* Change section about Square-free decomposition reflecting the recent

  bugfix in the sqrfree() function.

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index c86114df5b9e07a415190953923634203d6fae81..237aa3c4582cbf4e2e36d9286ed563dbf24d6e88 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -3617,28 +3617,32 @@ GiNaC still lacks proper factorization support.  Some form of
 factorization is, however, easily implemented by noting that factors
 appearing in a polynomial with power two or more also appear in the
 derivative and hence can easily be found by computing the GCD of the
 factorization is, however, easily implemented by noting that factors
 appearing in a polynomial with power two or more also appear in the
 derivative and hence can easily be found by computing the GCD of the

-original polynomial and its derivatives.  Any system has an interface
-for this so called square-free factorization.  So we provide one, too:
+original polynomial and its derivatives.  Any decent system has an
+interface for this so called square-free factorization.  So we provide
+one, too:

 @example
 ex sqrfree(const ex & a, const lst & l = lst());
 @end example
 @example
 ex sqrfree(const ex & a, const lst & l = lst());
 @end example

-Here is an example that by the way illustrates how the result may depend
-on the order of differentiation:
+Here is an example that by the way illustrates how the exact form of the
+result may slightly depend on the order of differentiation, calling for
+some care with subsequent processing of the result:

 @example
     ...
     symbol x("x"), y("y");
 @example
     ...
     symbol x("x"), y("y");

-    ex BiVarPol = expand(pow(x-2*y*x,3) * pow(x+y,2) * (x-y));
+    ex BiVarPol = expand(pow(2-2*y,3) * pow(1+x*y,2) * pow(x-2*y,2) * (x+y));

 
     cout << sqrfree(BiVarPol, lst(x,y)) << endl;
 
     cout << sqrfree(BiVarPol, lst(x,y)) << endl;

-     // -> (y+x)^2*(-1+6*y+8*y^3-12*y^2)*(y-x)*x^3
+     // -> 8*(1-y)^3*(y*x^2-2*y+x*(1-2*y^2))^2*(y+x)

 
     cout << sqrfree(BiVarPol, lst(y,x)) << endl;
 
     cout << sqrfree(BiVarPol, lst(y,x)) << endl;

-     // -> (1-2*y)^3*(y+x)^2*(-y+x)*x^3
+     // -> 8*(1-y)^3*(-y*x^2+2*y+x*(-1+2*y^2))^2*(y+x)

 
     cout << sqrfree(BiVarPol) << endl;
      // -> depending on luck, any of the above
     ...
 @end example
 
     cout << sqrfree(BiVarPol) << endl;
      // -> depending on luck, any of the above
     ...
 @end example

+Note also, how factors with the same exponents are not fully factorized
+with this method.

 
 
 @node Rational Expressions, Symbolic Differentiation, Polynomial Arithmetic, Methods and Functions
 
 
 @node Rational Expressions, Symbolic Differentiation, Polynomial Arithmetic, Methods and Functions