<example>
<title>My first GiNaC program (a bivariate polynomial)</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
<example>
<title>My second GiNaC program (Hermite polynomials)</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
ex HermitePoly(symbol x, int deg)
{
will be shortly described in what follows:
<itemizedlist>
<listitem>
- <para><literal>--enable-shared</literal>: When given, this option
- switches on the build of a shared library, i.e. a
- <literal>.so</literal>-file. A static libarary (i.e. a
- <literal>.a</literal>-file) is still built. For this to succeed,
- GNU libtool needs to be installed on your system. Hence,
- <literal>configure</literal> checks if it can find an executable
- <literal>libtool</literal> in the <literal>PATH</literal>. If it
- doesn't this option is ignored and the default restored, which
- means that only a static library will be build.</para>
+ <para><literal>--disable-shared</literal>: When given, this option
+ switches off the build of a shared library, i.e. a
+ <literal>.so</literal>-file. This may be convenient when developing
+ because it considerably speeds up compilation.</para>
</listitem>
<listitem>
<para><literal>--prefix=</literal><emphasis>PREFIX</emphasis>: The
<para><literal>--includedir=</literal><emphasis>INCLUDEDIR</emphasis>:
Use this option in case you want to have the header files
installed in some other directory than
- <emphasis>PREFIX</emphasis><literal>/include/GiNaC/</literal>. For
+ <emphasis>PREFIX</emphasis><literal>/include/ginac/</literal>. For
instance, if you specify
<literal>--includedir=/usr/include</literal> you will end up with
the header files sitting in the directory
- <literal>/usr/include/GiNaC/</literal>. Note that the subdirectory
+ <literal>/usr/include/ginac/</literal>. Note that the subdirectory
<literal>GiNaC</literal> is enforced by this process in order to
keep the header files separated from others. This avoids some
clashes and allows for an easier deinstallation of GiNaC. This ought
</listitem>
<listitem>
<para>All the header files will be installed into
- <emphasis>PREFIX</emphasis><literal>/include/GiNaC/</literal> (or
- <emphasis>INCLUDEDIR</emphasis><literal>/GiNaC/</literal>, if
+ <emphasis>PREFIX</emphasis><literal>/include/ginac/</literal> (or
+ <emphasis>INCLUDEDIR</emphasis><literal>/ginac/</literal>, if
specified).</para>
</listitem>
<listitem>
Consider the simple sequence of code:
<example><title>Simple copy-on-write semantics</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
make clear how powerful this can be. <example><title>Advanced
copy-on-write semantics</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
shows the four most important constructors: construction from
C-integer, construction of fractions from two integers, construction
from C-float and construction from a string.
-<example><title>Sample C++ program</title>
+<example><title>Construction of numbers</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
<example><title>Controlling the precision of floating point numbers</title>
<programlisting>
#include
-<GiNaC/ginac.h>
+<ginac/ginac.h>
void foo()
{
with some multiple of its denominator and check what comes out:
<example><title>Sample test on objects of type numeric</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
<literal>mul</literal> object and the number one:
<example><title>Construction of <literal>add</literal> and <literal>mul</literal> objects</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
the simple example:
<example><title>Methods vs. wrapper functions</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
being polynomials in the remaining variables. The method
<literal>collect()</literal> accomplishes this task:
<funcsynopsis>
- <funcsynopsisinfo>#include <GiNaC/ginac.h></funcsynopsisinfo>
+ <funcsynopsisinfo>#include <ginac/ginac.h></funcsynopsisinfo>
<funcdef>ex <function>ex::collect</function></funcdef>
<paramdef>symbol const & <parameter>s</parameter></paramdef>
</funcsynopsis>
order to be able to find the coefficients properly. The range of
occuring coefficients can be checked using the two methods
<funcsynopsis>
- <funcsynopsisinfo>#include <GiNaC/ginac.h></funcsynopsisinfo>
+ <funcsynopsisinfo>#include <ginac/ginac.h></funcsynopsisinfo>
<funcdef>int <function>ex::degree</function></funcdef>
<paramdef>symbol const & <parameter>s</parameter></paramdef>
</funcsynopsis>
<example><title>Collecting expressions in multivariate polynomials</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
<literal>a</literal> and <literal>b</literal>.
<example><title>Polynomal GCD/LCM</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
<para>
<example><title>Simple polynomial differentiation</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
<para>
<example><title>Differentiation with nontrivial functions</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
storing the order of the series. A sample program could read:
<example><title>Series expansion</title>
<programlisting>
-#include <GiNaC/ginac.h>
+#include <ginac/ginac.h>
int main()
{
ex MyExpr2 = 1/(x - pow(x, 2) - pow(x, 3));
ex MyTailor, MySeries;
- MyTailor = MyExpr1.series(x, numZERO(), 5);
+ MyTailor = MyExpr1.series(x, point, 5);
cout << MyExpr1 << " == " << MyTailor
<< " for small " << x << endl;
- MySeries = MyExpr2.series(x, numZERO(), 7);
+ MySeries = MyExpr2.series(x, point, 7);
cout << MyExpr2 << " == " << MySeries
<< " for small " << x << endl;
\\ ...
</example>
</para>
+<para>As an instructive application, let us calculate the numerical
+value of Archimedes' constant (for which there already exists the
+built-in constant <literal>Pi</literal>) using Méchain's
+wonderful formula <literal>Pi==16*atan(1/5)-4*atan(1/239)</literal>.
+We may expand the arcus tangent around <literal>0</literal> and insert
+the fractions <literal>1/5</literal> and <literal>1/239</literal>.
+But, as we have seen, a series in GiNaC carries an order term with it.
+The preprocessor-macro <literal>series_to_poly</literal> may be used
+to strip this off:
+<example><title>Series expansion using Méchain's formula</title>
+<programlisting>
+#include <ginac/ginac.h>
+
+ex mechain_pi(int degr)
+{
+ symbol x("x");
+ ex pi_expansion = series_to_poly(atan(x).series(x,0,degr));
+ ex pi_approx = 16*pi_expansion.subs(x==numeric(1,5))
+ -4*pi_expansion.subs(x==numeric(1,239));
+ return pi_approx;
+}
+
+int main()
+{
+ ex pi_frac;
+ for (int i=2; i<12; i+=2) {
+ pi_frac = mechain_pi(i);
+ cout << i << ":\t" << pi_frac << endl
+ << "\t" << pi_frac.evalf() << endl;
+ }
+ return 0;
+}
+</programlisting>
+<para>When you run this program, it will type out:</para>
+<screen>
+2: 3804/1195
+ 3.1832635983263598326
+4: 5359397032/1706489875
+ 3.1405970293260603143
+6: 38279241713339684/12184551018734375
+ 3.141621029325034425
+8: 76528487109180192540976/24359780855939418203125
+ 3.141591772182177295
+10: 327853873402258685803048818236/104359128170408663038552734375
+ 3.1415926824043995174
+</screen>
+</example>
+</para>
+
</sect1>
</chapter>