index 86bd12abb1e728ecbde9deb3139103a890f14a63..13152f2707ed183e281c2758b4e07f62b7385d5d 100644 (file)
@@ -1,8 +1,9 @@
/** @file exam_misc.cpp
*
*/
+
/*
- *  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
*
*  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 "ginac.h"
+using namespace GiNaC;

-#include "exams.h"
+#include <iostream>
+using namespace std;

#define VECSIZE 30
-static unsigned exam_expand_subs(void)
+static unsigned exam_expand_subs()
{
-    unsigned result = 0;
-    symbol a1("a1");
-    symbol a[VECSIZE];
-    ex e, aux;
-
-    a = a1;
-    for (unsigned i=0; i<VECSIZE; ++i) {
-        e = e + a[i];
-    }
-
-    // prepare aux so it will swallow anything but a1^2:
-    aux = -e + a + a;
-    e = expand(subs(expand(pow(e, 2)), a == aux));
-
-    if (e != pow(a1,2)) {
-        clog << "Denny Fliegner's quick consistency check erroneously returned "
-             << e << "." << endl;
-        ++result;
-    }
-
-    return result;
+       unsigned result = 0;
+       symbol a[VECSIZE];
+       ex e, aux;
+
+       for (unsigned i=0; i<VECSIZE; ++i)
+               e = e + a[i];
+
+       // prepare aux so it will swallow anything but a1^2:
+       aux = -e + a + a;
+       e = expand(subs(expand(pow(e, 2)), a == aux));
+
+       if (e != pow(a,2)) {
+               clog << "Denny Fliegner's quick consistency check erroneously returned "
+                    << e << "." << endl;
+               ++result;
+       }
+
+       return result;
}

/*  A simple modification of Denny Fliegner's three step consistency test:
@@ -53,40 +54,269 @@ static unsigned exam_expand_subs(void)
*  2)  expand e
*  3)  substitute a0 by -a1 in e
*  after which e should return 0 (without expanding). */
-static unsigned exam_expand_subs2(void)
+static unsigned exam_expand_subs2()
+{
+       unsigned result = 0;
+       symbol a("a"), b("b");
+       ex e, f;
+
+       e = pow(a+b,200).expand();
+       f = e.subs(a == -b);
+
+       if (f != 0) {
+               clog << "e = pow(a+b,200).expand(); f = e.subs(a == -b); erroneously returned "
+                    << f << " instead of simplifying to 0." << endl;
+               ++result;
+       }
+
+       return result;
+}
+
+static unsigned exam_expand_power()
+{
+       unsigned result = 0;
+       symbol x("x"), a("a"), b("b");
+       ex e;
+
+       e = pow(x,pow(a+b,2)-pow(a,2)-pow(b,2)-a*b*2).expand();
+
+       if (e != 1) {
+               clog << "e = pow(x,pow(a+b,2)-pow(a,2)-pow(b,2)-a*b*2).expand(); erroneously returned "
+                    << e << " instead of simplifying to 1." << endl;
+               ++result;
+       }
+
+       return result;
+}
+
+static unsigned exam_sqrfree()
+{
+       unsigned result = 0;
+       symbol x("x"), y("y");
+       ex e1, e2;
+
+       e1 = (1+x)*pow((2+x),2)*pow((3+x),3)*pow((4+x),4);
+       e2 = sqrfree(expand(e1),lst{x});
+       if (e1 != e2) {
+               clog << "sqrfree(expand(" << e1 << ")) erroneously returned "
+                    << e2 << endl;
+               ++result;
+       }
+
+       e1 = (x+y)*pow((x+2*y),2)*pow((x+3*y),3)*pow((x+4*y),4);
+       e2 = sqrfree(expand(e1));
+       if (e1 != e2) {
+               clog << "sqrfree(expand(" << e1 << ")) erroneously returned "
+                    << e2 << endl;
+               ++result;
+       }
+       e2 = sqrfree(expand(e1),lst{x});
+       if (e1 != e2) {
+               clog << "sqrfree(expand(" << e1 << "),[x]) erroneously returned "
+                    << e2 << endl;
+               ++result;
+       }
+       e2 = sqrfree(expand(e1),lst{y});
+       if (e1 != e2) {
+               clog << "sqrfree(expand(" << e1 << "),[y]) erroneously returned "
+                    << e2 << endl;
+               ++result;
+       }
+       e2 = sqrfree(expand(e1),lst{x,y});
+       if (e1 != e2) {
+               clog << "sqrfree(expand(" << e1 << "),[x,y]) erroneously returned "
+                    << e2 << endl;
+               ++result;
+       }
+
+       return result;
+}
+
+/* Arithmetic Operators should behave just as one expects from built-in types.
+ * When somebody screws up the operators this routine will most probably fail
+ * to compile.  Unfortunately we can only test the stuff that is allowed, not
+ * what is forbidden (e.g. e1+e2 = 42) since that must not compile.  :-(   */
+static unsigned exam_operator_semantics()
+{
+       unsigned result = 0;
+       ex e1, e2;
+       int i1, i2;
+
+       // Assignment should not return const ex though it may be obfuscated:
+       e1 = 7; e2 = 4;
+       i1 = 7; i2 = 4;
+       (e1 = e2) = 2;
+       (i1 = i2) = 2;
+       if (e1!=i1 || e2!=i2) {
+               clog << "Semantics of ex::operator=() screwed." << endl;
+               ++result;
+       }
+       (e1 += e2) = 2;
+       (i1 += i2) = 2;
+       if (e1!=i1 || e2!=i2) {
+               clog << "Semantics of ex::operator=() screwed." << endl;
+               ++result;
+       }
+       (e1 -= e2) = 2;
+       (i1 -= i2) = 2;
+       if (e1!=i1 || e2!=i2) {
+               clog << "Semantics of ex::operator=() screwed." << endl;
+               ++result;
+       }
+
+       // Prefix/postfix increment/decrement behavior:
+       e1 = 7; e2 = 4;
+       i1 = 7; i2 = 4;
+       e1 = (--e2 = 2)++;
+       i1 = (--i2 = 2)++;
+       if (e1!=i1 || e2!=i2) {
+               clog << "Semantics of increment/decrement operators screwed." << endl;
+               ++result;
+       }
+       e1 = (++e2 = 2)--;
+       i1 = (++i2 = 2)--;
+       if (e1!=i1 || e2!=i2) {
+               clog << "Semantics of increment/decrement operators screwed." << endl;
+               ++result;
+       }
+
+       // prefix increment/decrement must return an lvalue (contrary to postfix):
+       e1 = 7; e2 = 4;
+       i1 = 7; i2 = 4;
+       --++----e1;  ++(++++++++(++++e2));
+       --++----i1;  ++(++++++++(++++i2));
+       if (e1!=i1 || e2!=i2) {
+               clog << "Semantics of prefix increment/decrement operators screwed." << endl;
+               ++result;
+       }
+
+       // This one has a good chance of detecting problems in self-assignment:
+       // (which incidentally was severely broken from version 0.7.3 to 0.8.2).
+       ex selfprobe = numeric("65536");
+       selfprobe = selfprobe;
+       if (!is_exactly_a<numeric>(selfprobe)) {
+               clog << "ex (of numeric) after self-assignment became " << selfprobe << endl;
+               ++result;
+       }
+
+       return result;
+}
+
+/* This checks whether subs() works as intended in some special cases. */
+static unsigned exam_subs()
+{
+       unsigned result = 0;
+       symbol x("x");
+       ex e1, e2;
+
+       // This used to fail in GiNaC 1.0.5 because it first substituted
+       // x+1 -> (x-1)+1 -> x, and then substituted again x -> x-1, giving
+       // the wrong result
+       e1 = x+1;
+       e2 = e1.subs(x == x-1);
+       if (!e2.is_equal(x)) {
+               clog << "(x+1).subs(x==x-1) erroneously returned " << e2 << " instead of x" << endl;
+               ++result;
+       }
+
+       // And this used to fail in GiNaC 1.5.8 because it first substituted
+       // exp(x) -> exp(log(x)) -> x, and then substituted again x -> log(x)
+       e1 = exp(x);
+       e2 = e1.subs(x == log(x));
+       if (!e2.is_equal(x)) {
+               clog << "exp(x).subs(x==log(x)) erroneously returned " << e2 << " instead of x" << endl;
+               ++result;
+       }
+
+       e1 = sin(1+sin(x));
+       e2 = e1.subs(sin(wild()) == cos(wild()));
+       if (!e2.is_equal(cos(1+cos(x)))) {
+               clog << "sin(1+sin(x)).subs(sin(\$1)==cos(\$1)) erroneously returned " << e2 << " instead of cos(1+cos(x))" << endl;
+               ++result;
+       }
+
+       return result;
+}
+
+/* Joris van der Hoeven (he of TeXmacs fame) is a funny guy.  He has his own
+ * ideas what a symbolic system should do.  Let's make sure we won't disappoint
+ * him some day.  Incidentally, this seems to always have worked. */
+static unsigned exam_joris()
+{
+       unsigned result = 0;
+       symbol x("x");
+
+       ex e = expand(pow(x, x-1) * x);
+       if (e != pow(x, x)) {
+               clog << "x^(x-1)*x did not expand to x^x.  Please call Joris!" << endl;
+               ++result;
+       }
+
+       return result;
+}
+
+/* Test Chris Dams' algebraic substitutions. */
+static unsigned exam_subs_algebraic()
+{
+       unsigned result = 0;
+       symbol x("x"), y("y");
+
+       ex e = ex(x*x*x*y*y).subs(x*y==2, subs_options::algebraic);
+       if (e != 4*x) {
+               clog << "(x^3*y^2).subs(x*y==2,subs_options::algebraic) erroneously returned " << e << endl;
+               ++result;
+       }
+
+       e = ex(x*x*x*x*x).subs(x*x==y, subs_options::algebraic);
+       if (e != y*y*x) {
+               clog << "x^5.subs(x^2==y,subs_options::algebraic) erroneously returned " << e << endl;
+               ++result;
+       }
+
+       e=x*x*y;
+       if (!e.has(x*y, has_options::algebraic))
+       {       clog << "(x^2*y).has(x*y, has_options::algebraic) erroneously returned false." << endl;
+               ++result;
+       }
+
+       if (e.has(x*y*y, has_options::algebraic))
+       {       clog << "(x^2*y).has(x*y*y, has_options::algebraic) erroneously returned true." << endl;
+               ++result;
+       }
+
+       e=x*x*x*y;
+       if (!e.has(x*x, has_options::algebraic))
+       {       clog << "(x^3*y).has(x*x, has_options::algebraic) erroneously returned false." << endl;
+               ++result;
+       }
+
+       if (e.has(y*y, has_options::algebraic))
+       {       clog << "(x^3*y).has(y*y, has_options::algebraic) erroneously returned true." << endl;
+               ++result;
+       }
+
+       return result;
+}
+
+unsigned exam_misc()
{
-    unsigned result = 0;
-    symbol a("a"), b("b");
-    ex e, f;
-
-    e = pow(a+b,200).expand();
-    f = e.subs(a == -b);
-
-    if (f != 0) {
-        clog << "e = pow(a+b,200).expand(); f = e.subs(a == -b); erroneously returned "
-             << f << " instead of simplifying to 0." << endl;
-        ++result;
-    }
-
-    return result;
+       unsigned result = 0;
+
+       cout << "examining miscellaneous other things" << flush;
+
+       result += exam_expand_subs();  cout << '.' << flush;
+       result += exam_expand_subs2();  cout << '.' << flush;
+       result += exam_expand_power(); cout << '.' << flush;
+       result += exam_sqrfree(); cout << '.' << flush;
+       result += exam_operator_semantics(); cout << '.' << flush;
+       result += exam_subs(); cout << '.' << flush;
+       result += exam_joris(); cout << '.' << flush;
+       result += exam_subs_algebraic(); cout << '.' << flush;
+
+       return result;
}

-unsigned exam_misc(void)
+int main(int argc, char** argv)
{
-    unsigned result = 0;
-
-    cout << "examining miscellaneous other things" << flush;
-    clog << "----------miscellaneous other things:" << endl;
-
-    result += exam_expand_subs();  cout << '.' << flush;
-    result += exam_expand_subs2();  cout << '.' << flush;
-
-    if (!result) {
-        cout << " passed " << endl;
-        clog << "(no output)" << endl;
-    } else {
-        cout << " failed " << endl;
-    }
-
-    return result;
+       return exam_misc();
}