- fixed example of evalf-function.

[ginac.git] / doc / tutorial / ginac.texi

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 5934347c7ddb7e21fa1278d553cfc62ec3fbea2d..81bfb7f7b4725b573b2fcf39f87026a5fd72d75b 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -2265,8 +2265,14 @@ The unity element of a Clifford algebra is constructed by
 ex dirac_ONE(unsigned char rl = 0);
 @end example
 
+@strong{Note:} You must always use @code{dirac_ONE()} when referring to
+multiples of the unity element, even though it's customary to omit it.
+E.g. instead of @code{dirac_gamma(mu)*(dirac_slash(q,4)+m)} you have to
+write @code{dirac_gamma(mu)*(dirac_slash(q,4)+m*dirac_ONE())}. Otherwise,
+GiNaC may produce incorrect results.
+
 @cindex @code{dirac_gamma5()}
-and there's a special element @samp{gamma5} that commutes with all other
+There's a special element @samp{gamma5} that commutes with all other
 gammas and in 4 dimensions equals @samp{gamma~0 gamma~1 gamma~2 gamma~3},
 provided by
 
@@ -2429,9 +2435,15 @@ The unity element of a color algebra is constructed by
 ex color_ONE(unsigned char rl = 0);
 @end example
 
+@strong{Note:} You must always use @code{color_ONE()} when referring to
+multiples of the unity element, even though it's customary to omit it.
+E.g. instead of @code{color_T(a)*(color_T(b)*indexed(X,b)+1)} you have to
+write @code{color_T(a)*(color_T(b)*indexed(X,b)+color_ONE())}. Otherwise,
+GiNaC may produce incorrect results.
+
 @cindex @code{color_d()}
 @cindex @code{color_f()}
-and the functions
+The functions
 
 @example
 ex color_d(const ex & a, const ex & b, const ex & c);
@@ -3189,6 +3201,42 @@ This function object could then be used like this:
 @}
 @end example
 
+Here is another example for you to meditate over. It removes quadratic
+terms in a variable from an expanded polynomial:
+
+@example
+struct map_rem_quad : public map_function @{
+    ex var;
+    map_rem_quad(const ex & var_) : var(var_) @{@}
+
+    ex operator()(const ex & e)
+    @{
+        if (is_a<add>(e) || is_a<mul>(e))
+           return e.map(*this);
+        else if (is_a<power>(e) && e.op(0).is_equal(var) && e.op(1).info(info_flags::even))
+            return 0;
+        else
+            return e;
+    @}
+@};
+
+...
+
+@{
+    symbol x("x"), y("y");
+
+    ex e;
+    for (int i=0; i<8; i++)
+        e += pow(x, i) * pow(y, 8-i) * (i+1);
+    cout << e << endl;
+     // -> 4*y^5*x^3+5*y^4*x^4+8*y*x^7+7*y^2*x^6+2*y^7*x+6*y^3*x^5+3*y^6*x^2+y^8
+
+    map_rem_quad rem_quad(x);
+    cout << rem_quad(e) << endl;
+     // -> 4*y^5*x^3+8*y*x^7+2*y^7*x+6*y^3*x^5+y^8
+@}
+@end example
+
 @command{ginsh} offers a slightly different implementation of @code{map()}
 that allows applying algebraic functions to operands. The second argument
 to @code{map()} is an expression containing the wildcard @samp{$0} which
@@ -3845,7 +3893,7 @@ GiNaC contains the following predefined mathematical functions:
 @item @code{csgn(x)}
 @tab complex sign
 @item @code{sqrt(x)}
-@tab square root (not a GiNaC function proper but equivalent to @code{pow(x, numeric(1, 2)})
+@tab square root (not a GiNaC function, rather an alias for @code{pow(x, numeric(1, 2))})
 @item @code{sin(x)}
 @tab sine
 @item @code{cos(x)}
@@ -3898,8 +3946,6 @@ GiNaC contains the following predefined mathematical functions:
 @tab binomial coefficients
 @item @code{Order(x)}
 @tab order term function in truncated power series
-@item @code{Derivative(x, l)}
-@tab inert partial differentiation operator (used internally)
 @end multitable
 @end cartouche
 
@@ -4391,7 +4437,10 @@ function that does so, in this case the one in class @code{numeric}:
 @example
 static ex cos_evalf(const ex & x)
 @{
-    return cos(ex_to<numeric>(x));
+    if (is_a<numeric>(x))
+        return cos(ex_to<numeric>(x));
+    else
+        return cos(x).hold();
 @}
 @end example
 
@@ -5556,6 +5605,10 @@ and George Labahn, ISBN 0-7923-9259-0, 1992, Kluwer Academic Publishers, Norwell
 J.H. Davenport, Y. Siret, and E. Tournier, ISBN 0-12-204230-1, 1988, 
 Academic Press, London
 
+@item
+@cite{The Art of Computer Programming, Vol 2: Seminumerical Algorithms},
+D.E. Knuth, ISBN 0-201-89684-2, 1998, Addison Wesley
+
 @item
 @cite{The Role of gamma5 in Dimensional Regularization}, D. Kreimer, hep-ph/9401354