-    ex e = (exp(-x)-2*x*exp(-x)+pow(x,2)/2*exp(-x))/exp(-x);
-    ex f = e.normal();
+	ex e = (exp(-x)-2*x*exp(-x)+pow(x,2)/2*exp(-x))/exp(-x);
+	ex f = e.normal();
 
-    if (!f.is_equal(1-2*x+pow(x,2)/2)) {
-        clog << "normal(" << e << ") returns " << f << " instead of 1-2*x+1/2*x^2\n";
-        ++result;
-    }
-    return result;
+	if (!f.is_equal(1-2*x+pow(x,2)/2)) {
+		clog << "normal(" << e << ") returns " << f << " instead of 1-2*x+1/2*x^2\n";
+		++result;
+	}
+	return result;
 }
 
 // I have no idea when this broke.  It has been working long ago, before 0.4.0
 // and on Feb 13th 2000 I found out that things like 2^(3/2) throw an exception
 // "power::eval(): pow(0,0) is undefined" instead of simplifying to 2*2^(1/2).
 // It was fixed that same day.
-static unsigned exam_paranoia10(void)
+static unsigned exam_paranoia10()
 {
-    unsigned result = 0;
-    
-    ex b = numeric(2);
-    ex e = numeric(3,2);
-    ex r;
-    
-    try {
-        r = pow(b,e).eval();
-        if (!(r-2*sqrt(ex(2))).is_zero()) {
-            clog << "2^(3/2) erroneously returned " << r << " instead of 2*sqrt(2)" << endl;
-            ++result;
-        }
-    } catch (const exception &err) {
-        clog << "2^(3/2) throws " << err.what() << endl;
-        ++result;
-    }
-    return result;
+	unsigned result = 0;
+	
+	ex b = numeric(2);
+	ex e = numeric(3,2);
+	ex r;
+	
+	try {
+		r = pow(b, e);
+		if (!(r-2*sqrt(ex(2))).is_zero()) {
+			clog << "2^(3/2) erroneously returned " << r << " instead of 2*sqrt(2)" << endl;
+			++result;
+		}
+	} catch (const exception &err) {
+		clog << "2^(3/2) throws " << err.what() << endl;
+		++result;
+	}
+	return result;
 }
 
 // After the rewriting of basic::normal() & Co. to return {num, den} lists,
 // add::normal() forgot to multiply the denominator of the overall_coeff of
 // its expanded and normalized children with the denominator of the expanded
 // child (did you get this? Well, never mind...). Fixed on Feb 21th 2000.
-static unsigned exam_paranoia11(void)
+static unsigned exam_paranoia11()
 {
-    unsigned result = 0;
+	unsigned result = 0;
 	symbol x("x");
 
 	ex e = ((-5-2*x)-((2-5*x)/(-2+x))*(3+2*x))/(5-4*x);
 	ex f = e.normal();
-	ex d = (4+10*x+8*pow(x,2))/(x-2)/(5-4*x);
+	ex d = normal((4+10*x+8*pow(x,2))/(x-2)/(5-4*x));
 
 	if (!(f - d).expand().is_zero()) {
 		clog << "normal(" << e << ") returns " << f << " instead of " << d << endl;
 		++result;
 	}
-    return result;
+	return result;
 }
 
 // This one returned 0 because add::normal() incorrectly assumed that if the
 // common denominator is 1, all the denominators would be 1 (they can in fact
 // be +/-1). Fixed on Aug 2nd 2000.
-static unsigned exam_paranoia12(void)
+static unsigned exam_paranoia12()
 {
-    unsigned result = 0;
+	unsigned result = 0;
 	symbol x("x");
-
+	
 	ex e = 2-2*(1+x)/(-1-x);
 	ex f = e.normal();
 	ex d = 4;
-
+	
 	if (!(f - d).expand().is_zero()) {
 		clog << "normal(" << e << ") returns " << f
-             << " instead of " << d << endl;
+		     << " instead of " << d << endl;
 		++result;
 	}
 	return result;
@@ -314,55 +290,389 @@ static unsigned exam_paranoia12(void)
 
 // This one caused a division by 0 because heur_gcd() didn't check its
 // input polynomials against 0. Fixed on Aug 4th 2000.
-static unsigned exam_paranoia13(void)
+static unsigned exam_paranoia13()
 {
-    unsigned result = 0;
+	unsigned result = 0;
 	symbol a("a"), b("b"), c("c");
-    
+	
 	ex e = (b*a-c*a)/(4-a);
 	ex d = (c*a-b*a)/(a-4);
-    
-    try {
-        ex f = e.normal();    
-        if (!(f - d).expand().is_zero()) {
-            clog << "normal(" << e << ") returns " << f
-                 << " instead of " << d << endl;
-            ++result;
-        }
-    } catch (const exception &err) {
-        clog << "normal(" << e << ") throws " << err.what() << endl;
-        ++result;
-    }
+	
+	try {
+		ex f = e.normal();	
+		if (!(f - d).expand().is_zero()) {
+			clog << "normal(" << e << ") returns " << f
+			     << " instead of " << d << endl;
+			++result;
+		}
+	} catch (const exception &err) {
+		clog << "normal(" << e << ") throws " << err.what() << endl;
+		++result;
+	}
+	return result;
+}
+
+// A bug introduced on July 19, 2001. quo() and rem() would sometimes call
+// vector::reserve() with a negative argument. Fixed on Dec 20, 2001.
+static unsigned exam_paranoia14()
+{
+	unsigned result = 0;
+	symbol x("x");
+
+	ex q = quo(1, pow(x, 3), x);
+	if (!q.is_zero()) {
+		clog << "quo(1,x^3,x) erroneously returned " << q << " instead of 0\n";
+		++result;
+	}
+
+	return result;
+}
+
+// Under certain conditions, power::expand_add_2() could produce non-canonical
+// numeric expairs. Fixed on Oct 24, 2002.
+static unsigned exam_paranoia15()
+{
+	unsigned result = 0;
+
+	ex q = (pow(pow(2, numeric(1, 2))*2+1, 2)).expand();
+	// this used to produce "1+4*sqrt(2)+4*2" which would never evaluate
+	// to "9+4*sqrt(2)"
+
+	if (!(q-9-4*pow(2, numeric(1, 2))).is_zero()) {
+		clog << "expand((sqrt(2)*2+1)^2) erroneously returned " << q << " instead of 9-4*sqrt(2)\n";
+		++result;
+	}
+
+	return result;
+}
+
+// Expanding products containing powers of sums could return results that
+// were not fully expanded. Fixed on Dec 10, 2003.
+static unsigned exam_paranoia16()
+{
+	unsigned result = 0;
+	symbol a("a"), b("b"), c("c"), d("d"), e("e");
+	ex e1, e2, e3;
+
+	e1 = pow(1+a*sqrt(b+c), 2);
+	e2 = e1.expand();
+
+	if (e2.has(pow(a, 2)*(b+c))) {
+		clog << "expand(" << e1 << ") didn't fully expand\n";
+		++result;
+	}
+
+	e1 = (d*sqrt(a+b)+a*sqrt(c+d))*(b*sqrt(a+b)+a*sqrt(c+d));
+	e2 = e1.expand();
+
+	if (e2.has(pow(a, 2)*(c+d))) {
+		clog << "expand(" << e1 << ") didn't fully expand\n";
+		++result;
+	}
+
+	e1 = (a+sqrt(b+c))*sqrt(b+c)*(d+sqrt(b+c));
+	e2 = e1.expand();
+
+	if (e2.has(a*(b+c))) {
+		clog << "expand(" << e1 << ") didn't fully expand\n";
+		++result;
+	}
+
+	e1 = pow(sqrt(a+b)+sqrt(c+d), 3);
+	e2 = e1.expand();
+
+	if (e2.has(3*(a+b)*sqrt(c+d)) || e2.has(3*(c+d)*sqrt(a+b))) {
+		clog << "expand(" << e1 << ") didn't fully expand\n";
+		++result;
+	}
+
+	e1 = a*(b+c*(d+e));
+	e2 = e1.expand();
+
+	if (e2.has(c*(d+e))) {
+		clog << "expand(" << e1 << ") didn't fully expand\n";
+		++result;
+	}
+
+	e1 = 2*pow(1+a, 2)/a;
+	e2 = e1.expand();
+
+	if (e2.has(pow(a, 2))) {
+		clog << "expand(" << e1 << ") didn't fully expand\n";
+		++result;
+	}
+
+	e1 = a*(a+b);
+	e2 = pow(pow(e1, -1), -1);
+
+	if (e2.has(a*b)) {
+		clog << "double reciprocal expanded where it should not\n";
+		++result;
+	}
+
+	return result;
+}
+
+// Bug in reposition_dummy_indices() could result in correct expression
+// turned into one with inconsistent indices. Fixed on Aug 29, 2006
+static unsigned exam_paranoia17()
+{
+	varidx mu1(symbol("mu1"), 4);
+	varidx mu2(symbol("mu2"), 4);
+	varidx mu3(symbol("mu3"), 4);
+	varidx mu4(symbol("mu4"), 4);
+	varidx mu5(symbol("mu5"), 4);
+	varidx mu6(symbol("mu6"), 4);
+
+	exvector ev2;
+	ev2.push_back(mu3.toggle_variance());
+	ev2.push_back(mu6);
+	ev2.push_back(mu5.toggle_variance());
+	ev2.push_back(mu6.toggle_variance());
+	ev2.push_back(mu5);
+	ev2.push_back(mu3); 
+	// notice: all indices are contracted ...
+
+	ex test_cycl = indexed(symbol("A"), sy_cycl(), ev2);
+	test_cycl = test_cycl.simplify_indexed();
+	// ... so there should be zero free indices in the end.
+	return test_cycl.get_free_indices().size();
+}
+
+// Bug in add::eval() could result in numeric terms not being collected into
+// the overall coefficient. Fixed first on Sep 22, 2010 and again on Dec 17 2015
+static unsigned exam_paranoia18()
+{
+	unsigned result = 0;
+
+	ex sqrt2 = sqrt(ex(2));
+	ex e1 = 1 + 2*(sqrt2+1)*(sqrt2-1);
+	if (e1.real_part() != 3) {
+		clog << "real_part(1+2*(sqrt(2)+1)*(sqrt(2)-1)) failed to evaluate to 3\n";
+		++result;
+	}
+
+	ex sqrt3 = sqrt(ex(3));
+	ex e2 = 2 + 2*(sqrt2+1)*(sqrt2-1) - 2*(sqrt3+1)*(sqrt3-1);
+	if (e2.real_part() != 0) {
+		clog << "real_part(2+2*(sqrt(2)+1)*(sqrt(2)-1)-3*(sqrt(3)+1)*(sqrt(3)-1)) failed to evaluate to 0\n";
+		++result;
+	}
+
+	return result;
+}
+
+// Bug in mul::conjugate when factors are evaluated at branch cuts, reported as
+// Sage bug #10964.
+static unsigned exam_paranoia19()
+{
+	symbol a("a");
+	ex e = conjugate(a*sqrt(ex(-2))*sqrt(ex(-3)));
+	ex c = a*conjugate(sqrt(ex(-2)))*conjugate(sqrt(ex(-3)));
+	if (!subs(e-c, a==42).is_zero()) {
+		clog << "subs(a*conjugate(sqrt(-2))*conjugate(sqrt(-3))-conjugate(a*sqrt(-2)*sqrt(-3)),a==42) failed to evaluate to 0\n";
+		return 1;
+	}
+	return 0;
+}
+
+// Bugs in is_polynomial (fixed 2011-05-20 and 2014-07-26).
+static unsigned exam_paranoia20()
+{
+	unsigned result = 0;
+	symbol x("x"), y("y");
+	ex e1 = sqrt(x*x+1)*sqrt(x+1);
+	if (e1.is_polynomial(x)) {
+		clog << "sqrt(x*x+1)*sqrt(x+1) is wrongly reported to be a polynomial in x\n";
+		++result;
+	}
+	ex e2 = sqrt(Pi)*x;
+	if (!e2.is_polynomial(x)) {
+		clog << "sqrt(Pi)*x is wrongly reported to be no polynomial in x\n";
+		++result;
+	}
+	ex e3 = sqrt(x);
+	if (!e3.is_polynomial(y)) {
+		clog << "sqrt(x) is wrongly reported to be no polynomial in y\n";
+		++result;
+	}
+	ex e4 = (1+y)/(2+x);
+	if (e4.is_polynomial(x)) {
+		clog << "(1+y)/(2+x) is wrongly reported to be a polynomial in x\n";
+		++result;
+	}
+	return result;
+}
+
+static unsigned is_polynomial_false_positive()
+{
+	unsigned result = 0;
+	symbol x("x"), n("n");
+	exvector nonpoly_exprs;
+	nonpoly_exprs.push_back(1/(1-x));
+	nonpoly_exprs.push_back(1/(x+1));
+	nonpoly_exprs.push_back(-1/(x-1));
+	nonpoly_exprs.push_back(1/(1-x*x));
+	nonpoly_exprs.push_back(1/(1-pow(x,n)));
+	nonpoly_exprs.push_back(x-1/(x-1));
+	for (exvector::const_iterator ep = nonpoly_exprs.begin();
+	     ep != nonpoly_exprs.end(); ++ep) {
+		if (ep->is_polynomial(x)) {
+			clog << "(" << *ep << ").is_polynomial(" << x << ") "
+			        "erroneously returned true" << endl;
+			++result;
+		}
+	}
+	return result;
+}
+
+// Bug in power::expand reported by Isuru Fernando (fixed 2015-05-07).
+static unsigned exam_paranoia21()
+{
+	symbol x("x");
+	ex e = pow(x + sqrt(ex(2))*x, 2).expand();
+	if (e.nops() != 2) {
+		clog << "(x+sqrt(2)*x)^2 was wrongly expanded to " << e << "\n";
+		return 1;
+	}
+	return 0;
+}
+
+// Bug in power::expand (fixed 2015-07-18).
+static unsigned exam_paranoia22()
+{
+	symbol x("x"), y("y");
+	ex e = pow(sqrt(1+x)+y*sqrt(1+x), 2).expand();
+	if (e.nops() != 6) {
+		clog << "(sqrt(1+x)+y*sqrt(1+x))^2 was wrongly expanded to " << e << "\n";
+		return 1;
+	}
+	return 0;
+}
+
+// Bug in expairseq::evalchildren().
+static unsigned exam_paranoia23()
+{
+	unsigned result = 0;
+	symbol x("x");
+
+	epvector v1;
+	v1.push_back(expair(1, 1));
+	v1.push_back(expair(2*x, -1));
+	ex e1 = add(v1);  // Should be e==1-2*x,
+	if (!e1.is_equal(1-2*x)) {
+		clog << "Failure constructing " << e1 << " from add.\n";
+		++result;
+	}
+
+	epvector v2;
+	v2.push_back(expair(x, 1));
+	v2.push_back(expair(1,-1));
+	ex e2 = mul(v2);  // Should be e==x;
+	if (!e2.is_equal(x)) {
+		clog << "Failure constructing " << e2 << " from mul.\n";
+		++result;
+	}
+
+	return result;
+}
+
+// Bug in sqrfree_yun (fixed 2016-02-02).
+static unsigned exam_paranoia24()
+{
+	unsigned result = 0;
+	symbol x("x");
+	ex e;
+
+	e = (x-1)*(x+1) - x*x + 1;  // an unexpanded 0...
+	try {
+		ex f = sqrfree(e);
+		if (!f.is_zero()) {
+			clog << "sqrfree(" << e << ") returns " << f << " instead of 0\n";
+			++result;
+		}
+	} catch (const exception &err) {
+		clog << "sqrfree(" << e << ") throws " << err.what() << endl;
+		++result;
+	}
+
+	e = pow(x-1,3) - expand(pow(x-1,3));  // ...still after differentiating...
+	try {
+		ex f = sqrfree(e);
+		if (!f.is_zero()) {
+			clog << "sqrfree(" << e << ") returns " << f << " instead of 0\n";
+			++result;
+		}
+	} catch (const exception &err) {
+		clog << "sqrfree(" << e << ") throws " << err.what() << endl;
+		++result;
+	}
+
+	e = pow(x-1,4) - expand(pow(x-1,4));  // ...and after differentiating twice.
+	try {
+		ex f = sqrfree(e);
+		if (!f.is_zero()) {
+			clog << "sqrfree(" << e << ") returns " << f << " instead of 0\n";
+			++result;
+		}
+	} catch (const exception &err) {
+		clog << "sqrfree(" << e << ") throws " << err.what() << endl;
+		++result;
+	}
+
+	return result;
+}
+
+// Bug in add ctor
+unsigned exam_paranoia25()
+{
+	symbol a("a"), b("b"), c("c");
+	ex e = -a + 2*b + c;
+
+	if (e.diff(c).nops() > 1) {
+		clog << "diff(" << e << ",c) was not fully evaluated.\n";
+		return 1;
+	}
+	return 0;
+}
+
+unsigned exam_paranoia()
+{
+	unsigned result = 0;
+	
+	cout << "examining several historic failures just out of paranoia" << flush;
+	
+	result += exam_paranoia1();  cout << '.' << flush;
+	result += exam_paranoia2();  cout << '.' << flush;
+	result += exam_paranoia3();  cout << '.' << flush;
+	result += exam_paranoia4();  cout << '.' << flush;
+	result += exam_paranoia5();  cout << '.' << flush;
+	result += exam_paranoia6();  cout << '.' << flush;
+	result += exam_paranoia7();  cout << '.' << flush;
+	result += exam_paranoia8();  cout << '.' << flush;
+	result += exam_paranoia9();  cout << '.' << flush;
+	result += exam_paranoia10();  cout << '.' << flush;
+	result += exam_paranoia11();  cout << '.' << flush;
+	result += exam_paranoia12();  cout << '.' << flush;
+	result += exam_paranoia13();  cout << '.' << flush;
+	result += exam_paranoia14();  cout << '.' << flush;
+	result += exam_paranoia15();  cout << '.' << flush;
+	result += exam_paranoia16();  cout << '.' << flush;
+	result += exam_paranoia17();  cout << '.' << flush;
+	result += exam_paranoia18();  cout << '.' << flush;
+	result += exam_paranoia19();  cout << '.' << flush;
+	result += exam_paranoia20();  cout << '.' << flush;
+	result += is_polynomial_false_positive(); cout << '.' << flush;
+	result += exam_paranoia21();  cout << '.' << flush;
+	result += exam_paranoia22();  cout << '.' << flush;
+	result += exam_paranoia23();  cout << '.' << flush;
+	result += exam_paranoia24();  cout << '.' << flush;
+	result += exam_paranoia25();  cout << '.' << flush;
+	
 	return result;
 }
 
-unsigned exam_paranoia(void)
+int main(int argc, char** argv)
 {
-    unsigned result = 0;
-    
-    cout << "examining several historic failures just out of paranoia" << flush;
-    clog << "----------several historic failures:" << endl;
-    
-    result += exam_paranoia1();  cout << '.' << flush;
-    result += exam_paranoia2();  cout << '.' << flush;
-    result += exam_paranoia3();  cout << '.' << flush;
-    result += exam_paranoia4();  cout << '.' << flush;
-    result += exam_paranoia5();  cout << '.' << flush;
-    result += exam_paranoia6();  cout << '.' << flush;
-    result += exam_paranoia7();  cout << '.' << flush;
-    result += exam_paranoia8();  cout << '.' << flush;
-    result += exam_paranoia9();  cout << '.' << flush;
-    result += exam_paranoia10();  cout << '.' << flush;
-    result += exam_paranoia11();  cout << '.' << flush;
-    result += exam_paranoia12();  cout << '.' << flush;
-    result += exam_paranoia13();  cout << '.' << flush;
-    
-    if (!result) {
-        cout << " passed " << endl;
-        clog << "(no output)" << endl;
-    } else {
-        cout << " failed " << endl;
-    }
-    
-    return result;
+	return exam_paranoia();
 }