Cadabra Computer algebra system for field theory problems
Core

## Module Description

All computer algebra functionality in the form of C++ classes.

## Modules

Cleanup
Functionality to clean up expressions so that they satisfy the requirements of a consistent expression tree.

Expression display
Classes to handle printing of expressions in various formats.

Expression comparison
Functions to compare and match expressions stored in Ex objects.

Notebooks and packages
Graphical notebook interface and Cadabra packages.

Python Core
Python wrapper around the C++ core module.

Scalar algebra
Functionality to make Cadabra interface with scalar computer algebra systems such as Sympy or Mathematica.

Numerical evaluation
Functionality to evaluate mathematical expressions numerically.

Algorithms
Containing all algorithms acting on symbolic expression trees.

Properties
Containing all properties that can be attached to symbolic expressions.

## Namespaces

Functions to handle the exchange properties of two or more symbols in a product.

## Classes

class  PermutationException

class  preprocessor

class  ProgressMonitor

FIXME: the above two need to be merged, because parse may need access to the actual pattern tree, and once we are there, we may as well do checking. More...

## Functions

void cadabra::do_list (const Ex &tr, Ex::iterator it, std::function< bool(Ex::iterator)> f)

int cadabra::list_size (const Ex &tr, Ex::iterator it)

Ex::iterator cadabra::find_in_list (const Ex &tr, Ex::iterator it, std::function< Ex::iterator(Ex::iterator)> f)

Ex::iterator cadabra::find_in_subtree (const Ex &tr, Ex::iterator it, std::function< bool(Ex::iterator)> f, bool including_head)

Ex cadabra::make_list (Ex el)

template<typename T >
T::iterator cadabra::do_subtree (const T &tr, typename T::iterator it, std::function< typename T::iterator(typename T::iterator)> f)

void cadabra::multiply (rset_t::iterator &num, multiplier_t fac)

std::ostream & operator<< (std::ostream &, const cadabra::Ex &)

## ◆ do_list()

 void cadabra::do_list ( const Ex & tr, Ex::iterator it, std::function< bool(Ex::iterator)> f )

Apply a function on every element of a list, or if the iterator 'it' does not point to a list, only on that single element. Handles lists wrapped in an \expression node as well. It is safe to remove the node pointed to by 'it' in 'f'. If your 'f' returns false, the loop is aborted immediately.

## ◆ do_subtree()

template<typename T >
 T::iterator cadabra::do_subtree ( const T & tr, typename T::iterator it, std::function< typename T::iterator(typename T::iterator)> f )

Apply a function on every node in the tree at and below the given node, depth-first. Return an iterator to the top node, which replaces 'it' (may be the same).

## ◆ find_in_list()

 Ex::iterator cadabra::find_in_list ( const Ex & tr, Ex::iterator it, std::function< Ex::iterator(Ex::iterator)> f )

Returns an iterator to the first element for which 'f' does not return tr.end().

## ◆ find_in_subtree()

 Ex::iterator cadabra::find_in_subtree ( const Ex & tr, Ex::iterator it, std::function< bool(Ex::iterator)> f, bool including_head = true )

Returns an iterator to the first element for which 'f' returns 'true', or 'tr.end()'.

## ◆ list_size()

 int cadabra::list_size ( const Ex & tr, Ex::iterator it )

For lists as defined above for 'do_list', return their size (in case you really need to know the size before iterating over the elements).

## ◆ make_list()

 Ex cadabra::make_list ( Ex el )

Ensure that the tree is a list, even if it contains only a single element.

## ◆ multiply()

 void cadabra::multiply ( rset_t::iterator & , multiplier_t )

Helper functions for manipulation of multipliers.

## ◆ operator<<()

 std::ostream& operator<< ( std::ostream & , const cadabra::Ex & )

Bare output operator for Ex objects, mainly to provide a simple way to generate debugging output. Does not do any fancy formatting; just prints a nested list representation. For more fancy output, look at DisplayTeX, DisplaySympy and DisplayTerminal.