The general rule is that when you construct expressions, GiNaC automatically
creates them in canonical form, which might differ from the form you typed in
your program. This may create some awkward looking output (@samp{-y+x} instead
-of @samp{y-x}) but allows for more efficient operation and usually yields
+of @samp{x-y}) but allows for more efficient operation and usually yields
some immediate simplifications.
@cindex @code{eval()}
The optional last argument to @code{subs()} is a combination of
@code{subs_options} flags. There are two options available:
-@code{subs_options::subs_no_pattern} disables pattern matching, which makes
+@code{subs_options::no_pattern} disables pattern matching, which makes
large @code{subs()} operations significantly faster if you are not using
-patterns. The second option, @code{subs_options::subs_algebraic} enables
+patterns. The second option, @code{subs_options::algebraic} enables
algebraic substitutions in products and powers.
@ref{Pattern Matching and Advanced Substitutions}, for more information
about patterns and algebraic substitutions.
@end example
@subsection Algebraic substitutions
-Supplying the @code{subs_options::subs_algebraic} option to @code{subs()}
+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
@example
cout << (a*a*a*a+b*b*b*b+pow(x+y,4)).subs(wild()*wild()==pow(wild(),3),
- subs_options::subs_algebraic) << endl;
+ subs_options::algebraic) << endl;
// --> (y+x)^6+b^6+a^6
-cout << ((a+b+c)*(a+b+c)).subs(a+b==x,subs_options::subs_algebraic) << endl;
+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::subs_algebraic)
+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::subs_algebraic) << endl;
+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::subs_algebraic)
+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::subs_algebraic) << endl;
+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::subs_algebraic) << endl;
+ 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::subs_algebraic) << endl;
+ 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::subs_algebraic)) << endl;
+ subs_options::algebraic)) << endl;
// --> b+a
@end example