* Factorization test suite. */
/*
- * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2020 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
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include <iostream>
#include "ginac.h"
-using namespace std;
using namespace GiNaC;
-static symbol w("w"), x("x"), y("y"), z("z");
+#include <iostream>
+using namespace std;
static unsigned check_factor(const ex& e)
{
static unsigned exam_factor1()
{
unsigned result = 0;
- ex e, d;
+ ex e;
symbol x("x");
- lst syms;
- syms.append(x);
+ lst syms = {x};
e = ex("1+x-x^3", syms);
result += check_factor(e);
static unsigned exam_factor2()
{
unsigned result = 0;
- ex e, d;
+ ex e;
symbol x("x"), y("y"), z("z");
- lst syms;
- syms = x, y, z;
+ lst syms = {x, y, z};
e = ex("x+y", syms);
result += check_factor(e);
- e = ex("x+y", syms);
+ e = ex("(x^2-y+1)*(x+y)", syms);
result += check_factor(e);
e = ex("-2*(x+y)*(x-y)", syms);
result += check_factor(e);
+ e = ex("(16+x^2*z^3)*(-17+3*x-5*z)*(2*x+3*z)*(x-y^2-z^3)", syms);
+ result += check_factor(e);
+
+ e = ex("(x-y*z)*(x-y^2-z^3)*(x+y+z)", syms);
+ result += check_factor(e);
+
+ e = ex("-(y^2-x+z^3)*x*(x+y+z)", syms);
+ result += check_factor(e);
+
+ e = ex("-316*(3*x-4*z)*(2*x+3*z)*(x+y)*(-1+x)", syms);
+ result += check_factor(e);
+
+ e = ex("(x+x^3+z^2)*(3*x-4*z)", syms);
+ result += check_factor(e);
+
+ e = ex("250*(-3+x)*(4*z-3*x)*(x^3+z^2+x)*x", syms);
+ result += check_factor(e);
+
+ e = ex("327*(x+z^2+x^3)*(3*x-4*z)*(-7+5*x-x^3)*(1+x+x^2)", syms);
+ result += check_factor(e);
+
+ e = ex("x-y^2-z^3", syms);
+ result += check_factor(e);
+
+ e = ex("-390*(7+3*x^4)*(2+x^2)*(x-z^3-y^2)", syms);
+ result += check_factor(e);
+
+ e = ex("55*(1+x)^2*(3*x-4*z)*(1+x+x^2)*(x+x^3+z^2)", syms);
+ result += check_factor(e);
+
+ e = ex("x+y*x-1", syms);
+ result += check_factor(e);
+
+ e = ex("390*(-1+x^6-x)*(7+3*x^4)*(2+x^2)*(y+x)*(-1+y-x^2)*(1+x^2+x)^2", syms);
+ result += check_factor(e);
+
+ e = ex("310*(y+x)*(-1+y-x^2)", syms);
+ result += check_factor(e);
+
+ return result;
+}
+
+static unsigned exam_factor3()
+{
+ unsigned result = 0;
+ ex e;
+ symbol k("k"), n("n");
+ lst syms = {k, n};
+
+ e = ex("1/2*(-3+3*k-n)*(-2+3*k-n)*(-1+3*k-n)", syms);
+ result += check_factor(e);
+
+ e = ex("1/4*(2*k-n)*(-1+2*k-n)", syms);
+ result += check_factor(e);
+
return result;
}
+static unsigned check_factor_expanded(const ex& e)
+{
+ ex ee = e.expand();
+ ex answer = factor(ee);
+ if ( answer.expand() != ee || (!is_a<mul>(answer) && !is_a<power>(answer)) ) {
+ clog << "factorization of " << e << " == " << ee << " gave wrong result: " << answer << endl;
+ return 1;
+ }
+ return 0;
+}
+
+static unsigned exam_factor_wang()
+{
+ // these 15 polynomials are from the appendix of P.S.Wang,
+ // "An Improved Multivariate Polynomial Factoring Algorithm"
+ unsigned result = 0;
+ ex e;
+ symbol u("u"), w("w"), x("x"), y("y"), z("z");
+
+ e = ex("(z+x*y+10)*(x*z+y+30)*(y*z+x+20)", lst{x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(x^3*(z+y)+y-11)*(x^2*(z^2+y^2)+y+90)", lst{x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(y*z^3+x*y*z+y^2+x^3)*(x*(z^4+1)+z+x^3*y^2)", lst{x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(z^2-x^3*y+3)*(z^2+x*y^3)*(z^2+x^3*y^4)*(y^4*z^2+x^2*z+5)", lst{x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(z^2+x^3*y^4+u^2)*((y^2+x)*z^2+3*u^2*x^3*y^4*z+19*y^2)*(u^2*y^4*z^2+x^2*z+5)", lst{u, x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(w^4*z^3-x*y^2*z^2-w^4*x^5*y^6-w^2*x^3*y)*(-x^5*z^3+y*z+x^2*y^3)"
+ "*(w^4*z^6+y^2*z^3-w^2*x^2*y^2*z^2+x^5*z-x^4*y^2-w^3*x^3*y)", lst{w, x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(z+y+x-3)^3*(z+y+x-2)^2", lst{x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(-15*y^2*z^16+29*w^4*x^12*y^12*z^3+21*x^3*z^2+3*w^15*y^20)"
+ "*(-z^31-w^12*z^20+y^18-y^14+x^2*y^2+x^21+w^2)", lst{w, x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("u^4*x*z^2*(6*w^2*y^3*z^2+18*u^2*w^3*x*z^2+15*u*z^2+10*u^2*w*x*y^3)"
+ "*(-44*u*w*x*y^4*z^4-25*u^2*w^3*y*z^4+8*u*w*x^3*z^4-32*u^2*w^4*y^4*z^3"
+ "+48*u^2*x^2*y^3*z^3-12*y^3*z^2+2*u^2*w*x^2*y^2-11*u*w^2*x^3*y-4*w^2*x)", lst{u, w, x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(31*u^2*x*z+35*w^2*y^2+6*x*y+40*w*x^2)*(u^2*w^2*x*y^2*z^2+24*u^2*w*x*y^2*z^2"
+ "+12*u^2*x*y^2*z^2+24*u^2*x^2*y*z^2+43*w*x*y*z^2+31*w^2*y*z^2+8*u^2*w^2*z^2"
+ "+44*u*w^2*z^2+37*u^2*y^2*z+41*y^2*z+12*w*x^2*y*z+21*u^2*w*x*y*z+23*x*y*z"
+ "+47*u^2*w^2*z+13*u*w^2*x^2*y^2+22*x*y^2+42*u^2*w^2*y^2+29*w^2*y^2+27*u*w^2*x^2*y"
+ "+37*w^2*x*z+39*u*w*x*z+43*u*x^2*y+24*x*y+9*u^2*w*x^2+22*u^2*w^2)", lst{u, w, x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("x*y*(-13*u^3*w^2*x*y*z^3+w^3*z^3+4*u*x*y^2+47*x*y)"
+ "*(43*u*x^3*y^3*z^3+36*u^2*w^3*x*y*z^3+14*w^3*x^3*y^3*z^2-29*w^3*x*y^3*z^2"
+ "-20*u^2*w^2*x^2*y^2*z^2+36*u^2*w*x*y^3*z-48*u*x^3*y^2*z+5*u*w*x^2*y^3"
+ "+36*u*w^2*y^3-9*u*w*y^3-23*u*w*x^3*y^2+46*u*x^3*y^2+8*x*y^2+31*u^2*w^3*y^2"
+ "-9*u^2*y^2+45*x^3-46*u^2*w*x)", lst{u, w, x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(z+y+x-3)^3", lst{x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(3*z^3+2*w*z-9*y^3-y^2+45*x^3)*(w^2*z^3+47*x*y-w^2)", lst{w, x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("(-18*x^4*y^5+22*y^5-26*x^3*y^4-38*x^2*y^4+29*x^2*y^3-41*x^4*y^2+37*x^4)"
+ "*(33*x^5*y^6+11*y^2+35*x^3*y-22*x^4)", lst{x, y, z});
+ result += check_factor_expanded(e);
+
+ e = ex("x^6*y^3*z^2*(3*z^3+2*w*z-8*x*y^2+14*w^2*y^2-y^2+18*x^3*y)"
+ "*(-12*w^2*x*y*z^3+w^2*z^3+3*x*y^2+29*x-w^2)", lst{w, x, y, z});
+ result += check_factor_expanded(e);
+
+ return result;
+}
+
+static unsigned check_factorization(const exvector& factors)
+{
+ ex e = dynallocate<mul>(factors);
+ ex ef = factor(e.expand());
+ if (ef.nops() != factors.size()) {
+ clog << "wrong number of factors, expected " << factors.size() <<
+ ", got " << ef.nops();
+ return 1;
+ }
+ for (size_t i = 0; i < ef.nops(); ++i) {
+ if (find(factors.begin(), factors.end(), ef.op(i)) == factors.end()) {
+ clog << "wrong factorization: term not found: " << ef.op(i);
+ return 1;
+ }
+ }
+ return 0;
+}
+
+static unsigned factor_integer_content_bug()
+{
+ parser reader;
+ exvector factors;
+ factors.push_back(reader("x+y+x*y"));
+ factors.push_back(reader("3*x+2*y"));
+ return check_factorization(factors);
+}
+
unsigned exam_factor()
{
unsigned result = 0;
result += exam_factor1(); cout << '.' << flush;
result += exam_factor2(); cout << '.' << flush;
+ result += exam_factor3(); cout << '.' << flush;
+ result += exam_factor_wang(); cout << '.' << flush;
+ result += factor_integer_content_bug();
+ cout << '.' << flush;
return result;
}
git://www.ginac.de / ginac.git / blobdiff