This is a tutorial that documents GiNaC @value{VERSION}, an open
framework for symbolic computation within the C++ programming language.
-Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+Copyright (C) 1999-2017 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
@page
@vskip 0pt plus 1filll
-Copyright @copyright{} 1999-2015 Johannes Gutenberg University Mainz, Germany
+Copyright @copyright{} 1999-2017 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
@section License
The GiNaC framework for symbolic computation within the C++ programming
-language is Copyright @copyright{} 1999-2015 Johannes Gutenberg
+language is Copyright @copyright{} 1999-2017 Johannes Gutenberg
University Mainz, Germany.
This program is free software; you can redistribute it and/or
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.).
+greek letters (@samp{alpha}, @samp{mu}, etc.). You can retrive the name
+and the LaTeX name of a symbol using the respective methods:
+@cindex @code{get_name()}
+@cindex @code{get_TeX_name()}
+@example
+symbol::get_name() const;
+symbol::get_TeX_name() const;
+@end example
@cindex @code{subs()}
Symbols in GiNaC can't be assigned values. If you need to store results of
@example
ex clifford_prime(const ex & e)
- inline ex clifford_star(const ex & e) @{ return e.conjugate(); @}
- inline ex clifford_bar(const ex & e) @{ return clifford_prime(e.conjugate()); @}
+ inline ex clifford_star(const ex & e)
+ inline ex clifford_bar(const ex & e)
@end example
The automorphism of a Clifford algebra @code{clifford_prime()} simply
changes signs of all Clifford units in the expression. The reversion
-of a Clifford algebra @code{clifford_star()} coincides with the
-@code{conjugate()} method and effectively reverses the order of Clifford
+of a Clifford algebra @code{clifford_star()} reverses the order of Clifford
units in any product. Finally the main anti-automorphism
of a Clifford algebra @code{clifford_bar()} is the composition of the
previous two, i.e. it makes the reversion and changes signs of all Clifford units
predicates to the STL:
@example
-class ex_is_less : public std::binary_function<ex, ex, bool> @{
+class ex_is_less @{
public:
bool operator()(const ex &lh, const ex &rh) const;
@};
-class ex_is_equal : public std::binary_function<ex, ex, bool> @{
+class ex_is_equal @{
public:
bool operator()(const ex &lh, const ex &rh) const;
@};
// count the number of expressions equal to '1'
unsigned num_ones = std::count_if(v.begin(), v.end(),
- std::bind2nd(ex_is_equal(), 1));
+ [](const ex& e) @{ return ex_is_equal()(e, 1); @});
@end example
The implementation of @code{ex_is_less} uses the member function
To evaluate them using floating-point arithmetic you need to call
@example
-ex ex::evalf(int level = 0) const;
+ex ex::evalf() const;
@end example
@cindex @code{Digits}
@example
ex ex::to_polynomial(exmap & m);
-ex ex::to_polynomial(lst & l);
@end example
or
@example
ex ex::to_rational(exmap & m);
-ex ex::to_rational(lst & l);
@end example
-on the expression to be converted. The supplied @code{exmap} or @code{lst}
-will be filled with the generated temporary symbols and their replacement
-expressions in a format that can be used directly for the @code{subs()}
-method. It can also already contain a list of replacements from an earlier
-application of @code{.to_polynomial()} or @code{.to_rational()}, so it's
-possible to use it on multiple expressions and get consistent results.
+on the expression to be converted. The supplied @code{exmap} will be filled
+with the generated temporary symbols and their replacement expressions in a
+format that can be used directly for the @code{subs()} method. It can also
+already contain a list of replacements from an earlier application of
+@code{.to_polynomial()} or @code{.to_rational()}, so it's possible to use
+it on multiple expressions and get consistent results.
The difference between @code{.to_polynomial()} and @code{.to_rational()}
is probably best illustrated with an example:
ex a = 2*x/sin(x) - y/(3*sin(x));
cout << a << endl;
- lst lp;
- ex p = a.to_polynomial(lp);
- cout << " = " << p << "\n with " << lp << endl;
+ exmap mp;
+ ex p = a.to_polynomial(mp);
+ cout << " = " << p << "\n with " << mp << endl;
// = symbol3*symbol2*y+2*symbol2*x
// with @{symbol2==sin(x)^(-1),symbol3==-1/3@}
- lst lr;
- ex r = a.to_rational(lr);
- cout << " = " << r << "\n with " << lr << endl;
+ exmap mr;
+ ex r = a.to_rational(mr);
+ cout << " = " << r << "\n with " << mr << endl;
// = -1/3*symbol4^(-1)*y+2*symbol4^(-1)*x
// with @{symbol4==sin(x)@}
@}
the maximal expansion. For example, for the exponent GiNaC firstly expands
the argument and then the function. For the logarithm and absolute value,
GiNaC uses the opposite order: firstly expands the function and then its
-argument. Of course, a user can fine-tune this behaviour by sequential
+argument. Of course, a user can fine-tune this behavior by sequential
calls of several @code{expand()} methods with desired flags.
@node Multiple polylogarithms, Complex expressions, Built-in functions, Methods and functions
@cindex ginac-excompiler
@code{compile_ex} uses the shell script @code{ginac-excompiler} to start the C
compiler and produce the object files. This shell script comes with GiNaC and
-will be installed together with GiNaC in the configured @code{$PREFIX/bin}
-directory. You can also export additional compiler flags via the $CXXFLAGS
-variable:
+will be installed together with GiNaC in the configured @code{$LIBEXECDIR}
+(typically @code{$PREFIX/libexec} or @code{$PREFIX/lib/ginac}). You can also
+export additional compiler flags via the @env{$CXXFLAGS} variable:
@example
setenv("CXXFLAGS", "-O3 -fomit-frame-pointer -ffast-math", 1);
@example
bool info(unsigned inf) const override;
-ex evalf(int level = 0) const override;
+ex evalf() const override;
ex series(const relational & r, int order, unsigned options = 0) const override;
ex derivative(const symbol & s) const override;
@end example