- corrected a bunch of typos.

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 4032cf241789f2de9bd9202b91026190f48b1c04..b7ac73ad25fcf804fa632ea3eef741a7612ef067 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -97,7 +97,7 @@ under one roof.
 
 This tutorial is intended for the novice user who is new to
 GiNaC but already has some background in C++ programming.  However,
 
 This tutorial is intended for the novice user who is new to
 GiNaC but already has some background in C++ programming.  However,

-since a hand made documentation like this one is difficult to keep in
+since a hand-made documentation like this one is difficult to keep in

 sync with the development the actual documentation is inside the
 sources in the form of comments.  That documentation may be parsed by
 one of the many Javadoc-like documentation systems.  If you fail at
 sync with the development the actual documentation is inside the
 sources in the form of comments.  That documentation may be parsed by
 one of the many Javadoc-like documentation systems.  If you fail at


@@ -134,7 +134,7 @@ MA 02111-1307, USA.
 @c    node-name, next, previous, up
 @chapter A Tour of GiNaC
 
 @c    node-name, next, previous, up
 @chapter A Tour of GiNaC
 

-This quick tour of GiNaC wants to rise your interest in the
+This quick tour of GiNaC wants to arise your interest in the

 subsequent chapters by showing off a bit.  Please excuse us if it
 leaves many open questions.
 
 subsequent chapters by showing off a bit.  Please excuse us if it
 leaves many open questions.
 


@@ -381,7 +381,7 @@ installation.
 @c    node-name, next, previous, up
 @section Prerequisites
 
 @c    node-name, next, previous, up
 @section Prerequisites
 

-In order to install GiNaC on your system, some prerequistes need
+In order to install GiNaC on your system, some prerequisites need

 to be met.  First of all, you need to have a C++-compiler adhering to
 the ANSI-standard @cite{ISO/IEC 14882:1998(E)}.  We used @acronym{GCC} for
 development so if you have a different compiler you are on your own.
 to be met.  First of all, you need to have a C++-compiler adhering to
 the ANSI-standard @cite{ISO/IEC 14882:1998(E)}.  We used @acronym{GCC} for
 development so if you have a different compiler you are on your own.


@@ -476,7 +476,7 @@ $ ./configure
 
 Configuration for a private static GiNaC library with several components
 sitting in custom places (site-wide @acronym{GCC} and private @acronym{CLN}),
 
 Configuration for a private static GiNaC library with several components
 sitting in custom places (site-wide @acronym{GCC} and private @acronym{CLN}),

-the compiler pursueded to be picky and full assertions switched on:
+the compiler pursuaded to be picky and full assertions switched on:

 
 @example
 $ export CXX=/usr/local/gnu/bin/c++
 
 @example
 $ export CXX=/usr/local/gnu/bin/c++


@@ -570,7 +570,7 @@ now know where all the files went during installation.}.
 @chapter Basic Concepts
 
 This chapter will describe the different fundamental objects
 @chapter Basic Concepts
 
 This chapter will describe the different fundamental objects

-that can be handled with GiNaC.  But before doing so, it is worthwhile
+that can be handled by GiNaC.  But before doing so, it is worthwhile

 introducing you to the more commonly used class of expressions,
 representing a flexible meta-class for storing all mathematical
 objects.
 introducing you to the more commonly used class of expressions,
 representing a flexible meta-class for storing all mathematical
 objects.


@@ -774,8 +774,8 @@ This also allows for a better handling of numeric radicals, since
 clear, why both classes @code{add} and @code{mul} are derived from the
 same abstract class: the data representation is the same, only the
 semantics differs.  In the class hierarchy, methods for polynomial
 clear, why both classes @code{add} and @code{mul} are derived from the
 same abstract class: the data representation is the same, only the
 semantics differs.  In the class hierarchy, methods for polynomial

-expansion and such are reimplemented for @code{add} and @code{mul}, but
-the data structure is inherited from @code{expairseq}.
+expansion and the like are reimplemented for @code{add} and @code{mul},
+but the data structure is inherited from @code{expairseq}.

 
 
 @node Symbols, Numbers, The Class Hierarchy, Basic Concepts
 
 
 @node Symbols, Numbers, The Class Hierarchy, Basic Concepts


@@ -953,7 +953,7 @@ using namespace GiNaC;
 // some very important constants:
 const numeric twentyone(21);
 const numeric ten(10);
 // some very important constants:
 const numeric twentyone(21);
 const numeric ten(10);

-const numeric fife(5);
+const numeric five(5);

 
 int main()
 @{
 
 int main()
 @{


@@ -1012,7 +1012,7 @@ table.
 @c    node-name, next, previous, up
 @section Constants
 
 @c    node-name, next, previous, up
 @section Constants
 

-Constants behave pretty much like symbols except that that they return
+Constants behave pretty much like symbols except that they return

 some specific number when the method @code{.evalf()} is called.
 
 The predefined known constants are:
 some specific number when the method @code{.evalf()} is called.
 
 The predefined known constants are:


@@ -1150,8 +1150,8 @@ gamma(x+1/2) -> gamma(x+1/2)
 gamma(15/2) -> (135135/128)*Pi^(1/2)
 @end example
 
 gamma(15/2) -> (135135/128)*Pi^(1/2)
 @end example
 

-Most of these functions can be differentiated, series expanded so on.
-Read the next chapter in order to learn more about this..
+Most of these functions can be differentiated, series expanded and so
+on.  Read the next chapter in order to learn more about this..

 
 
 @node Important Algorithms, Polynomial Expansion, Built-in functions, Top
 
 
 @node Important Algorithms, Polynomial Expansion, Built-in functions, Top


@@ -1343,16 +1343,16 @@ int main()
 @subsection The @code{normal} method
 
 While in common symbolic code @code{gcd()} and @code{lcm()} are not too
 @subsection The @code{normal} method
 
 While in common symbolic code @code{gcd()} and @code{lcm()} are not too

-heavily used, simplification occurs frequently.  Therefore @code{.normal()},
-which provides some basic form of simplification, has become a method of
-class @code{ex}, just like @code{.expand()}.
-It converts a rational function into an equivalent rational function
-where numererator and denominator are coprime.  This means, it finds
-the GCD of numerator and denominator and cancels it.  If it encounters
-some object which does not belong to the domain of rationals (a
-function for instance), that object is replaced by a temporary symbol.
-This means that both expressions @code{t1} and
-@code{t2} are indeed simplified in this little program:
+heavily used, simplification is called for frequently.  Therefore
+@code{.normal()}, which provides some basic form of simplification, has
+become a method of class @code{ex}, just like @code{.expand()}.  It
+converts a rational function into an equivalent rational function where
+numerator and denominator are coprime.  This means, it finds the GCD of
+numerator and denominator and cancels it.  If it encounters some object
+which does not belong to the domain of rationals (a function for
+instance), that object is replaced by a temporary symbol.  This means
+that both expressions @code{t1} and @code{t2} are indeed simplified in
+this little program:

 
 @subheading Cancellation of polynomial GCD (with obstacles)
 @example
 
 @subheading Cancellation of polynomial GCD (with obstacles)
 @example


@@ -1445,11 +1445,11 @@ When you run it, it produces the sequence @code{1}, @code{-1}, @code{5},
 @c    node-name, next, previous, up
 @section Series Expansion
 
 @c    node-name, next, previous, up
 @section Series Expansion
 

-Expressions know how to expand themselves as a Taylor series or
-(more generally) a Laurent series.  As in most conventional Computer
-Algebra Systems no distinction is made between those two.  There is a
-class of its own for storing such series as well as a class for
-storing the order of the series.  A sample program could read:
+Expressions know how to expand themselves as a Taylor series or (more
+generally) a Laurent series.  Similar to most conventional Computer
+Algebra Systems, no distinction is made between those two.  There is a
+class of its own for storing such series as well as a class for storing
+the order of the series.  A sample program could read:

 
 @subheading Series expansion
 @example
 
 @subheading Series expansion
 @example


@@ -1476,7 +1476,7 @@ int main()
 
 As an instructive application, let us calculate the numerical
 value of Archimedes' constant (for which there already exists the
 
 As an instructive application, let us calculate the numerical
 value of Archimedes' constant (for which there already exists the

-built-in constant @code{Pi}) using M@'echain's
+exbuilt-in constant @code{Pi}) using M@'echain's

 mysterious formula @code{Pi==16*atan(1/5)-4*atan(1/239)}.
 We may expand the arcus tangent around @code{0} and insert
 the fractions @code{1/5} and @code{1/239}.
 mysterious formula @code{Pi==16*atan(1/5)-4*atan(1/239)}.
 We may expand the arcus tangent around @code{0} and insert
 the fractions @code{1/5} and @code{1/239}.