cadabra Namespace Reference

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

Namespaces
	symbols

Classes
class	Accent
class	ActionAddCell
class	ActionBase
class	ActionEraseText
class	ActionInsertText
class	ActionPositionCursor
class	ActionRemoveCell
class	ActionSetRunStatus
class	ActionSplitCell
class	Algorithm
class	AntiCommuting
class	AntiSymmetric
class	BoundProperty
class	BoundPropertyBase
class	CadabraJupyter
class	canonicalise
class	chain_rule
class	ChooseColoursDialog
class	CodeInput
class	collect_components
class	collect_factors
class	collect_terms
class	combine
class	Commuting
class	CommutingAsProduct
class	CommutingAsSum
class	CommutingBehaviour
class	complete
class	ComputeThread
class	Console
class	Coordinate
class	DAntiSymmetric
class	DataCell
class	decompose
class	decompose_product
class	Depends
class	DependsBase
class	DependsInherit
class	Derivative
class	Determinant
class	Diagonal
class	DifferentialForm
class	DifferentialFormBase
class	DiracBar
class	DisplayBase
class	DisplayMMA
class	DisplaySympy
class	DisplayTerminal
class	DisplayTeX
class	Distributable
class	distribute
class	DocumentThread
class	drop_keep_weight
class	drop_weight
class	einsteinify
class	eliminate_converter
class	eliminate_kronecker
class	eliminate_metric
class	eliminate_vielbein
class	epsilon_to_delta
class	EpsilonTensor
class	evaluate
class	Evaluator
class	Ex
class	Ex_comparator
class	Ex_hasher
class	Ex_is_equivalent
class	Ex_is_less
class	exchange
class	expand
class	expand_delta
class	expand_diracbar
class	expand_power
class	explicit_indices
class	ExteriorDerivative
class	factor_in
class	factor_out
class	fierz
class	FilledTableau
class	flatten_product
class	flatten_sum
class	GammaMatrix
class	GammaTraceless
class	GUIBase
class	ImageView
class	ImaginaryI
class	ImplicitIndex
class	index_iterator
class	IndexClassifier
class	IndexInherit
class	indexsort
class	Indices
class	Inherit
	If a property X derives from Inherit<Y>, and get<Y> is called on an object which has an X property (but no Y property), then the get<Y> will look at the non-index child of the object to see if that has a Y property. More...
class	Integer
class	integrate_by_parts
class	InverseMetric
class	InverseVielbein
class	join_gamma
class	keep_terms
class	keep_weight
class	Kernel
class	keyval_t
	Arguments to properties get parsed into a keyval_t structure. More...
class	KroneckerDelta
class	labelled_property
class	LaTeXForm
class	list_property
	Something cannot be both a list property and a normal property at the same time, so we can safely inherit without virtual. More...
class	lower_free_indices
class	lr_tensor
class	map_mma
class	map_sympy
class	Matrix
class	Metric
class	NonCommuting
class	NotebookCanvas
class	NotebookWindow
class	nset_it_less
class	NumericalFlat
	Property indicating that an operator is numerically flat, so that numerical factors in the argument can be taken outside. More...
class	order
class	Parser
class	PartialDerivative
class	pattern
class	product_rule
class	Properties
class	property
	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...
class	PropertyInherit
	PropertyInherit is like Inherit<T> for all properties. More...
class	reduce_delta
class	rename_dummies
class	replace_match
class	rewrite_indices
class	RiemannTensor
class	SatisfiesBianchi
class	SelfAntiCommuting
class	SelfCommuting
class	SelfCommutingBehaviour
class	SelfNonCommuting
class	simplify
class	sort_product
class	sort_spinors
class	sort_sum
class	SortOrder
class	Spinor
class	split_gamma
class	split_index
class	str_node
class	substitute
class	sym
class	Symbol
class	Symmetric
class	tab_basics
class	tabdimension
class	Tableau
class	TableauBase
class	TableauSymmetry
class	take_match
class	TerminalStream
class	TeXEngine
class	TextViewProxy
class	TeXView
class	Trace
class	Traceless
class	tree_equal_obj
class	tree_exact_equal_mod_prel_obj
class	tree_exact_equal_obj
class	tree_exact_less_for_indexmap_obj
	Compare for indexmap_t. More...
class	tree_exact_less_mod_prel_obj
class	tree_exact_less_no_wildcards_mod_prel_obj
class	tree_exact_less_no_wildcards_obj
	Compare two trees exactly, treat wildcard names as ordinary names. More...
class	tree_exact_less_obj
	Compare two trees exactly, i.e. including exact index names. More...
class	tree_less_modprel_obj
class	tree_less_obj
	Compare two trees by pattern logic, i.e. modulo index names. More...
class	untrace
class	unwrap
class	unzoom
class	vary
class	Vielbein
class	VisualCell
class	Weight
class	WeightBase
class	WeightInherit
class	WeylTensor
class	young_project
class	young_project_product
class	young_project_tensor
class	young_reduce
class	zoom

Typedefs
typedef void(*	dispatcher_t) (const Kernel &k, Ex &, Ex::iterator &it)
typedef tree< DataCell >	DTree
using	flags_base_t = std::underlying_type_t< HashFlags >
typedef mpq_class	multiplier_t
typedef std::set< std::string >	nset_t
typedef std::set< multiplier_t >	rset_t
typedef uintptr_t	hashval_t
using	Ex_ptr = std::shared_ptr< Ex >
using	tab_t = TableauBase::tab_t

Enumerations
enum	HashFlags : unsigned int {   HASH_DEFAULT = 0x0, HASH_IGNORE_TOP_MULTIPLIER = 0x1, HASH_IGNORE_MULTIPLIER = 0x2, HASH_IGNORE_PRODUCT_ORDER = 0x4,   HASH_IGNORE_SUM_ORDER = 0x8, HASH_IGNORE_INDEX_ORDER = 0x10, HASH_IGNORE_PARENT_REL = 0x20, HASH_IGNORE_BRACKET_TYPE = 0x40,   HASH_IGNORE_CHILDREN = 0x80, HASH_IGNORE_NAMES = 0x100, HASH_IGNORE_INDICES = 0x200, HASH_IGNORE_CHILD_ORDER = 0x400 }

Functions
std::string	escape_quotes (const std::string &)
std::string	cdb2python (const std::string &, bool display)
std::string	cdb2python_string (const std::string &, bool display)
std::string	convert_line (const std::string &, std::string &lhs, std::string &rhs, std::string &op, std::string &indent, bool display)
std::string	cnb2python (const std::string &, bool display)
void	cleanup_dispatch (const Kernel &kernel, Ex &tr, Ex::iterator &it)
void	check_index_consistency (const Kernel &k, Ex &tr, Ex::iterator it)
	Generic tool to check for index inconsistencies independent of running any algorithm. More...
bool	cleanup_powlike (const Kernel &k, Ex &, Ex::iterator &it)
	Individual node cleanup routines. More...
bool	cleanup_productlike (const Kernel &k, Ex &tr, Ex::iterator &it)
bool	cleanup_sumlike (const Kernel &k, Ex &tr, Ex::iterator &it)
bool	push_down_multiplier (const Kernel &k, Ex &tr, Ex::iterator it)
	Given a node with a non-unit multiplier, push this multiplier down the tree if the node is not allowed to have a non-unit multiplier. More...
bool	cleanup_components (const Kernel &k, Ex &tr, Ex::iterator &it)
bool	cleanup_partialderivative (const Kernel &, Ex &tr, Ex::iterator &it)
bool	cleanup_derivative (const Kernel &k, Ex &tr, Ex::iterator &it)
bool	cleanup_numericalflat (const Kernel &, Ex &tr, Ex::iterator &it)
bool	cleanup_diagonal (const Kernel &, Ex &tr, Ex::iterator &it)
bool	cleanup_kronecker (const Kernel &, Ex &tr, Ex::iterator &it)
bool	cleanup_exterior_derivative (const Kernel &k, Ex &tr, Ex::iterator &it)
void	cleanup_dispatch_deep (const Kernel &k, Ex &tr, dispatcher_t dispatch)
void	cleanup_dispatch_deep (const Kernel &k, Ex &tr, Ex::iterator &, dispatcher_t dispatch)
int	subtree_compare (const Properties *properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool, int compare_multiplier, bool literal_wildcards)
bool	tree_less (const Properties *, const Ex &one, const Ex &two, int mod_prel=-2, bool checksets=true, int compare_multiplier=-2)
	Various comparison functions, some exact, some with pattern logic. More...
bool	tree_equal (const Properties *properties, const Ex &one, const Ex &two, int mod_prel, bool checksets, int compare_multiplier)
bool	tree_exact_less (const Properties *properties, const Ex &one, const Ex &two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)
bool	tree_exact_equal (const Properties *properties, const Ex &one, const Ex &two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)
bool	subtree_less (const Properties *properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier)
bool	subtree_equal (const Properties *properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier)
bool	subtree_exact_less (const Properties *properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)
bool	subtree_exact_equal (const Properties *properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)
std::string	JSON_serialise (const DTree &)
	Serialise a document into .cj format, which is a JSON version of the document tree. More...
void	JSON_recurse (const DTree &, DTree::iterator, Json::Value &)
void	JSON_deserialise (const std::string &, DTree &)
	Load a document from .cj format, i.e. the inverse of the above. More...
void	JSON_in_recurse (DTree &doc, DTree::iterator loc, const Json::Value &cells)
std::string	export_as_HTML (const DTree &doc, bool for_embedding=false, bool strip_code=false, std::string title="")
	Export a document to a single self-contained HTML file containing inline CSS. More...
void	HTML_recurse (const DTree &doc, DTree::iterator it, std::ostringstream &str, const std::string &preamble_string, bool for_embedding=false, bool strip_code=false, std::string title="")
std::string	latex_to_html (const std::string &)
	Convert various LaTeX constructions to HTML-with-Mathjax, e.g. More...
std::string	export_as_LaTeX (const DTree &doc, const std::string &image_file_base)
	Export a document to a single self-contained LaTeX file, with the exception of images which get saved as separate numbered files. More...
void	LaTeX_recurse (const DTree &doc, DTree::iterator it, std::ostringstream &str, const std::string &preamble_string, const std::string &image_file_base, int &image_num)
std::string	export_as_python (const DTree &doc)
	Export a document to a python-like file (converting text cells to comments and python cells to python code, dropping output cells). More...
void	python_recurse (const DTree &doc, DTree::iterator it, std::ostringstream &str)
const char *	unichar (kunichar c)
bool	operator< (const exchange::tensor_type_t &one, const exchange::tensor_type_t &two)
void	do_list (const Ex &tr, Ex::iterator it, std::function< bool(Ex::iterator)> f)
int	list_size (const Ex &tr, Ex::iterator it)
Ex::iterator	find_in_subtree (const Ex &tr, Ex::iterator it, std::function< bool(Ex::iterator)> f, bool including_head)
Ex::iterator	find_in_list (const Ex &tr, Ex::iterator it, std::function< Ex::iterator(Ex::iterator)> f)
Ex	make_list (Ex el)
template<typename T >
T::iterator	do_subtree (const T &tr, typename T::iterator it, std::function< typename T::iterator(typename T::iterator)> f)
HashFlags	operator~ (HashFlags flags)
HashFlags	operator| (HashFlags lhs, HashFlags rhs)
HashFlags	operator& (HashFlags lhs, HashFlags rhs)
HashFlags &	operator|= (HashFlags &lhs, HashFlags rhs)
HashFlags &	operator&= (HashFlags &lhs, HashFlags rhs)
Ex_hasher::result_t	hash_ex (Ex::iterator it, HashFlags flags)
bool	hash_compare (Ex::iterator lhs, Ex::iterator rhs, HashFlags flags)
std::string	install_prefix ()
	Return an absolute path to the installation path. More...
void	pre_clean_dispatch (const Kernel &kernel, Ex &ex, Ex::iterator &it)
void	pre_clean_dispatch_deep (const Kernel &k, Ex &tr)
void	cleanup_updown (const Kernel &k, Ex &, Ex::iterator &it)
	Cleanup for individual node types. More...
void	cleanup_rational (const Kernel &, Ex &, Ex::iterator &st)
void	cleanup_frac (const Kernel &, Ex &tr, Ex::iterator &st)
void	cleanup_sqrt (const Kernel &, Ex &tr, Ex::iterator &st)
void	cleanup_sub (const Kernel &, Ex &tr, Ex::iterator &it)
void	cleanup_indexbracket (const Kernel &k, Ex &, Ex::iterator &it)
	Convert parser output which indicates an indexbracket to an actual indexbracket node. More...
std::string	replace_all (std::string const &original, std::string const &from, std::string const &to)
	Replace all occurrances of 'from' with 'to', return result (does not replace in-place). More...
long	to_long (multiplier_t mul)
std::string	to_string (long num)
void	multiply (rset_t::iterator &num, multiplier_t fac)
void	add (rset_t::iterator &num, multiplier_t fac)
void	zero (rset_t::iterator &num)
void	one (rset_t::iterator &num)
void	flip_sign (rset_t::iterator &num)
void	half (rset_t::iterator &num)
template<typename T >
bool	is_in (const T &val, const std::initializer_list< T > &list)
void	init_algorithms (py::module &m)
template<class Algo >
Ex_ptr	apply_algo_base (Algo &algo, Ex_ptr ex, bool deep, bool repeat, unsigned int depth, bool pre_order=false)
template<class Algo >
Ex_ptr	apply_algo (Ex_ptr ex, bool deep, bool repeat, unsigned int depth)
template<class Algo , typename Arg1 >
Ex_ptr	apply_algo (Ex_ptr ex, Arg1 arg1, bool deep, bool repeat, unsigned int depth)
template<class Algo , typename Arg1 , typename Arg2 >
Ex_ptr	apply_algo (Ex_ptr ex, Arg1 arg1, Arg2 arg2, bool deep, bool repeat, unsigned int depth)
template<class Algo , typename Arg1 , typename Arg2 , typename Arg3 >
Ex_ptr	apply_algo (Ex_ptr ex, Arg1 arg1, Arg2 arg2, Arg3 arg3, bool deep, bool repeat, unsigned int depth)
template<class Algo , typename... Args, typename... PyArgs>
void	def_algo (pybind11::module &m, const char *name, bool deep, bool repeat, unsigned int depth, PyArgs... pyargs)
template<class Algo >
Ex_ptr	apply_algo_preorder (Ex_ptr ex, bool deep, bool repeat, unsigned int depth)
template<class Algo , typename Arg1 >
Ex_ptr	apply_algo_preorder (Ex_ptr ex, Arg1 arg1, bool deep, bool repeat, unsigned int depth)
template<class Algo , typename Arg1 , typename Arg2 >
Ex_ptr	apply_algo_preorder (Ex_ptr ex, Arg1 arg1, Arg2 arg2, bool deep, bool repeat, unsigned int depth)
template<class Algo , typename... Args, typename... PyArgs>
void	def_algo_preorder (pybind11::module &m, const char *name, bool deep, bool repeat, unsigned int depth, PyArgs... pyargs)
void	init_algorithms (pybind11::module &m)
bool	Ex_compare (Ex_ptr one, Ex_ptr other)
bool	Ex_compare (Ex_ptr one, int other)
Ex_ptr	Ex_add (const Ex_ptr ex1, const ExNode ex2)
Ex_ptr	Ex_add (const Ex_ptr ex1, const Ex_ptr ex2)
Ex_ptr	Ex_add (const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2)
Ex_ptr	Ex_mul (const Ex_ptr ex1, const Ex_ptr ex2)
Ex_ptr	Ex_mul (const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2)
Ex_ptr	Ex_sub (const Ex_ptr ex1, const ExNode ex2)
Ex_ptr	Ex_sub (const Ex_ptr ex1, const Ex_ptr ex2)
Ex_ptr	Ex_sub (const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2)
Ex_ptr	fetch_from_python (const std::string &nm)
Ex_ptr	fetch_from_python (const std::string &nm, pybind11::object scope)
std::string	Ex_as_str (Ex_ptr ex)
std::string	Ex_as_repr (Ex_ptr ex)
std::string	Ex_as_latex (Ex_ptr ex)
pybind11::object	Ex_as_sympy (Ex_ptr ex)
std::string	Ex_as_sympy_string (Ex_ptr)
	Similar to Ex_to_Sympy, but only producing a string which can be parsed by Sympy, instead of a full-fledged Sympy expression. More...
std::string	Ex_as_input (Ex_ptr ex)
std::string	Ex_as_MMA (Ex_ptr ex, bool use_unicode)
std::string	print_tree (Ex *ex)
Ex	lhs (Ex_ptr ex)
Ex	rhs (Ex_ptr ex)
Ex	Ex_getslice (Ex_ptr ex, pybind11::slice slice)
Ex	Ex_getitem (Ex &ex, int index)
void	Ex_setitem (Ex_ptr ex, int index, Ex val)
void	Ex_setitem_iterator (Ex_ptr ex, ExNode en, Ex_ptr val)
size_t	Ex_len (Ex_ptr ex)
std::string	Ex_head (Ex_ptr ex)
pybind11::object	Ex_get_mult (Ex_ptr ex)
pybind11::list	terms (Ex_ptr ex)
std::shared_ptr< sympy::SympyBridge >	SympyBridge_init (std::shared_ptr< Ex > ex)
Ex_ptr	Ex_from_string (const std::string &ex_, bool, Kernel *kernel)
Ex_ptr	Ex_from_int (int num, bool)
void	call_post_process (Kernel &kernel, Ex_ptr ex)
Ex_ptr	map_sympy_wrapper (Ex_ptr ex, std::string head, pybind11::args args)
void	init_ex (py::module &m)
std::string	Ex_as_tree (Ex *ex)
void	init_ex (pybind11::module &m)
py::object	get_locals ()
py::object	get_globals ()
bool	scope_has (const py::dict &dict, const std::string &obj)
std::string	read_manual (const char *category, const char *name)
bool	scope_has (const pybind11::dict &dict, const std::string &obj)
Kernel *	create_scope ()
Kernel *	create_scope_from_global ()
Kernel *	create_empty_scope ()
Kernel *	get_kernel_from_scope ()
void	inject_defaults (Kernel *k)
void	init_kernel (pybind11::module &m)
std::string	init_ipython ()
	PYBIND11_MODULE (cadabra2, m)
void	compile_package (const std::string &in_name, const std::string &out_name)
void	init_packages (pybind11::module &m)
py::list	ProgressMonitor_totals_helper (ProgressMonitor &self)
ProgressMonitor *	get_progress_monitor ()
void	init_progress_monitor (py::module &m)
void	init_progress_monitor (pybind11::module &m)
template<typename BoundPropT >
BoundPropT::py_type	def_abstract_prop (pybind11::module &m, const std::string &name)
template<typename BoundPropT >
BoundPropT::py_type	def_prop (pybind11::module &m)
pybind11::list	list_properties ()
void	init_properties (py::module &m)
template<typename PropT >
std::string	get_name ()
template<typename BoundPropT >
BoundPropT::py_type	def_abstract_prop (pybind11::module &m)
void	init_properties (pybind11::module &m)
void	init_stopwatch (py::module &m)
void	init_stopwatch (pybind11::module &m)
std::string	tab_str (const tab_t &tab)
void	init_tableau (pybind11::module &m)
std::string	capitalize_first (std::string in)

Variables
nset_t	name_set
rset_t	rat_set
bool	post_process_enabled = true

Detailed Description

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

NotebookCanvas is an actual view on the document.

See tests/components.cdb for basic samples.

Class to deal with index scanning and classification.

This module is only concerned with the exchange properties of tensors as a whole, not with index permutation symmetries (which are handled in the canonicalise class of algebra.cc).

Cadabra kernel that keeps all state information that needs to be passed around to algorithms and properties. Stores property information and global settings.

Parser module, which takes the string output of the preprocessor.hh module and turns it into an Ex expression tree. The output of preprocessor.hh is assumed to be valid and consistent, so the code here is rather simple.

Handle the entire preclean stage, which turns a parsed expression into an expression which satisfies the Cadabra conventions. This does not involve the property system.

• All numerical multipliers in a product on the product node, no multiplier on a sum node.
• Any '\frac' nodes with a purely numerical denominator should be rewritten as a rational multiplier for the numerator node.
• Any \sub nodes get converted to \sum nodes.

Evaluate a tensorial expression to components, performing all dummy index sums.

Components nodes have the following structure:

\components_{a b ... n}({t,t,...r}=value, {t,t,...r}=value, ...)

        \verbatim

        \components
 _{m}            // index names/types
 _{n}
            \comma          // last child
                \equals
                    \comma   // list of index values
                r
                t
        [value]  // value of tensor for above values of indices
                \equals
            ...
                \equals
            ...


ex:= A_{m n} ( A_{m n} + B_{m n} );
crds:= m -> { t, r, \phi, \theta };
vals:= { A_{t t} -> r, A_{r r} -> r**2, A_{t \phi} -> t, B_{t t} -> 1 };
evaluate(ex, crds, vals);
tst:= r * ( r + 1 ) + r**2 * r**2 + t*t - @(ex);

The algorithm performs the following steps. First, all free and dummy indices are classified using members of Algorithm (maybe later?). For all indices, the 'crds' argument to the algorithm is scanned for a

    \verbatim

m -> { a,b,c }

type pattern.

Do a dept-first scan until the first sum or product node.

In a sum node, all terms must have the same index structure, so we can now make a map from the subtree pattern to all possible index values. For each such index value set, lookup if there is a replacement pattern, if not replace by zero. This map can be reused later for equal sub-expressions (here it is important that a normal tensor expression can be used as a pattern immediately, though I would search both on explicit iterator (for things that we have just seen) and on pattern (for things that occur again later in the tree)).

In a product node, find all dummies and free indices. Create a set of all index value sets, e.g.

    \verbatim

        {m, n, p} ->
        { {t, t, t}, {r,t,t}, {t,r,t}, ... }

For each such index value set, lookup replacement rules.

KEY: quick way to lookup, for a given set of index values on a (found) pattern/pattern pointed to by iterator, whether and what is the value of the pattern.

There can be any number of them active inside the NotebookWindow. Each DataCell in the notebook document has a corresponding VisualCell in the NotebookCanvas, which gets added by NotebookCanvas::add_cell.

Cells which contain child cells (e.g. CodeInput, which can contain child cells corresponding to the TeXView output) will also be hierarchically ordered in the visual tree. That is, any visual cell which can contain a child cell will have it stored inside a Gtk::Box inside the visual cell. Removing any cell will therefore also immediately remove the child cells.

Typedef Documentation

dispatcher_t

typedef void(* cadabra::dispatcher_t) (const Kernel &k, Ex &, Ex::iterator &it)

DTree

typedef tree<DataCell> cadabra::DTree

Ex_ptr

using cadabra::Ex_ptr = typedef std::shared_ptr<Ex>

flags_base_t

using cadabra::flags_base_t = typedef std::underlying_type_t<HashFlags>

hashval_t

typedef uintptr_t cadabra::hashval_t

multiplier_t

typedef mpq_class cadabra::multiplier_t

nset_t

typedef std::set<std::string> cadabra::nset_t

rset_t

typedef std::set<multiplier_t> cadabra::rset_t

tab_t

using cadabra::tab_t = typedef TableauBase::tab_t

Enumeration Type Documentation

HashFlags

enum cadabra::HashFlags : unsigned int

Enumerator
HASH_DEFAULT
HASH_IGNORE_TOP_MULTIPLIER
HASH_IGNORE_MULTIPLIER
HASH_IGNORE_PRODUCT_ORDER
HASH_IGNORE_SUM_ORDER
HASH_IGNORE_INDEX_ORDER
HASH_IGNORE_PARENT_REL
HASH_IGNORE_BRACKET_TYPE
HASH_IGNORE_CHILDREN
HASH_IGNORE_NAMES
HASH_IGNORE_INDICES
HASH_IGNORE_CHILD_ORDER

Function Documentation

add()

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

apply_algo() [1/4]

template<class Algo , typename Arg1 , typename Arg2 , typename Arg3 >

Ex_ptr cadabra::apply_algo	(	Ex_ptr	ex,
		Arg1	arg1,
		Arg2	arg2,
		Arg3	arg3,
		bool	deep,
		bool	repeat,
		unsigned int	depth
	)

apply_algo() [2/4]

template<class Algo , typename Arg1 , typename Arg2 >

Ex_ptr cadabra::apply_algo	(	Ex_ptr	ex,
		Arg1	arg1,
		Arg2	arg2,
		bool	deep,
		bool	repeat,
		unsigned int	depth
	)

apply_algo() [3/4]

template<class Algo , typename Arg1 >

Ex_ptr cadabra::apply_algo	(	Ex_ptr	ex,
		Arg1	arg1,
		bool	deep,
		bool	repeat,
		unsigned int	depth
	)

apply_algo() [4/4]

template<class Algo >

Ex_ptr cadabra::apply_algo	(	Ex_ptr	ex,
		bool	deep,
		bool	repeat,
		unsigned int	depth
	)

apply_algo_preorder() [1/3]

template<class Algo , typename Arg1 , typename Arg2 >

Ex_ptr cadabra::apply_algo_preorder	(	Ex_ptr	ex,
		Arg1	arg1,
		Arg2	arg2,
		bool	deep,
		bool	repeat,
		unsigned int	depth
	)

apply_algo_preorder() [2/3]

template<class Algo , typename Arg1 >

Ex_ptr cadabra::apply_algo_preorder	(	Ex_ptr	ex,
		Arg1	arg1,
		bool	deep,
		bool	repeat,
		unsigned int	depth
	)

apply_algo_preorder() [3/3]

template<class Algo >

Ex_ptr cadabra::apply_algo_preorder	(	Ex_ptr	ex,
		bool	deep,
		bool	repeat,
		unsigned int	depth
	)

call_post_process()

void cadabra::call_post_process	(	Kernel &	kernel,
		Ex_ptr	ex
	)

capitalize_first()

std::string cadabra::capitalize_first

(

std::string

in

)

cdb2python_string()

std::string cadabra::cdb2python_string	(	const std::string &	blk,
		bool	display
	)

check_index_consistency()

void cadabra::check_index_consistency	(	const Kernel &	k,
		Ex &	tr,
		Ex::iterator	it
	)

Generic tool to check for index inconsistencies independent of running any algorithm.

cleanup_components()

bool cadabra::cleanup_components	(	const Kernel &	k,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_derivative()

bool cadabra::cleanup_derivative	(	const Kernel &	k,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_diagonal()

bool cadabra::cleanup_diagonal	(	const Kernel &	,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_dispatch_deep()

void cadabra::cleanup_dispatch_deep	(	const Kernel &	k,
		Ex &	tr,
		Ex::iterator &	,
		dispatcher_t	dispatch
	)

cleanup_exterior_derivative()

bool cadabra::cleanup_exterior_derivative	(	const Kernel &	k,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_frac()

void cadabra::cleanup_frac	(	const Kernel &	,
		Ex &	tr,
		Ex::iterator &	st
	)

cleanup_indexbracket()

void cadabra::cleanup_indexbracket	(	const Kernel &	,
		Ex &	tr,
		Ex::iterator &	it
	)

Convert parser output which indicates an indexbracket to an actual indexbracket node.

cleanup_kronecker()

bool cadabra::cleanup_kronecker	(	const Kernel &	,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_numericalflat()

bool cadabra::cleanup_numericalflat	(	const Kernel &	,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_partialderivative()

bool cadabra::cleanup_partialderivative	(	const Kernel &	,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_powlike()

bool cadabra::cleanup_powlike	(	const Kernel &	k,
		Ex &	,
		Ex::iterator &	it
	)

Individual node cleanup routines.

Do not call these yourself.

Once more, these algorithms clean up the tree at the current node and the first layer of child nodes, but do NOT descend deeper down the tree, except when that is necessary to ensure that the tree remains consistent. As with any algorithms, the iterator pointing to the starting node may be changed, but these functions are not allowed to modify anything except the node and nodes below (in particular, they will leave sibling nodes untouched).

cleanup_productlike()

bool cadabra::cleanup_productlike	(	const Kernel &	k,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_rational()

void cadabra::cleanup_rational	(	const Kernel &	,
		Ex &	,
		Ex::iterator &	st
	)

cleanup_sqrt()

void cadabra::cleanup_sqrt	(	const Kernel &	,
		Ex &	tr,
		Ex::iterator &	st
	)

cleanup_sub()

void cadabra::cleanup_sub	(	const Kernel &	,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_sumlike()

bool cadabra::cleanup_sumlike	(	const Kernel &	k,
		Ex &	tr,
		Ex::iterator &	it
	)

cleanup_updown()

void cadabra::cleanup_updown	(	const Kernel &	k,
		Ex &	,
		Ex::iterator &	it
	)

Cleanup for individual node types.

These are not needed during any later stages of the manipulation of an expression (and are hence defined here, not in 'Cleanup.hh').

create_empty_scope()

Kernel * cadabra::create_empty_scope

(

)

create_scope_from_global()

Kernel * cadabra::create_scope_from_global

(

)

def_abstract_prop() [1/2]

template<typename BoundPropT >

BoundPropT::py_type cadabra::def_abstract_prop

(

pybind11::module &

m

)

def_abstract_prop() [2/2]

template<typename BoundPropT >

BoundPropT::py_type cadabra::def_abstract_prop	(	pybind11::module &	m,
		const std::string &	name
	)

def_prop()

template<typename BoundPropT >

BoundPropT::py_type cadabra::def_prop

(

pybind11::module &

m

)

escape_quotes()

std::string cadabra::escape_quotes

(

const std::string &

line

)

Ex_add() [1/2]

Ex_ptr cadabra::Ex_add	(	const Ex_ptr	ex1,
		const Ex_ptr	ex2
	)

Ex_add() [2/2]

Ex_ptr cadabra::Ex_add	(	const Ex_ptr	ex1,
		const Ex_ptr	ex2,
		Ex::iterator	top2
	)

Ex_as_input()

std::string cadabra::Ex_as_input

(

Ex_ptr

ex

)

Ex_as_MMA()

std::string cadabra::Ex_as_MMA	(	Ex_ptr	ex,
		bool	use_unicode
	)

Ex_as_repr()

std::string cadabra::Ex_as_repr

(

Ex_ptr

ex

)

Ex_as_sympy_string()

std::string cadabra::Ex_as_sympy_string

(

Ex_ptr

ex

)

Similar to Ex_to_Sympy, but only producing a string which can be parsed by Sympy, instead of a full-fledged Sympy expression.

Ex_as_tree()

std::string cadabra::Ex_as_tree

(

Ex *

ex

)

Ex_compare()

bool cadabra::Ex_compare	(	Ex_ptr	one,
		int	other
	)

Ex_from_int()

Ex_ptr cadabra::Ex_from_int	(	int	num,
		bool
	)

Ex_from_string()

Ex_ptr cadabra::Ex_from_string	(	const std::string &	ex_,
		bool	,
		Kernel *	kernel
	)

Ex_get_mult()

pybind11::object cadabra::Ex_get_mult

(

Ex_ptr

ex

)

Ex_getitem()

Ex cadabra::Ex_getitem	(	Ex &	ex,
		int	index
	)

Ex_getslice()

Ex cadabra::Ex_getslice	(	Ex_ptr	ex,
		pybind11::slice	slice
	)

Ex_head()

std::string cadabra::Ex_head

(

Ex_ptr

ex

)

Ex_len()

size_t cadabra::Ex_len

(

Ex_ptr

ex

)

Ex_mul()

Ex_ptr cadabra::Ex_mul	(	const Ex_ptr	ex1,
		const Ex_ptr	ex2,
		Ex::iterator	top2
	)

Ex_setitem()

void cadabra::Ex_setitem	(	Ex_ptr	ex,
		int	index,
		Ex	val
	)

Ex_setitem_iterator()

void cadabra::Ex_setitem_iterator	(	Ex_ptr	ex,
		ExNode	en,
		Ex_ptr	val
	)

Ex_sub() [1/2]

Ex_ptr cadabra::Ex_sub	(	const Ex_ptr	ex1,
		const Ex_ptr	ex2
	)

Ex_sub() [2/2]

Ex_ptr cadabra::Ex_sub	(	const Ex_ptr	ex1,
		const Ex_ptr	ex2,
		Ex::iterator	top2
	)

export_as_HTML()

std::string cadabra::export_as_HTML	(	const DTree &	doc,
		bool	for_embedding = false,
		bool	strip_code = false,
		std::string	title = ""
	)

Export a document to a single self-contained HTML file containing inline CSS.

export_as_LaTeX()

std::string cadabra::export_as_LaTeX	(	const DTree &	doc,
		const std::string &	image_file_base
	)

Export a document to a single self-contained LaTeX file, with the exception of images which get saved as separate numbered files.

export_as_python()

std::string cadabra::export_as_python

(

const DTree &

doc

)

Export a document to a python-like file (converting text cells to comments and python cells to python code, dropping output cells).

fetch_from_python()

Ex_ptr cadabra::fetch_from_python	(	const std::string &	nm,
		pybind11::object	scope
	)

flip_sign()

void cadabra::flip_sign

(

rset_t::iterator &

num

)

get_globals()

pybind11::object cadabra::get_globals

(

)

get_locals()

pybind11::object cadabra::get_locals

(

)

get_name()

template<typename PropT >

std::string cadabra::get_name

(

)

get_progress_monitor()

ProgressMonitor * cadabra::get_progress_monitor

(

)

half()

void cadabra::half

(

rset_t::iterator &

num

)

hash_compare()

bool cadabra::hash_compare	(	Ex::iterator	lhs,
		Ex::iterator	rhs,
		HashFlags	flags
	)

hash_ex()

Ex_hasher::result_t cadabra::hash_ex	(	Ex::iterator	it,
		HashFlags	flags
	)

HTML_recurse()

void cadabra::HTML_recurse	(	const DTree &	doc,
		DTree::iterator	it,
		std::ostringstream &	str,
		const std::string &	preamble_string,
		bool	for_embedding = false,
		bool	strip_code = false,
		std::string	title = ""
	)

init_algorithms() [1/2]

void cadabra::init_algorithms

(

py::module &

m

)

init_algorithms() [2/2]

void cadabra::init_algorithms

(

pybind11::module &

m

)

init_ex() [1/2]

void cadabra::init_ex

(

py::module &

m

)

init_ex() [2/2]

void cadabra::init_ex

(

pybind11::module &

m

)

init_ipython()

std::string cadabra::init_ipython

(

)

init_kernel()

void cadabra::init_kernel

(

pybind11::module &

m

)

init_packages()

void cadabra::init_packages

(

pybind11::module &

m

)

init_progress_monitor() [1/2]

void cadabra::init_progress_monitor

(

py::module &

m

)

init_progress_monitor() [2/2]

void cadabra::init_progress_monitor

(

pybind11::module &

m

)

init_properties() [1/2]

void cadabra::init_properties

(

py::module &

m

)

init_properties() [2/2]

void cadabra::init_properties

(

pybind11::module &

m

)

init_stopwatch() [1/2]

void cadabra::init_stopwatch

(

py::module &

m

)

init_stopwatch() [2/2]

void cadabra::init_stopwatch

(

pybind11::module &

m

)

init_tableau()

void cadabra::init_tableau

(

pybind11::module &

m

)

install_prefix()

std::string cadabra::install_prefix

(

)

Return an absolute path to the installation path.

This is determined at runtime, to allow for binary distributions to be installed at any location.

is_in()

template<typename T >

bool cadabra::is_in	(	const T &	val,
		const std::initializer_list< T > &	list
	)

JSON_deserialise()

void cadabra::JSON_deserialise	(	const std::string &	cj,
		DTree &	doc
	)

Load a document from .cj format, i.e. the inverse of the above.

JSON_in_recurse()

void cadabra::JSON_in_recurse	(	DTree &	doc,
		DTree::iterator	loc,
		const Json::Value &	cells
	)

JSON_recurse()

void cadabra::JSON_recurse	(	const DTree &	doc,
		DTree::iterator	it,
		Json::Value &	json
	)

JSON_serialise()

std::string cadabra::JSON_serialise

(

const DTree &

doc

)

Serialise a document into .cj format, which is a JSON version of the document tree.

LaTeX_recurse()

void cadabra::LaTeX_recurse	(	const DTree &	doc,
		DTree::iterator	it,
		std::ostringstream &	str,
		const std::string &	preamble_string,
		const std::string &	image_file_base,
		int &	image_num
	)

latex_to_html()

std::string cadabra::latex_to_html

(

const std::string &

str

)

Convert various LaTeX constructions to HTML-with-Mathjax, e.g.

\section{...}, \begin{verbatim}...\end{verbatim}, \verb.

lhs()

cadabra::Ex cadabra::lhs

(

Ex_ptr

ex

)

list_properties()

pybind11::list cadabra::list_properties

(

)

map_sympy_wrapper()

Ex_ptr cadabra::map_sympy_wrapper	(	Ex_ptr	ex,
		std::string	head,
		pybind11::args	args
	)

one()

void cadabra::one

(

rset_t::iterator &

num

)

operator&()

HashFlags cadabra::operator&	(	HashFlags	lhs,
		HashFlags	rhs
	)

operator&=()

HashFlags & cadabra::operator&=	(	HashFlags &	lhs,
		HashFlags	rhs
	)

operator<()

bool cadabra::operator<	(	const exchange::tensor_type_t &	one,
		const exchange::tensor_type_t &	two
	)

operator|()

HashFlags cadabra::operator|	(	HashFlags	lhs,
		HashFlags	rhs
	)

operator|=()

HashFlags & cadabra::operator|=	(	HashFlags &	lhs,
		HashFlags	rhs
	)

operator~()

HashFlags cadabra::operator~

(

HashFlags

flags

)

pre_clean_dispatch()

void cadabra::pre_clean_dispatch	(	const Kernel &	kernel,
		Ex &	ex,
		Ex::iterator &	it
	)

pre_clean_dispatch_deep()

void cadabra::pre_clean_dispatch_deep	(	const Kernel &	k,
		Ex &	tr
	)

print_tree()

std::string cadabra::print_tree

(

Ex *

ex

)

ProgressMonitor_totals_helper()

pybind11::list cadabra::ProgressMonitor_totals_helper

(

ProgressMonitor &

self

)

push_down_multiplier()

bool cadabra::push_down_multiplier	(	const Kernel &	k,
		Ex &	tr,
		Ex::iterator	it
	)

Given a node with a non-unit multiplier, push this multiplier down the tree if the node is not allowed to have a non-unit multiplier.

This is a recursive procedure as the node onto which the multiplier gets pushed may itself not allow for a non-unit multiplier. Note that some nodes disallow non-unit multipliers on their children, but that should be handled individually (see cleanup of product nodes for an example).

PYBIND11_MODULE()

cadabra::PYBIND11_MODULE	(	cadabra2	,
		m
	)

python_recurse()

void cadabra::python_recurse	(	const DTree &	doc,
		DTree::iterator	it,
		std::ostringstream &	str
	)

read_manual()

std::string cadabra::read_manual	(	const char *	category,
		const char *	name
	)

replace_all()

std::string cadabra::replace_all	(	std::string const &	original,
		std::string const &	from,
		std::string const &	to
	)

Replace all occurrances of 'from' with 'to', return result (does not replace in-place).

rhs()

cadabra::Ex cadabra::rhs

(

Ex_ptr

ex

)

scope_has() [1/2]

bool cadabra::scope_has	(	const py::dict &	dict,
		const std::string &	obj
	)

scope_has() [2/2]

bool cadabra::scope_has	(	const pybind11::dict &	dict,
		const std::string &	obj
	)

subtree_equal()

bool cadabra::subtree_equal	(	const Properties *	properties,
		Ex::iterator	one,
		Ex::iterator	two,
		int	mod_prel,
		bool	checksets,
		int	compare_multiplier
	)

subtree_exact_equal()

bool cadabra::subtree_exact_equal	(	const Properties *	properties,
		Ex::iterator	one,
		Ex::iterator	two,
		int	mod_prel,
		bool	checksets,
		int	compare_multiplier,
		bool	literal_wildcards
	)

subtree_exact_less()

bool cadabra::subtree_exact_less	(	const Properties *	properties,
		Ex::iterator	one,
		Ex::iterator	two,
		int	mod_prel,
		bool	checksets,
		int	compare_multiplier,
		bool	literal_wildcards
	)

subtree_less()

bool cadabra::subtree_less	(	const Properties *	properties,
		Ex::iterator	one,
		Ex::iterator	two,
		int	mod_prel,
		bool	checksets,
		int	compare_multiplier
	)

SympyBridge_init()

std::shared_ptr<sympy::SympyBridge> cadabra::SympyBridge_init

(

std::shared_ptr< Ex >

ex

)

tab_str()

std::string cadabra::tab_str

(

const tab_t &

tab

)

terms()

pybind11::list cadabra::terms

(

Ex_ptr

ex

)

to_long()

long cadabra::to_long

(

multiplier_t

mul

)

to_string()

std::string cadabra::to_string

(

long

num

)

tree_equal()

bool cadabra::tree_equal	(	const Properties *	properties,
		const Ex &	one,
		const Ex &	two,
		int	mod_prel,
		bool	checksets,
		int	compare_multiplier
	)

tree_exact_equal()

bool cadabra::tree_exact_equal	(	const Properties *	properties,
		const Ex &	one,
		const Ex &	two,
		int	mod_prel,
		bool	checksets,
		int	compare_multiplier,
		bool	literal_wildcards
	)

tree_exact_less()

bool cadabra::tree_exact_less	(	const Properties *	properties,
		const Ex &	one,
		const Ex &	two,
		int	mod_prel,
		bool	checksets,
		int	compare_multiplier,
		bool	literal_wildcards
	)

tree_less()

bool cadabra::tree_less	(	const Properties *	properties,
		const Ex &	one,
		const Ex &	two,
		int	mod_prel,
		bool	checksets,
		int	compare_multiplier
	)

Various comparison functions, some exact, some with pattern logic.

unichar()

const char * cadabra::unichar

(

kunichar

c

)

zero()

void cadabra::zero

(

rset_t::iterator &

num

)

Variable Documentation

name_set

nset_t cadabra::name_set

post_process_enabled

bool cadabra::post_process_enabled = true

rat_set

rset_t cadabra::rat_set