- Changes reflect beautifying of floating-point output.

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 20d7c5440cc0c884197e8abf4c7f053efeb86ba0..1d060689837613c748f78bc52102d9423c5d36f2 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -280,8 +280,23 @@ integers:
 1/3
 @end example
 
-All numbers occuring in GiNaC's expressions can be converted into floating
-point numbers with the @code{evalf} method, to arbitrary accuracy:
+Exact numbers are always retained as exact numbers and only evaluated as
+floating point numbers if requested.  For instance, with numeric
+radicals is dealt pretty much as with symbols.  Products of sums of them
+can be expanded:
+
+@example
+> expand((1+a^(1/5)-a^(2/5))^3);
+1+3*a+3*a^(1/5)-5*a^(3/5)-a^(6/5)
+> expand((1+3^(1/5)-3^(2/5))^3);
+10-5*3^(3/5)
+> evalf((1+3^(1/5)-3^(2/5))^3);
+0.33408977534118624228
+@end example
+
+The function @code{evalf} that was used above converts any number in
+GiNaC's expressions into floating point numbers.  This can be done to
+arbitrary predefined accuracy:
 
 @example
 > evalf(1/7);
@@ -302,11 +317,11 @@ numeric expressions (as an inexact number):
 > a=Pi^2+x;
 x+Pi^2
 > evalf(a);
-x+9.869604401089358619L0
+9.869604401089358619+x
 > x=2;
 2
 > evalf(a);
-11.869604401089358619L0
+11.869604401089358619
 @end example
 
 Built-in functions evaluate immediately to exact numbers if
@@ -333,7 +348,7 @@ a matrix class for this purpose but we can see what it can do using
 @example
 > lsolve(a+x*y==z,x);
 y^(-1)*(z-a);
-lsolve([3*x+5*y == 7, -2*x+10*y == -5], [x, y]);
+> lsolve([3*x+5*y == 7, -2*x+10*y == -5], [x, y]);
 [x==19/8,y==-1/40]
 > M = [[ [[1, 3]], [[-3, 2]] ]];
 [[ [[1,3]], [[-3,2]] ]]
@@ -376,8 +391,8 @@ x^(-1)-1/3*x+Order(x^2)
 x^(-1)-EulerGamma+(1/12*Pi^2+1/2*EulerGamma^2)*x
 +(-1/3*zeta(3)-1/12*Pi^2*EulerGamma-1/6*EulerGamma^3)*x^2+Order(x^3)
 > evalf(");
-x^(-1.0)-0.5772156649015328606+(0.98905599532797255544)*x
--(0.90747907608088628905)*x^2+Order(x^(3.0))
+x^(-1)-0.5772156649015328606+(0.9890559953279725555)*x
+-(0.90747907608088628905)*x^2+Order(x^3)
 > 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)
@@ -545,21 +560,24 @@ takes to compile GiNaC depends not only on the speed of your machines
 but also on other parameters, for instance what value for @env{CXXFLAGS}
 you entered.  Optimization may be very time-consuming.
 
-Just to make sure GiNaC works properly you may run a simple test
-suite by typing
+Just to make sure GiNaC works properly you may run a collection of
+regression tests by typing
 
 @example
 $ make check
 @end example
 
-This will compile some sample programs, run them and compare the output
-to reference output. Each of the checks should return a message @samp{passed}
-together with the CPU time used for that particular test.  If it does
-not, something went wrong.  This is mostly intended to be a QA-check
-if something was broken during the development, not a sanity check
-of your system.  Another intent is to allow people to fiddle around
-with optimization.  If @acronym{CLN} was installed all right
-this step is unlikely to return any errors.
+This will compile some sample programs, run them and check the output
+for correctness.  The regression tests fall in three categories.  First,
+the so called @emph{exams} are performed, simple tests where some
+predefined input is evaluated (like a pupils' exam).  Second, the
+@emph{checks} test the coherence of results among each other with
+possible random input.  Third, some @emph{timings} are performed, which
+benchmark some predefined problems with different sizes and display the
+CPU time used in seconds.  Each individual test should return a message
+@samp{passed}.  This is mostly intended to be a QA-check if something
+was broken during development, not a sanity check of your system.
+Another intent is to allow people to fiddle around with optimization.
 
 Generally, the top-level Makefile runs recursively to the
 subdirectories.  It is therfore safe to go into any subdirectory
@@ -828,11 +846,13 @@ using namespace GiNaC;
 
 int main()
 @{
-    numeric two(2);                     // exact integer 2
-    numeric r(2,3);                     // exact fraction 2/3
-    numeric e(2.71828);                 // floating point number
-    numeric p("3.1415926535897932385"); // floating point number
-
+    numeric two(2);                       // exact integer 2
+    numeric r(2,3);                       // exact fraction 2/3
+    numeric e(2.71828);                   // floating point number
+    numeric p("3.1415926535897932385");   // floating point number
+    // Trott's constant in scientific notation:
+    numeric trott("1.0841015122311136151E-2");
+    
     cout << two*p << endl;  // floating point 6.283...
     // ...
 @}