- changed behaviour of numeric::is_rational() and added numeric::is_cinteger()

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 5e47963a71ab70dc75cb5687036f3b0bc3a7e796..5a7ad9dfa2803db940a351a8fc61e2a128c028df 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -360,9 +360,9 @@ polynomials):
 3*y^2+x^2
 @end example
 
 3*y^2+x^2
 @end example
 

-You can differentiate functions and expand them as Taylor or
-Laurent series (the third argument of series is the evaluation point,
-the fourth defines the order):
+You can differentiate functions and expand them as Taylor or Laurent
+series (the third argument of @code{series} is the evaluation point, the
+fourth defines the order):

 
 @example
 > diff(tan(x),x);
 
 @example
 > diff(tan(x),x);


@@ -371,6 +371,9 @@ tan(x)^2+1
 x-1/6*x^3+Order(x^4)
 > series(1/tan(x),x,0,4);
 x^(-1)-1/3*x+Order(x^2)
 x-1/6*x^3+Order(x^4)
 > series(1/tan(x),x,0,4);
 x^(-1)-1/3*x+Order(x^2)

+> series(gamma(2*sin(x)-2),x,Pi/2,6);
+-(x-1/2*Pi)^(-2)+(-1/12*Pi^2-1/2*EulerGamma^2-1/240)*(x-1/2*Pi)^2
+-EulerGamma-1/12+Order((x-1/2*Pi)^3)

 @end example
 
 If you ever wanted to convert units in C or C++ and found this
 @end example
 
 If you ever wanted to convert units in C or C++ and found this


@@ -675,8 +678,9 @@ implement its own arithmetic.
 
 To give an idea about what kinds of symbolic composits may be built we
 have a look at the most important classes in the class hierarchy.  The
 
 To give an idea about what kinds of symbolic composits may be built we
 have a look at the most important classes in the class hierarchy.  The

-dashed line symbolizes a "points to" or "handles" relationship while the
-solid lines stand for "inherits from" relationship in the class
+oval classes are atomic ones and the squared classes are containers.
+The dashed line symbolizes a "points to" or "handles" relationship while
+the solid lines stand for "inherits from" relationship in the class

 hierarchy:
 
 @image{classhierarchy}
 hierarchy:
 
 @image{classhierarchy}


@@ -912,9 +916,13 @@ following table.
 @item @code{.is_prime()}
 @tab object is a prime integer (probabilistic primality test)
 @item @code{.is_rational()}
 @item @code{.is_prime()}
 @tab object is a prime integer (probabilistic primality test)
 @item @code{.is_rational()}

-@tab object is an exact rational number (integers are rational, too, as are complex extensions like @math{2/3+7/2*I})
+@tab object is an exact rational number (integers are rational, too)

 @item @code{.is_real()}
 @tab object is a real integer, rational or float (i.e. is not complex)
 @item @code{.is_real()}
 @tab object is a real integer, rational or float (i.e. is not complex)

+@item @code{.is_cinteger()}
+@tab object is a (complex) integer, such as @math{2-3*I}
+@item @code{.is_crational()}
+@tab object is an exact (complex) rational number (such as @math{2/3+7/2*I})

 @end multitable
 @end cartouche
 
 @end multitable
 @end cartouche
 


@@ -1566,9 +1574,15 @@ REGISTER_FUNCTION(cos, cos_eval_method, cos_evalf_method, cos_diff, NULL);
 
 The first argument is the function's name, the second, third and fourth
 bind the corresponding methods to this objects and the fifth is a slot
 
 The first argument is the function's name, the second, third and fourth
 bind the corresponding methods to this objects and the fifth is a slot

-for inserting a method for series expansion.  Also, the new function
-needs to be declared somewhere.  This may also be done by a convenient
-preprocessor macro:
+for inserting a method for series expansion.  (If set to @code{NULL} it
+defaults to simple Taylor expansion, which is correct if there are no
+poles involved.  The way GiNaC handles poles in case there are any is
+best understood by studying one of the examples, like the Gamma function
+for instance.  In essence the function first checks if there is a pole
+at the evaluation point and falls back to Taylor expansion if there
+isn't.  Then, the pole is regularized by some suitable transformation.)
+Also, the new function needs to be declared somewhere.  This may also be
+done by a convenient preprocessor macro:

 
 @example
 DECLARE_FUNCTION_1P(cos)
 
 @example
 DECLARE_FUNCTION_1P(cos)