-@subsection Algebraic substitutions
-Supplying the @code{subs_options::algebraic} option to @code{subs()}
-enables smarter, algebraic substitutions in products and powers. If you want
-to substitute some factors of a product, you only need to list these factors
-in your pattern. Furthermore, if an (integer) power of some expression occurs
-in your pattern and in the expression that you want the substitution to occur
-in, it can be substituted as many times as possible, without getting negative
-powers.
-
-An example clarifies it all (hopefully):
-
-@example
-cout << (a*a*a*a+b*b*b*b+pow(x+y,4)).subs(wild()*wild()==pow(wild(),3),
- subs_options::algebraic) << endl;
-// --> (y+x)^6+b^6+a^6
-
-cout << ((a+b+c)*(a+b+c)).subs(a+b==x,subs_options::algebraic) << endl;
-// --> (c+b+a)^2
-// Powers and products are smart, but addition is just the same.
-
-cout << ((a+b+c)*(a+b+c)).subs(a+b+wild()==x+wild(), subs_options::algebraic)
- << endl;
-// --> (x+c)^2
-// As I said: addition is just the same.
-
-cout << (pow(a,5)*pow(b,7)+2*b).subs(b*b*a==x,subs_options::algebraic) << endl;
-// --> x^3*b*a^2+2*b
-
-cout << (pow(a,-5)*pow(b,-7)+2*b).subs(1/(b*b*a)==x,subs_options::algebraic)
- << endl;
-// --> 2*b+x^3*b^(-1)*a^(-2)
-
-cout << (4*x*x*x-2*x*x+5*x-1).subs(x==a,subs_options::algebraic) << endl;
-// --> -1-2*a^2+4*a^3+5*a
-
-cout << (4*x*x*x-2*x*x+5*x-1).subs(pow(x,wild())==pow(a,wild()),
- subs_options::algebraic) << endl;
-// --> -1+5*x+4*x^3-2*x^2
-// You should not really need this kind of patterns very often now.
-// But perhaps this it's-not-a-bug-it's-a-feature (c/sh)ould still change.
-
-cout << ex(sin(1+sin(x))).subs(sin(wild())==cos(wild()),
- subs_options::algebraic) << endl;
-// --> cos(1+cos(x))
-
-cout << expand((a*sin(x+y)*sin(x+y)+a*cos(x+y)*cos(x+y)+b)
- .subs((pow(cos(wild()),2)==1-pow(sin(wild()),2)),
- subs_options::algebraic)) << endl;
-// --> b+a
-@end example
-
-
-@node Applying a Function on Subexpressions, Visitors and Tree Traversal, Pattern Matching and Advanced Substitutions, Methods and Functions
+@subsection The option algebraic
+Both @code{has()} and @code{subs()} take an optional argument to pass them
+extra options. This section describes what happens if you give the former
+the option @code{has_options::algebraic} or the latter
+@code{subs:options::algebraic}. In that case the matching condition for
+powers and multiplications is changed in such a way that they become
+more intuitive. Intuition says that @code{x*y} is a part of @code{x*y*z}.
+If you use these options you will find that
+@code{(x*y*z).has(x*y, has_options::algebraic)} indeed returns true.
+Besides matching some of the factors of a product also powers match as
+often as is possible without getting negative exponents. For example
+@code{(x^5*y^2*z).subs(x^2*y^2==c, subs_options::algebraic)} will return
+@code{x*c^2*z}. This also works with negative powers:
+@code{(x^(-3)*y^(-2)*z).subs(1/(x*y)==c, subs_options::algebraic)} will
+return @code{x^(-1)*c^2*z}. Note that this only works for multiplications
+and not for locating @code{x+y} within @code{x+y+z}.
+
+
+@node Applying a function on subexpressions, Visitors and tree traversal, Pattern matching and advanced substitutions, Methods and functions
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