fixed typos in examples

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 237aa3c4582cbf4e2e36d9286ed563dbf24d6e88..717d5b107909c665b06ad461cd98aded5bfcc4c8 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -23,7 +23,7 @@
 This is a tutorial that documents GiNaC @value{VERSION}, an open
 framework for symbolic computation within the C++ programming language.
 
 This is a tutorial that documents GiNaC @value{VERSION}, an open
 framework for symbolic computation within the C++ programming language.
 

-Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany

 
 Permission is granted to make and distribute verbatim copies of
 this manual provided the copyright notice and this permission notice
 
 Permission is granted to make and distribute verbatim copies of
 this manual provided the copyright notice and this permission notice


@@ -52,7 +52,7 @@ notice identical to this one.
 
 @page
 @vskip 0pt plus 1filll
 
 @page
 @vskip 0pt plus 1filll

-Copyright @copyright{} 1999-2001 Johannes Gutenberg University Mainz, Germany
+Copyright @copyright{} 1999-2002 Johannes Gutenberg University Mainz, Germany

 @sp 2
 Permission is granted to make and distribute verbatim copies of
 this manual provided the copyright notice and this permission notice
 @sp 2
 Permission is granted to make and distribute verbatim copies of
 this manual provided the copyright notice and this permission notice


@@ -135,7 +135,7 @@ the near future.
 
 @section License
 The GiNaC framework for symbolic computation within the C++ programming
 
 @section License
 The GiNaC framework for symbolic computation within the C++ programming

-language is Copyright @copyright{} 1999-2001 Johannes Gutenberg
+language is Copyright @copyright{} 1999-2002 Johannes Gutenberg

 University Mainz, Germany.
 
 This program is free software; you can redistribute it and/or
 University Mainz, Germany.
 
 This program is free software; you can redistribute it and/or


@@ -984,13 +984,22 @@ The above example prints the following output to screen:
 
 @example
 in 17 digits:
 
 @example
 in 17 digits:

-0.333333333333333333
-3.14159265358979324
+0.33333333333333333334
+3.1415926535897932385

 in 60 digits:
 in 60 digits:

-0.333333333333333333333333333333333333333333333333333333333333333333
-3.14159265358979323846264338327950288419716939937510582097494459231
+0.33333333333333333333333333333333333333333333333333333333333333333334
+3.1415926535897932384626433832795028841971693993751058209749445923078

 @end example
 
 @end example
 

+@cindex rounding
+Note that the last number is not necessarily rounded as you would
+naively expect it to be rounded in the decimal system.  But note also,
+that in both cases you got a couple of extra digits.  This is because
+numbers are internally stored by CLN as chunks of binary digits in order
+to match your machine's word size and to not waste precision.  Thus, on
+architectures with differnt word size, the above output might even
+differ with regard to actually computed digits.
+

 It should be clear that objects of class @code{numeric} should be used
 for constructing numbers or for doing arithmetic with them.  The objects
 one deals with most of the time are the polymorphic expressions @code{ex}.
 It should be clear that objects of class @code{numeric} should be used
 for constructing numbers or for doing arithmetic with them.  The objects
 one deals with most of the time are the polymorphic expressions @code{ex}.


@@ -3182,11 +3191,11 @@ Some examples:
 b^3+a^3+(x+y)^3
 > subs(a^4+b^4+(x+y)^4,$1^2==$1^3);
 b^4+a^4+(x+y)^4
 b^3+a^3+(x+y)^3
 > subs(a^4+b^4+(x+y)^4,$1^2==$1^3);
 b^4+a^4+(x+y)^4

-> subs((a+b+c)^2,a+b=x);
+> subs((a+b+c)^2,a+b==x);

 (a+b+c)^2
 > subs((a+b+c)^2,a+b+$1==x+$1);
 (x+c)^2
 (a+b+c)^2
 > subs((a+b+c)^2,a+b+$1==x+$1);
 (x+c)^2

-> subs(a+2*b,a+b=x);
+> subs(a+2*b,a+b==x);

 a+2*b
 > subs(4*x^3-2*x^2+5*x-1,x==a);
 -1+5*a-2*a^2+4*a^3
 a+2*b
 > subs(4*x^3-2*x^2+5*x-1,x==a);
 -1+5*a-2*a^2+4*a^3