@menu
* Introduction:: GiNaC's purpose.
-* A Tour of GiNaC:: A quick tour of the library.
+* A tour of GiNaC:: A quick tour of the library.
* Installation:: How to install the package.
-* Basic Concepts:: Description of fundamental classes.
-* Methods and Functions:: Algorithms for symbolic manipulations.
+* Basic concepts:: Description of fundamental classes.
+* Methods and functions:: Algorithms for symbolic manipulations.
* Extending GiNaC:: How to extend the library.
-* A Comparison With Other CAS:: Compares GiNaC to traditional CAS.
-* Internal Structures:: Description of some internal structures.
-* Package Tools:: Configuring packages to work with GiNaC.
+* A comparison with other CAS:: Compares GiNaC to traditional CAS.
+* Internal structures:: Description of some internal structures.
+* Package tools:: Configuring packages to work with GiNaC.
* Bibliography::
-* Concept Index::
+* Concept index::
@end menu
-@node Introduction, A Tour of GiNaC, Top, Top
+@node Introduction, A tour of GiNaC, Top, Top
@c node-name, next, previous, up
@chapter Introduction
@cindex history of GiNaC
MA 02110-1301, USA.
-@node A Tour of GiNaC, How to use it from within C++, Introduction, Top
+@node A tour of GiNaC, How to use it from within C++, Introduction, Top
@c node-name, next, previous, up
@chapter A Tour of GiNaC
@end menu
-@node How to use it from within C++, What it can do for you, A Tour of GiNaC, A Tour of GiNaC
+@node How to use it from within C++, What it can do for you, A tour of GiNaC, A tour of GiNaC
@c node-name, next, previous, up
@section How to use it from within C++
355687428096000*x*y+20922789888000*y^2+6402373705728000*x^2
@end example
-(@xref{Package Tools}, for tools that help you when creating a software
+(@xref{Package tools}, for tools that help you when creating a software
package that uses GiNaC.)
@cindex Hermite polynomial
convenient window into GiNaC's capabilities.
-@node What it can do for you, Installation, How to use it from within C++, A Tour of GiNaC
+@node What it can do for you, Installation, How to use it from within C++, A tour of GiNaC
@c node-name, next, previous, up
@section What it can do for you
@var{target} there in case something went wrong.
-@node Installing GiNaC, Basic Concepts, Building GiNaC, Installation
+@node Installing GiNaC, Basic concepts, Building GiNaC, Installation
@c node-name, next, previous, up
@section Installing GiNaC
@cindex installation
installation.}.
-@node Basic Concepts, Expressions, Installing GiNaC, Top
+@node Basic concepts, Expressions, Installing GiNaC, Top
@c node-name, next, previous, up
-@chapter Basic Concepts
+@chapter Basic concepts
This chapter will describe the different fundamental objects that can be
handled by GiNaC. But before doing so, it is worthwhile introducing you
* Expressions:: The fundamental GiNaC class.
* Automatic evaluation:: Evaluation and canonicalization.
* Error handling:: How the library reports errors.
-* The Class Hierarchy:: Overview of GiNaC's classes.
+* The class hierarchy:: Overview of GiNaC's classes.
* Symbols:: Symbolic objects.
* Numbers:: Numerical objects.
* Constants:: Pre-defined constants.
* Matrices:: Matrices.
* Indexed objects:: Handling indexed quantities.
* Non-commutative objects:: Algebras with non-commutative products.
-* Hash Maps:: A faster alternative to std::map<>.
+* Hash maps:: A faster alternative to std::map<>.
@end menu
-@node Expressions, Automatic evaluation, Basic Concepts, Basic Concepts
+@node Expressions, Automatic evaluation, Basic concepts, Basic concepts
@c node-name, next, previous, up
@section Expressions
@cindex expression (class @code{ex})
Expressions are handles to other more fundamental objects, that often
contain other expressions thus creating a tree of expressions
-(@xref{Internal Structures}, for particular examples). Most methods on
+(@xref{Internal structures}, for particular examples). Most methods on
@code{ex} therefore run top-down through such an expression tree. For
example, the method @code{has()} scans recursively for occurrences of
something inside an expression. Thus, if you have declared @code{MyEx4}
Unsorted containers such as @code{std::vector<>} and @code{std::list<>}
don't pose a problem. A @code{std::vector<ex>} works as expected.
-@xref{Information About Expressions}, for more about comparing and ordering
+@xref{Information about expressions}, for more about comparing and ordering
expressions.
-@node Automatic evaluation, Error handling, Expressions, Basic Concepts
+@node Automatic evaluation, Error handling, Expressions, Basic concepts
@c node-name, next, previous, up
@section Automatic evaluation and canonicalization of expressions
@cindex evaluation
re-evaluate their results.
-@node Error handling, The Class Hierarchy, Automatic evaluation, Basic Concepts
+@node Error handling, The class hierarchy, Automatic evaluation, Basic concepts
@c node-name, next, previous, up
@section Error handling
@cindex exceptions
@end example
-@node The Class Hierarchy, Symbols, Error handling, Basic Concepts
+@node The class hierarchy, Symbols, Error handling, Basic concepts
@c node-name, next, previous, up
@section The class hierarchy
pairs each consisting of one expression and a number (@code{numeric}).
What @emph{is} visible to the user are the derived classes @code{add}
and @code{mul}, representing sums and products. @xref{Internal
-Structures}, where these two classes are described in more detail. The
+structures}, where these two classes are described in more detail. The
following table shortly summarizes what kinds of mathematical objects
are stored in the different classes:
@end cartouche
-@node Symbols, Numbers, The Class Hierarchy, Basic Concepts
+@node Symbols, Numbers, The class hierarchy, Basic concepts
@c node-name, next, previous, up
@section Symbols
@cindex @code{symbol} (class)
As we said, the names of symbols primarily serve for purposes of expression
output. But there are actually two instances where GiNaC uses the names for
identifying symbols: When constructing an expression from a string, and when
-recreating an expression from an archive (@pxref{Input/Output}).
+recreating an expression from an archive (@pxref{Input/output}).
In addition to its name, a symbol may contain a special string that is used
in LaTeX output:
@end example
This creates a symbol that is printed as "@code{x}" in normal output, but
-as "@code{\Box}" in LaTeX code (@xref{Input/Output}, for more
+as "@code{\Box}" in LaTeX code (@xref{Input/output}, for more
information about the different output formats of expressions in GiNaC).
GiNaC automatically creates proper LaTeX code for symbols having names of
greek letters (@samp{alpha}, @samp{mu}, etc.).
calculations and give them a name, use C++ variables of type @code{ex}.
If you want to replace a symbol in an expression with something else, you
can invoke the expression's @code{.subs()} method
-(@pxref{Substituting Expressions}).
+(@pxref{Substituting expressions}).
@cindex @code{realsymbol()}
By default, symbols are expected to stand in for complex values, i.e. they live
in the complex domain. As a consequence, operations like complex conjugation,
-for example (@pxref{Complex Conjugation}), do @emph{not} evaluate if applied
+for example (@pxref{Complex expressions}), do @emph{not} evaluate if applied
to such symbols. Likewise @code{log(exp(x))} does not evaluate to @code{x},
because of the unknown imaginary part of @code{x}.
On the other hand, if you are sure that your symbols will hold only real values, you
@code{realsymbol x("x");} to tell GiNaC that @code{x} stands in for real values.
-@node Numbers, Constants, Symbols, Basic Concepts
+@node Numbers, Constants, Symbols, Basic concepts
@c node-name, next, previous, up
@section Numbers
@cindex @code{numeric} (class)
part of complex numbers.
-@node Constants, Fundamental containers, Numbers, Basic Concepts
+@node Constants, Fundamental containers, Numbers, Basic concepts
@c node-name, next, previous, up
@section Constants
@cindex @code{constant} (class)
@end cartouche
-@node Fundamental containers, Lists, Constants, Basic Concepts
+@node Fundamental containers, Lists, Constants, Basic concepts
@c node-name, next, previous, up
@section Sums, products and powers
@cindex polynomial
@code{3*x+4-x} to @code{2*x+4}.
-@node Lists, Mathematical functions, Fundamental containers, Basic Concepts
+@node Lists, Mathematical functions, Fundamental containers, Basic concepts
@c node-name, next, previous, up
@section Lists of expressions
@cindex @code{lst} (class)
@end example
-@node Mathematical functions, Relations, Lists, Basic Concepts
+@node Mathematical functions, Relations, Lists, Basic concepts
@c node-name, next, previous, up
@section Mathematical functions
@cindex @code{function} (class)
There are quite a number of useful functions hard-wired into GiNaC. For
instance, all trigonometric and hyperbolic functions are implemented
-(@xref{Built-in Functions}, for a complete list).
+(@xref{Built-in functions}, for a complete list).
These functions (better called @emph{pseudofunctions}) are all objects
of class @code{function}. They accept one or more expressions as
wrapped inside an @code{ex}.
-@node Relations, Integrals, Mathematical functions, Basic Concepts
+@node Relations, Integrals, Mathematical functions, Basic concepts
@c node-name, next, previous, up
@section Relations
@cindex @code{relational} (class)
however, that @code{==} here does not perform any simplifications, hence
@code{expand()} must be called explicitly.
-@node Integrals, Matrices, Relations, Basic Concepts
+@node Integrals, Matrices, Relations, Basic concepts
@c node-name, next, previous, up
@section Integrals
@cindex @code{integral} (class)
as expected. Note that it makes no sense to differentiate an integral
with respect to the integration variable.
-@node Matrices, Indexed objects, Integrals, Basic Concepts
+@node Matrices, Indexed objects, Integrals, Basic concepts
@c node-name, next, previous, up
@section Matrices
@cindex @code{matrix} (class)
overdetermined, an exception is thrown.
-@node Indexed objects, Non-commutative objects, Matrices, Basic Concepts
+@node Indexed objects, Non-commutative objects, Matrices, Basic concepts
@c node-name, next, previous, up
@section Indexed objects
for checking whether the value and dimension are numeric or symbolic
(non-numeric). Using the @code{info()} method of an index (see @ref{Information
-About Expressions}) returns information about the index value.
+about expressions}) returns information about the index value.
@cindex @code{varidx} (class)
If you need co- and contravariant indices, use the @code{varidx} class:
Sometimes you will want to substitute one symbolic index with another
symbolic or numeric index, for example when calculating one specific element
of a tensor expression. This is done with the @code{.subs()} method, as it
-is done for symbols (see @ref{Substituting Expressions}).
+is done for symbols (see @ref{Substituting expressions}).
You have two possibilities here. You can either substitute the whole index
by another index or expression:
of the metric tensor.
-@node Non-commutative objects, Hash Maps, Indexed objects, Basic Concepts
+@node Non-commutative objects, Hash maps, Indexed objects, Basic concepts
@c node-name, next, previous, up
@section Non-commutative objects
@end example
-@node Hash Maps, Methods and Functions, Non-commutative objects, Basic Concepts
+@node Hash maps, Methods and functions, Non-commutative objects, Basic concepts
@c node-name, next, previous, up
@section Hash Maps
@cindex hash maps
@end itemize
-@node Methods and Functions, Information About Expressions, Hash Maps, Top
+@node Methods and functions, Information about expressions, Hash maps, Top
@c node-name, next, previous, up
-@chapter Methods and Functions
+@chapter Methods and functions
@cindex polynomial
In this chapter the most important algorithms provided by GiNaC will be
avoided.
@menu
-* Information About Expressions::
-* Numerical Evaluation::
-* Substituting Expressions::
-* Pattern Matching and Advanced Substitutions::
-* Applying a Function on Subexpressions::
-* Visitors and Tree Traversal::
-* Polynomial Arithmetic:: Working with polynomials.
-* Rational Expressions:: Working with rational functions.
-* Symbolic Differentiation::
-* Series Expansion:: Taylor and Laurent expansion.
+* Information about expressions::
+* Numerical evaluation::
+* Substituting expressions::
+* Pattern matching and advanced substitutions::
+* Applying a function on subexpressions::
+* Visitors and tree traversal::
+* Polynomial arithmetic:: Working with polynomials.
+* Rational expressions:: Working with rational functions.
+* Symbolic differentiation::
+* Series expansion:: Taylor and Laurent expansion.
* Symmetrization::
-* Built-in Functions:: List of predefined mathematical functions.
+* Built-in functions:: List of predefined mathematical functions.
* Multiple polylogarithms::
-* Complex Conjugation::
-* Solving Linear Systems of Equations::
-* Input/Output:: Input and output of expressions.
+* Complex expressions::
+* Solving linear systems of equations::
+* Input/output:: Input and output of expressions.
@end menu
-@node Information About Expressions, Numerical Evaluation, Methods and Functions, Methods and Functions
+@node Information about expressions, Numerical evaluation, Methods and functions, Methods and functions
@c node-name, next, previous, up
@section Getting information about expressions
When the test made by @code{is_a<T>()} returns true, it is safe to call
one of the functions @code{ex_to<T>()}, where @code{T} is one of the
-class names (@xref{The Class Hierarchy}, for a list of all classes). For
+class names (@xref{The class hierarchy}, for a list of all classes). For
example, assuming @code{e} is an @code{ex}:
@example
@code{is_a<T>(e)} allows you to check whether the top-level object of
an expression @samp{e} is an instance of the GiNaC class @samp{T}
-(@xref{The Class Hierarchy}, for a list of all classes). This is most useful,
+(@xref{The class hierarchy}, for a list of all classes). This is most useful,
e.g., for checking whether an expression is a number, a sum, or a product:
@example
after @code{other}.
-@node Numerical Evaluation, Substituting Expressions, Information About Expressions, Methods and Functions
+@node Numerical evaluation, Substituting expressions, Information about expressions, Methods and functions
@c node-name, next, previous, up
@section Numerical evaluation
@cindex @code{evalf()}
@end example
-@node Substituting Expressions, Pattern Matching and Advanced Substitutions, Numerical Evaluation, Methods and Functions
+@node Substituting expressions, Pattern matching and advanced substitutions, Numerical evaluation, Methods and functions
@c node-name, next, previous, up
@section Substituting expressions
@cindex @code{subs()}
large @code{subs()} operations significantly faster if you are not using
patterns. The second option, @code{subs_options::algebraic} enables
algebraic substitutions in products and powers.
-@ref{Pattern Matching and Advanced Substitutions}, for more information
+@ref{Pattern matching and advanced substitutions}, for more information
about patterns and algebraic substitutions. The third option,
@code{subs_options::no_index_renaming} disables the feature that dummy
indices are renamed if the subsitution could give a result in which a
next section.
-@node Pattern Matching and Advanced Substitutions, Applying a Function on Subexpressions, Substituting Expressions, Methods and Functions
+@node Pattern matching and advanced substitutions, Applying a function on subexpressions, Substituting expressions, Methods and functions
@c node-name, next, previous, up
@section Pattern matching and advanced substitutions
@cindex @code{wildcard} (class)
and not for locating @code{x+y} within @code{x+y+z}.
-@node Applying a Function on Subexpressions, Visitors and Tree Traversal, Pattern Matching and Advanced Substitutions, Methods and Functions
+@node Applying a function on subexpressions, Visitors and tree traversal, Pattern matching and advanced substitutions, Methods and functions
@c node-name, next, previous, up
@section Applying a function on subexpressions
@cindex tree traversal
@end example
-@node Visitors and Tree Traversal, Polynomial Arithmetic, Applying a Function on Subexpressions, Methods and Functions
+@node Visitors and tree traversal, Polynomial arithmetic, Applying a function on subexpressions, Methods and functions
@c node-name, next, previous, up
@section Visitors and tree traversal
@cindex tree traversal
@end example
-@node Polynomial Arithmetic, Rational Expressions, Visitors and Tree Traversal, Methods and Functions
+@node Polynomial arithmetic, Rational expressions, Visitors and tree traversal, Methods and functions
@c node-name, next, previous, up
@section Polynomial arithmetic
with this method.
-@node Rational Expressions, Symbolic Differentiation, Polynomial Arithmetic, Methods and Functions
+@node Rational expressions, Symbolic differentiation, Polynomial arithmetic, Methods and functions
@c node-name, next, previous, up
@section Rational expressions
@end example
-@node Symbolic Differentiation, Series Expansion, Rational Expressions, Methods and Functions
+@node Symbolic differentiation, Series expansion, Rational expressions, Methods and functions
@c node-name, next, previous, up
@section Symbolic differentiation
@cindex differentiation
@code{i} by two since all odd Euler numbers vanish anyways.
-@node Series Expansion, Symmetrization, Symbolic Differentiation, Methods and Functions
+@node Series expansion, Symmetrization, Symbolic differentiation, Methods and functions
@c node-name, next, previous, up
@section Series expansion
@cindex @code{series()}
@end example
-@node Symmetrization, Built-in Functions, Series Expansion, Methods and Functions
+@node Symmetrization, Built-in functions, Series expansion, Methods and functions
@c node-name, next, previous, up
@section Symmetrization
@cindex @code{symmetrize()}
@}
@end example
-@node Built-in Functions, Multiple polylogarithms, Symmetrization, Methods and Functions
+@node Built-in functions, Multiple polylogarithms, Symmetrization, Methods and functions
@c node-name, next, previous, up
@section Predefined mathematical functions
@c
@cindex @code{conjugate()}
@item @code{conjugate(x)}
@tab complex conjugation
-@cindex @code{conjugate()}
+@cindex @code{real_part()}
+@item @code{real_part(x)}
+@tab real part
+@cindex @code{imag_part()}
+@item @code{imag_part(x)}
+@tab imaginary part
@item @code{sqrt(x)}
@tab square root (not a GiNaC function, rather an alias for @code{pow(x, numeric(1, 2))})
@cindex @code{sqrt()}
standard incorporate these functions in the complex domain in a manner
compatible with C99.
-@node Multiple polylogarithms, Complex Conjugation, Built-in Functions, Methods and Functions
+@node Multiple polylogarithms, Complex expressions, Built-in functions, Methods and functions
@c node-name, next, previous, up
@subsection Multiple polylogarithms
@cite{Numerical Evaluation of Multiple Polylogarithms},
J.Vollinga, S.Weinzierl, hep-ph/0410259
-@node Complex Conjugation, Solving Linear Systems of Equations, Multiple polylogarithms, Methods and Functions
+@node Complex expressions, Solving linear systems of equations, Multiple polylogarithms, Methods and functions
@c node-name, next, previous, up
-@section Complex conjugation
+@section Complex expressions
@c
@cindex @code{conjugate()}
-The method
+For dealing with complex expressions there are the methods
@example
ex ex::conjugate();
+ex ex::real_part();
+ex ex::imag_part();
@end example
-returns the complex conjugate of the expression. For all built-in functions and objects the
-conjugation gives the expected results:
+that return respectively the complex conjugate, the real part and the
+imaginary part of an expression. Complex conjugation works as expected
+for all built-in functinos and objects. Taking real and imaginary
+parts has not yet been implemented for all built-in functions. In cases where
+it is not known how to conjugate or take a real/imaginary part one
+of the functions @code{conjugate}, @code{real_part} or @code{imag_part}
+is returned. For instance, in case of a complex symbol @code{x}
+(symbols are complex by default), one could not simplify
+@code{conjugate(x)}. In the case of strings of gamma matrices,
+the @code{conjugate} method takes the Dirac conjugate.
+For example,
@example
@{
varidx a(symbol("a"), 4), b(symbol("b"), 4);
@}
@end example
-For symbols in the complex domain the conjugation can not be evaluated and the GiNaC function
-@code{conjugate} is returned. GiNaC functions conjugate by applying the conjugation to their
-arguments. This is the default strategy. If you want to define your own functions and want to
-change this behavior, you have to supply a specialized conjugation method for your function
-(see @ref{Symbolic functions} and the GiNaC source-code for @code{abs} as an example).
+If you declare your own GiNaC functions, then they will conjugate themselves
+by conjugating their arguments. This is the default strategy. If you want to
+change this behavior, you have to supply a specialized conjugation method
+for your function (see @ref{Symbolic functions} and the GiNaC source-code
+for @code{abs} as an example). Also, specialized methods can be provided
+to take real and imaginary parts of user-defined functions.
-@node Solving Linear Systems of Equations, Input/Output, Complex Conjugation, Methods and Functions
+@node Solving linear systems of equations, Input/output, Complex expressions, Methods and functions
@c node-name, next, previous, up
@section Solving linear systems of equations
@cindex @code{lsolve()}
Here, @code{eqns} is a @code{lst} of equalities (i.e. class
@code{relational}) while @code{symbols} is a @code{lst} of
-indeterminates. (@xref{The Class Hierarchy}, for an exposition of class
+indeterminates. (@xref{The class hierarchy}, for an exposition of class
@code{lst}).
It returns the @code{lst} of solutions as an expression. As an example,
around that method.
-@node Input/Output, Extending GiNaC, Solving Linear Systems of Equations, Methods and Functions
+@node Input/output, Extending GiNaC, Solving linear systems of equations, Methods and functions
@c node-name, next, previous, up
@section Input and output of expressions
@cindex I/O
class may change between GiNaC versions.
-@node Extending GiNaC, What does not belong into GiNaC, Input/Output, Top
+@node Extending GiNaC, What does not belong into GiNaC, Input/output, Top
@c node-name, next, previous, up
@chapter Extending GiNaC
@section GiNaC's expression output system
GiNaC allows the output of expressions in a variety of different formats
-(@pxref{Input/Output}). This section will explain how expression output
+(@pxref{Input/output}). This section will explain how expression output
is implemented internally, and how to define your own output formats or
change the output format of built-in algebraic objects. You will also want
to read this section if you plan to write your own algebraic classes or
@code{sprod::unarchive()} function.
-@node Adding classes, A Comparison With Other CAS, Structures, Extending GiNaC
+@node Adding classes, A comparison with other CAS, Structures, Extending GiNaC
@c node-name, next, previous, up
@section Adding classes
That's it. May the source be with you!
-@node A Comparison With Other CAS, Advantages, Adding classes, Top
+@node A comparison with other CAS, Advantages, Adding classes, Top
@c node-name, next, previous, up
@chapter A Comparison With Other CAS
@cindex advocacy
* Why C++?:: Attractiveness of C++.
@end menu
-@node Advantages, Disadvantages, A Comparison With Other CAS, A Comparison With Other CAS
+@node Advantages, Disadvantages, A comparison with other CAS, A comparison with other CAS
@c node-name, next, previous, up
@section Advantages
@end itemize
-@node Disadvantages, Why C++?, Advantages, A Comparison With Other CAS
+@node Disadvantages, Why C++?, Advantages, A comparison with other CAS
@c node-name, next, previous, up
@section Disadvantages
@end itemize
-@node Why C++?, Internal Structures, Disadvantages, A Comparison With Other CAS
+@node Why C++?, Internal structures, Disadvantages, A comparison with other CAS
@c node-name, next, previous, up
@section Why C++?
any other programming language.
-@node Internal Structures, Expressions are reference counted, Why C++? , Top
+@node Internal structures, Expressions are reference counted, Why C++? , Top
@c node-name, next, previous, up
-@appendix Internal Structures
+@appendix Internal structures
@menu
* Expressions are reference counted::
* Internal representation of products and sums::
@end menu
-@node Expressions are reference counted, Internal representation of products and sums, Internal Structures, Internal Structures
+@node Expressions are reference counted, Internal representation of products and sums, Internal structures, Internal structures
@c node-name, next, previous, up
@appendixsection Expressions are reference counted
implementation which is pretty close to the one in GiNaC.
-@node Internal representation of products and sums, Package Tools, Expressions are reference counted, Internal Structures
+@node Internal representation of products and sums, Package tools, Expressions are reference counted, Internal structures
@c node-name, next, previous, up
@appendixsection Internal representation of products and sums
but the data structure is inherited from @code{expairseq}.
-@node Package Tools, ginac-config, Internal representation of products and sums, Top
+@node Package tools, ginac-config, Internal representation of products and sums, Top
@c node-name, next, previous, up
-@appendix Package Tools
+@appendix Package tools
If you are creating a software package that uses the GiNaC library,
setting the correct command line options for the compiler and linker
@end menu
-@node ginac-config, AM_PATH_GINAC, Package Tools, Package Tools
+@node ginac-config, AM_PATH_GINAC, Package tools, Package tools
@c node-name, next, previous, up
@section @command{ginac-config}
@cindex ginac-config
work on any system, no matter how GiNaC was configured.
-@node AM_PATH_GINAC, Configure script options, ginac-config, Package Tools
+@node AM_PATH_GINAC, Configure script options, ginac-config, Package tools
@c node-name, next, previous, up
@section @samp{AM_PATH_GINAC}
@cindex AM_PATH_GINAC
@end example
-@node Bibliography, Concept Index, Example package, Top
+@node Bibliography, Concept index, Example package, Top
@c node-name, next, previous, up
@appendix Bibliography
@end itemize
-@node Concept Index, , Bibliography, Top
+@node Concept index, , Bibliography, Top
@c node-name, next, previous, up
-@unnumbered Concept Index
+@unnumbered Concept index
@printindex cp
'typedef ex (* conjugate_funcp_${N})(${SEQ1});'."\n",
'const ex &','','');
+$typedef_real_part_funcp=generate(
+'typedef ex (* real_part_funcp_${N})(${SEQ1});'."\n",
+'const ex &','','');
+
+$typedef_imag_part_funcp=generate(
+'typedef ex (* imag_part_funcp_${N})(${SEQ1});'."\n",
+'const ex &','','');
+
$typedef_derivative_funcp=generate(
'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
'const ex &','','');
$conjugate_func_interface=generate(' function_options & conjugate_func(conjugate_funcp_${N} d);'."\n",'','','');
+$real_part_func_interface=generate(' function_options & real_part_func(real_part_funcp_${N} d);'."\n",'','','');
+
+$imag_part_func_interface=generate(' function_options & imag_part_func(imag_part_funcp_${N} d);'."\n",'','','');
+
$derivative_func_interface=generate(' function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
$power_func_interface=generate(' function_options & power_func(power_funcp_${N} d);'."\n",'','','');
return ((conjugate_funcp_${N})(opt.conjugate_f))(${SEQ1});
END_OF_DIFF_SWITCH_STATEMENT
+$real_part_switch_statement=generate(
+ <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
+ case ${N}:
+ return ((real_part_funcp_${N})(opt.real_part_f))(${SEQ1});
+END_OF_DIFF_SWITCH_STATEMENT
+
+$imag_part_switch_statement=generate(
+ <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
+ case ${N}:
+ return ((imag_part_funcp_${N})(opt.imag_part_f))(${SEQ1});
+END_OF_DIFF_SWITCH_STATEMENT
+
$diff_switch_statement=generate(
<<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
case ${N}:
}
END_OF_CONJUGATE_FUNC_IMPLEMENTATION
+$real_part_func_implementation=generate(
+ <<'END_OF_REAL_PART_FUNC_IMPLEMENTATION','','','');
+function_options & function_options::real_part_func(real_part_funcp_${N} c)
+{
+ test_and_set_nparams(${N});
+ real_part_f = real_part_funcp(c);
+ return *this;
+}
+END_OF_REAL_PART_FUNC_IMPLEMENTATION
+
+$imag_part_func_implementation=generate(
+ <<'END_OF_IMAG_PART_FUNC_IMPLEMENTATION','','','');
+function_options & function_options::imag_part_func(imag_part_funcp_${N} c)
+{
+ test_and_set_nparams(${N});
+ imag_part_f = imag_part_funcp(c);
+ return *this;
+}
+END_OF_IMAG_PART_FUNC_IMPLEMENTATION
+
$derivative_func_implementation=generate(
<<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
function_options & function_options::derivative_func(derivative_funcp_${N} d)
typedef ex (* eval_funcp)();
typedef ex (* evalf_funcp)();
typedef ex (* conjugate_funcp)();
+typedef ex (* real_part_funcp)();
+typedef ex (* imag_part_funcp)();
typedef ex (* derivative_funcp)();
typedef ex (* power_funcp)();
typedef ex (* series_funcp)();
$typedef_eval_funcp
$typedef_evalf_funcp
$typedef_conjugate_funcp
+$typedef_real_part_funcp
+$typedef_imag_part_funcp
$typedef_derivative_funcp
$typedef_power_funcp
$typedef_series_funcp
typedef ex (* eval_funcp_exvector)(const exvector &);
typedef ex (* evalf_funcp_exvector)(const exvector &);
typedef ex (* conjugate_funcp_exvector)(const exvector &);
+typedef ex (* real_part_funcp_exvector)(const exvector &);
+typedef ex (* imag_part_funcp_exvector)(const exvector &);
typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
typedef ex (* power_funcp_exvector)(const exvector &, const ex &);
typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
$eval_func_interface
$evalf_func_interface
$conjugate_func_interface
+$real_part_func_interface
+$imag_part_func_interface
$derivative_func_interface
$power_func_interface
$series_func_interface
function_options & eval_func(eval_funcp_exvector e);
function_options & evalf_func(evalf_funcp_exvector ef);
function_options & conjugate_func(conjugate_funcp_exvector d);
+ function_options & real_part_func(real_part_funcp_exvector d);
+ function_options & imag_part_func(imag_part_funcp_exvector d);
function_options & derivative_func(derivative_funcp_exvector d);
function_options & power_func(power_funcp_exvector d);
function_options & series_func(series_funcp_exvector s);
eval_funcp eval_f;
evalf_funcp evalf_f;
conjugate_funcp conjugate_f;
+ real_part_funcp real_part_f;
+ imag_part_funcp imag_part_f;
derivative_funcp derivative_f;
power_funcp power_f;
series_funcp series_f;
bool eval_use_exvector_args;
bool evalf_use_exvector_args;
bool conjugate_use_exvector_args;
+ bool real_part_use_exvector_args;
+ bool imag_part_use_exvector_args;
bool derivative_use_exvector_args;
bool power_use_exvector_args;
bool series_use_exvector_args;
ex thiscontainer(const exvector & v) const;
ex thiscontainer(std::auto_ptr<exvector> vp) const;
ex conjugate() const;
+ ex real_part() const;
+ ex imag_part() const;
protected:
ex derivative(const symbol & s) const;
bool is_equal_same_type(const basic & other) const;
{
set_name("unnamed_function", "\\\\mbox{unnamed}");
nparams = 0;
- eval_f = evalf_f = conjugate_f = derivative_f = power_f = series_f = 0;
+ eval_f = evalf_f = real_part_f = imag_part_f = conjugate_f = derivative_f
+ = power_f = series_f = 0;
evalf_params_first = true;
use_return_type = false;
eval_use_exvector_args = false;
evalf_use_exvector_args = false;
conjugate_use_exvector_args = false;
+ real_part_use_exvector_args = false;
+ imag_part_use_exvector_args = false;
derivative_use_exvector_args = false;
power_use_exvector_args = false;
series_use_exvector_args = false;
$eval_func_implementation
$evalf_func_implementation
$conjugate_func_implementation
+$real_part_func_implementation
+$imag_part_func_implementation
$derivative_func_implementation
$power_func_implementation
$series_func_implementation
conjugate_f = conjugate_funcp(c);
return *this;
}
+function_options& function_options::real_part_func(real_part_funcp_exvector c)
+{
+ real_part_use_exvector_args = true;
+ real_part_f = real_part_funcp(c);
+ return *this;
+}
+function_options& function_options::imag_part_func(imag_part_funcp_exvector c)
+{
+ imag_part_use_exvector_args = true;
+ imag_part_f = imag_part_funcp(c);
+ return *this;
+}
+
function_options& function_options::derivative_func(derivative_funcp_exvector d)
{
derivative_use_exvector_args = true;
throw(std::logic_error("function::conjugate(): invalid nparams"));
}
+/** Implementation of ex::real_part for functions. */
+ex function::real_part() const
+{
+ GINAC_ASSERT(serial<registered_functions().size());
+ const function_options & opt = registered_functions()[serial];
+
+ if (opt.real_part_f==0)
+ return basic::real_part();
+
+ if (opt.real_part_use_exvector_args)
+ return ((real_part_funcp_exvector)(opt.real_part_f))(seq);
+
+ switch (opt.nparams) {
+ // the following lines have been generated for max. ${maxargs} parameters
+${real_part_switch_statement}
+ // end of generated lines
+ }
+ throw(std::logic_error("function::real_part(): invalid nparams"));
+}
+
+/** Implementation of ex::imag_part for functions. */
+ex function::imag_part() const
+{
+ GINAC_ASSERT(serial<registered_functions().size());
+ const function_options & opt = registered_functions()[serial];
+
+ if (opt.imag_part_f==0)
+ return basic::imag_part();
+
+ if (opt.imag_part_use_exvector_args)
+ return ((imag_part_funcp_exvector)(opt.imag_part_f))(seq);
+
+ switch (opt.nparams) {
+ // the following lines have been generated for max. ${maxargs} parameters
+${imag_part_switch_statement}
+ // end of generated lines
+ }
+ throw(std::logic_error("function::imag_part(): invalid nparams"));
+}
+
// protected
/** Implementation of ex::diff() for functions. It applies the chain rule,
return arg;
}
+static ex conjugate_real_part(const ex & arg)
+{
+ return arg.real_part();
+}
+
+static ex conjugate_imag_part(const ex & arg)
+{
+ return -arg.imag_part();
+}
+
REGISTER_FUNCTION(conjugate_function, eval_func(conjugate_eval).
evalf_func(conjugate_evalf).
print_func<print_latex>(conjugate_print_latex).
conjugate_func(conjugate_conjugate).
+ real_part_func(conjugate_real_part).
+ imag_part_func(conjugate_imag_part).
set_name("conjugate","conjugate"));
+//////////
+// real part
+//////////
+
+static ex real_part_evalf(const ex & arg)
+{
+ if (is_exactly_a<numeric>(arg)) {
+ return ex_to<numeric>(arg).real();
+ }
+ return real_part_function(arg).hold();
+}
+
+static ex real_part_eval(const ex & arg)
+{
+ return arg.real_part();
+}
+
+static void real_part_print_latex(const ex & arg, const print_context & c)
+{
+ c.s << "\\Re"; arg.print(c); c.s << "";
+}
+
+static ex real_part_conjugate(const ex & arg)
+{
+ return real_part_function(arg).hold();
+}
+
+static ex real_part_real_part(const ex & arg)
+{
+ return real_part_function(arg).hold();
+}
+
+static ex real_part_imag_part(const ex & arg)
+{
+ return 0;
+}
+
+REGISTER_FUNCTION(real_part_function, eval_func(real_part_eval).
+ evalf_func(real_part_evalf).
+ print_func<print_latex>(real_part_print_latex).
+ conjugate_func(real_part_conjugate).
+ real_part_func(real_part_real_part).
+ imag_part_func(real_part_imag_part).
+ set_name("real_part","real_part"));
+
+//////////
+// imag part
+//////////
+
+static ex imag_part_evalf(const ex & arg)
+{
+ if (is_exactly_a<numeric>(arg)) {
+ return ex_to<numeric>(arg).imag();
+ }
+ return imag_part_function(arg).hold();
+}
+
+static ex imag_part_eval(const ex & arg)
+{
+ return arg.imag_part();
+}
+
+static void imag_part_print_latex(const ex & arg, const print_context & c)
+{
+ c.s << "\\Im"; arg.print(c); c.s << "";
+}
+
+static ex imag_part_conjugate(const ex & arg)
+{
+ return imag_part_function(arg).hold();
+}
+
+static ex imag_part_real_part(const ex & arg)
+{
+ return imag_part_function(arg).hold();
+}
+
+static ex imag_part_imag_part(const ex & arg)
+{
+ return 0;
+}
+
+REGISTER_FUNCTION(imag_part_function, eval_func(imag_part_eval).
+ evalf_func(imag_part_evalf).
+ print_func<print_latex>(imag_part_print_latex).
+ conjugate_func(imag_part_conjugate).
+ real_part_func(imag_part_real_part).
+ imag_part_func(imag_part_imag_part).
+ set_name("imag_part","imag_part"));
+
//////////
// absolute value
//////////
return abs(arg);
}
+static ex abs_real_part(const ex & arg)
+{
+ return abs(arg).hold();
+}
+
+static ex abs_imag_part(const ex& arg)
+{
+ return 0;
+}
+
static ex abs_power(const ex & arg, const ex & exp)
{
if (arg.is_equal(arg.conjugate()) && is_a<numeric>(exp) && ex_to<numeric>(exp).is_even())
print_func<print_csrc_float>(abs_print_csrc_float).
print_func<print_csrc_double>(abs_print_csrc_float).
conjugate_func(abs_conjugate).
+ real_part_func(abs_real_part).
+ imag_part_func(abs_imag_part).
power_func(abs_power));
//////////
static ex step_conjugate(const ex& arg)
{
- return step(arg);
+ return step(arg).hold();
+}
+
+static ex step_real_part(const ex& arg)
+{
+ return step(arg).hold();
+}
+
+static ex step_imag_part(const ex& arg)
+{
+ return 0;
}
REGISTER_FUNCTION(step, eval_func(step_eval).
evalf_func(step_evalf).
series_func(step_series).
- conjugate_func(step_conjugate));
+ conjugate_func(step_conjugate).
+ real_part_func(step_real_part).
+ imag_part_func(step_imag_part));
//////////
// Complex sign
static ex csgn_conjugate(const ex& arg)
{
- return csgn(arg);
+ return csgn(arg).hold();
+}
+
+static ex csgn_real_part(const ex& arg)
+{
+ return csgn(arg).hold();
+}
+
+static ex csgn_imag_part(const ex& arg)
+{
+ return 0;
}
static ex csgn_power(const ex & arg, const ex & exp)
evalf_func(csgn_evalf).
series_func(csgn_series).
conjugate_func(csgn_conjugate).
+ real_part_func(csgn_real_part).
+ imag_part_func(csgn_imag_part).
power_func(csgn_power));
static ex eta_conjugate(const ex & x, const ex & y)
{
- return -eta(x,y);
+ return -eta(x, y);
+}
+
+static ex eta_real_part(const ex & x, const ex & y)
+{
+ return 0;
+}
+
+static ex eta_imag_part(const ex & x, const ex & y)
+{
+ return -I*eta(x, y).hold();
}
REGISTER_FUNCTION(eta, eval_func(eta_eval).
series_func(eta_series).
latex_name("\\eta").
set_symmetry(sy_symm(0, 1)).
- conjugate_func(eta_conjugate));
+ conjugate_func(eta_conjugate).
+ real_part_func(eta_real_part).
+ imag_part_func(eta_imag_part));
//////////
static ex factorial_conjugate(const ex & x)
{
- return factorial(x);
+ return factorial(x).hold();
+}
+
+static ex factorial_real_part(const ex & x)
+{
+ return factorial(x).hold();
+}
+
+static ex factorial_imag_part(const ex & x)
+{
+ return 0;
}
REGISTER_FUNCTION(factorial, eval_func(factorial_eval).
evalf_func(factorial_evalf).
print_func<print_dflt>(factorial_print_dflt_latex).
print_func<print_latex>(factorial_print_dflt_latex).
- conjugate_func(factorial_conjugate));
+ conjugate_func(factorial_conjugate).
+ real_part_func(factorial_real_part).
+ imag_part_func(factorial_imag_part));
//////////
// binomial
// function, also complex conjugation should be changed (or rather, deleted).
static ex binomial_conjugate(const ex & x, const ex & y)
{
- return binomial(x,y);
+ return binomial(x,y).hold();
+}
+
+static ex binomial_real_part(const ex & x, const ex & y)
+{
+ return binomial(x,y).hold();
+}
+
+static ex binomial_imag_part(const ex & x, const ex & y)
+{
+ return 0;
}
REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
evalf_func(binomial_evalf).
- conjugate_func(binomial_conjugate));
+ conjugate_func(binomial_conjugate).
+ real_part_func(binomial_real_part).
+ imag_part_func(binomial_imag_part));
//////////
// Order term function (for truncated power series)
static ex Order_conjugate(const ex & x)
{
- return Order(x);
+ return Order(x).hold();
+}
+
+static ex Order_real_part(const ex & x)
+{
+ return Order(x).hold();
+}
+
+static ex Order_imag_part(const ex & x)
+{
+ if(x.info(info_flags::real))
+ return 0;
+ return Order(x).hold();
}
// Differentiation is handled in function::derivative because of its special requirements
REGISTER_FUNCTION(Order, eval_func(Order_eval).
series_func(Order_series).
latex_name("\\mathcal{O}").
- conjugate_func(Order_conjugate));
+ conjugate_func(Order_conjugate).
+ real_part_func(Order_real_part).
+ imag_part_func(Order_imag_part));
//////////
// Solve linear system
git://www.ginac.de / ginac.git / commitdiff