cadabra::Ex Class Reference

Description

Basic storage class for symbolic mathemematical expressions.

The full meaning of an expression typically requires knowledge about properties of patterns in it, which this class does not contain. All property dependent algorithms acting on Ex objects are in Algorithm.hh.

#include <Storage.hh>

Inheritance diagram for cadabra::Ex:

Public Types
enum	result_t {   l_checkpointed , l_no_action , l_applied , l_applied_no_new_dummies ,   l_error , l_cached }
	Keeping track of what algorithms have done to this expression. More...

Public Member Functions
	Ex ()
	Ex (tree< str_node >::iterator)
	Ex (const str_node &)
	Ex (const Ex &)
	Ex (const std::string &)
	Initialise with given string as head node (does not parse this string). More...
	Ex (int)
	Ex (float)
Ex &	operator= (Ex)
result_t	state () const
void	update_state (result_t)
void	reset_state ()
bool	changed_state ()
	A status query method mainly to implement a simple method to apply algorithms until they converge. More...
bool	is_rational () const
	Test if the expression is a rational number. More...
multiplier_t	to_rational () const
bool	is_integer () const
long	to_integer () const
bool	is_empty () const
	Test if the expression is empty (no content at all). More...
std::ostream &	print_entire_tree (std::ostream &str) const
	Output helpers mainly for debugging purposes. More...
std::ostream &	print_repr (std::ostream &str, Ex::iterator it) const
	Print a representation like Python's 'repr'. More...
iterator	named_parent (iterator it, const std::string &) const
	Step up until matching node is found (if current node matches, do nothing) More...
iterator	erase_expression (iterator it)
hashval_t	calc_hash (iterator it) const
	Calculate the hash value for the subtree starting at 'it'. More...
multiplier_t	arg_to_num (sibling_iterator, unsigned int) const
unsigned int	number_of_steps (iterator it) const
unsigned int	number_of_equations () const
unsigned int	equation_number (iterator it) const
nset_t::iterator	equation_label (iterator it) const
iterator	equation_by_number (unsigned int i) const
iterator	equation_by_name (nset_t::iterator it) const
iterator	equation_by_name (nset_t::iterator it, unsigned int &) const
iterator	equation_by_number_or_name (iterator it, unsigned int last_used_equation) const
iterator	equation_by_number_or_name (iterator it, unsigned int last_used_equation, unsigned int &) const
std::string	equation_number_or_name (iterator it, unsigned int last_used_equation) const
iterator	procedure_by_name (nset_t::iterator it) const
bool	is_hidden (iterator) const
iterator	replace_index (iterator position, const iterator &from, bool keep_parent_rel=false)
	Replace the index-like object (originally intended to replace indices only, but now used also for e.g. More...
iterator	move_index (iterator position, const iterator &from)
	As in replace_index, but moves the index rather than making a copy (so that iterators pointing to the original remain valid). More...
void	list_wrap_single_element (iterator &)
	Make sure that the node pointed to is a \comma object, i.e. More...
void	list_unwrap_single_element (iterator &)
iterator	flatten_and_erase (iterator position)
	Replace the node with the children of the node, useful for e.g. More...
bool	operator== (const Ex &other) const
	Compare two Ex objects for exact equality; no dummy equivalence or other things that require property information. More...
void	push_history (const std::vector< Ex::path_t > &)
	Push a copy of the current state of the expression onto the history stack. More...
std::vector< Ex::path_t >	pop_history ()
	Pop the most recent state of the expression off the history stack; returns the set of paths that we are replacing. More...
int	history_size () const
	Return the size of the history; 0 means no history, just the current expression. More...

Static Public Member Functions
static std::ostream &	print_python (std::ostream &str, Ex::iterator it)
	Display expression in Python/Cadabra input form. More...
static std::ostream &	print_recursive_treeform (std::ostream &str, Ex::iterator it)
static std::ostream &	print_recursive_treeform (std::ostream &str, Ex::iterator it, unsigned int &number)
static sibling_iterator	arg (iterator, unsigned int)
	Quick access to arguments or argument lists for A(B)(C,D) type nodes. More...
static unsigned int	arg_size (sibling_iterator)

Private Attributes
result_t	state_
std::vector< tree< str_node > >	history
std::vector< std::vector< Ex::path_t > >	terms
	Patterns which describe how to get from one history step to the next. More...

Member Enumeration Documentation

result_t

enum cadabra::Ex::result_t

Keeping track of what algorithms have done to this expression.

After a reset_state (or at initialisation), the expression sits in the 'checkpointed' state. When an algorithm acts, it can then move to 'no_action' (unchanged), 'applied' (changed) or 'error'. Once it is in 'error', it will stay there until the next 'reset'. FIXME: the following should implement a stack of states, so that it can be used with nested functions.

Enumerator
l_checkpointed
l_no_action
l_applied
l_applied_no_new_dummies
l_error
l_cached

Constructor & Destructor Documentation

Ex() [1/7]

cadabra::Ex::Ex

(

)

Ex() [2/7]

cadabra::Ex::Ex

(

tree< str_node >::iterator

it

)

Ex() [3/7]

cadabra::Ex::Ex

(

const str_node &

x

)

Ex() [4/7]

cadabra::Ex::Ex

(

const Ex &

other

)

Ex() [5/7]

cadabra::Ex::Ex

(

const std::string &

str

)

Initialise with given string as head node (does not parse this string).

Ex() [6/7]

cadabra::Ex::Ex

(

int

val

)

Ex() [7/7]

cadabra::Ex::Ex

(

float

val

)

Member Function Documentation

arg()

Ex::sibling_iterator cadabra::Ex::arg ( iterator  it, unsigned int  num  )

static

Quick access to arguments or argument lists for A(B)(C,D) type nodes.

arg_size()

unsigned int cadabra::Ex::arg_size ( sibling_iterator  sib )

static

arg_to_num()

multiplier_t cadabra::Ex::arg_to_num	(	sibling_iterator	sib,
		unsigned int	num
	)		const

calc_hash()

hashval_t cadabra::Ex::calc_hash

(

iterator

it

)

const

Calculate the hash value for the subtree starting at 'it'.

changed_state()

bool cadabra::Ex::changed_state

(

)

A status query method mainly to implement a simple method to apply algorithms until they converge.

Returns true when the expression is in 'checkpointed' or 'applied' state. Will set the state to 'no_action'.

This is used in cadabra::convert_line defined in CdbPython.cc, which essentially defines converge(ex): [block] to mean

ex.reset_state() while ex.changed(): [block]

equation_by_name() [1/2]

Ex::iterator cadabra::Ex::equation_by_name

(

nset_t::iterator

it

)

const

equation_by_name() [2/2]

Ex::iterator cadabra::Ex::equation_by_name	(	nset_t::iterator	it,
		unsigned int &	tmp
	)		const

equation_by_number()

Ex::iterator cadabra::Ex::equation_by_number

(

unsigned int

i

)

const

equation_by_number_or_name() [1/2]

Ex::iterator cadabra::Ex::equation_by_number_or_name	(	iterator	it,
		unsigned int	last_used_equation
	)		const

equation_by_number_or_name() [2/2]

Ex::iterator cadabra::Ex::equation_by_number_or_name	(	iterator	it,
		unsigned int	last_used_equation,
		unsigned int &	real_eqno
	)		const

equation_label()

nset_t::iterator cadabra::Ex::equation_label

(

iterator

it

)

const

equation_number()

unsigned int cadabra::Ex::equation_number

(

iterator

it

)

const

equation_number_or_name()

std::string cadabra::Ex::equation_number_or_name	(	iterator	it,
		unsigned int	last_used_equation
	)		const

erase_expression()

Ex::iterator cadabra::Ex::erase_expression

(

iterator

it

)

flatten_and_erase()

Ex::iterator cadabra::Ex::flatten_and_erase

(

iterator

position

)

Replace the node with the children of the node, useful for e.g.

\prod{A} -> A. This algorithm takes care of the multiplier of the top node, i.e. it does 2\prod{A} -> 2 A. Returns an iterator to the new location of the first child of the original node.

history_size()

int cadabra::Ex::history_size

(

)

const

Return the size of the history; 0 means no history, just the current expression.

is_empty()

bool cadabra::Ex::is_empty

(

)

const

Test if the expression is empty (no content at all).

is_hidden()

bool cadabra::Ex::is_hidden

(

iterator

it

)

const

is_integer()

bool cadabra::Ex::is_integer

(

)

const

is_rational()

bool cadabra::Ex::is_rational

(

)

const

Test if the expression is a rational number.

FIXME: add tests for integers as well.

list_unwrap_single_element()

void cadabra::Ex::list_unwrap_single_element

(

iterator &

it

)

list_wrap_single_element()

void cadabra::Ex::list_wrap_single_element

(

iterator &

it

)

Make sure that the node pointed to is a \comma object, i.e.

wrap the node if not already inside such a \comma. DEPRECATED: in favour of 'do_list' in Functional.hh.

move_index()

Ex::iterator cadabra::Ex::move_index	(	iterator	position,
		const iterator &	from
	)

As in replace_index, but moves the index rather than making a copy (so that iterators pointing to the original remain valid).

named_parent()

Ex::iterator cadabra::Ex::named_parent	(	iterator	it,
		const std::string &
	)		const

Step up until matching node is found (if current node matches, do nothing)

number_of_equations()

unsigned int cadabra::Ex::number_of_equations

(

)

const

number_of_steps()

unsigned int cadabra::Ex::number_of_steps

(

iterator

it

)

const

operator=()

Ex & cadabra::Ex::operator=

(

Ex

other

)

operator==()

bool cadabra::Ex::operator==

(

const Ex &

other

)

const

Compare two Ex objects for exact equality; no dummy equivalence or other things that require property information.

pop_history()

std::vector< Ex::path_t > cadabra::Ex::pop_history

(

)

Pop the most recent state of the expression off the history stack; returns the set of paths that we are replacing.

DEPRECATED, only used by take_match/replace_match.

print_entire_tree()

std::ostream & cadabra::Ex::print_entire_tree

(

std::ostream &

str

)

const

Output helpers mainly for debugging purposes.

print_python()

std::ostream & cadabra::Ex::print_python ( std::ostream &  str, Ex::iterator  it  )

static

Display expression in Python/Cadabra input form.

This is fairly straightforward so not handled with a separate DisplayBase derived class.

print_recursive_treeform() [1/2]

std::ostream & cadabra::Ex::print_recursive_treeform ( std::ostream &  str, Ex::iterator  it  )

static

print_recursive_treeform() [2/2]

std::ostream & cadabra::Ex::print_recursive_treeform ( std::ostream &  str, Ex::iterator  it, unsigned int &  number  )

static

print_repr()

std::ostream & cadabra::Ex::print_repr	(	std::ostream &	str,
		Ex::iterator	it
	)		const

Print a representation like Python's 'repr'.

procedure_by_name()

Ex::iterator cadabra::Ex::procedure_by_name

(

nset_t::iterator

it

)

const

push_history()

void cadabra::Ex::push_history

(

const std::vector< Ex::path_t > &

paths

)

Push a copy of the current state of the expression onto the history stack.

Also pushes a set of paths to terms which will be kept in the next history step. DEPRECATED, only used by take_match/replace_match.

replace_index()

Ex::iterator cadabra::Ex::replace_index	(	iterator	position,
		const iterator &	from,
		bool	keep_parent_rel = false
	)

Replace the index-like object (originally intended to replace indices only, but now used also for e.g.

normal function arguments, as in

\[ \partial_{z}{ A(z) } \]

with a replacement of z).

Note: this originally kept the bracket and parent_rel, but that is not a good idea, because it prevents us from changing those. If we want to use a _{z} pattern replacing a A(z) index, it is better to make a rule that matches (z) and at the time we find and match _{z}. So this should be handled by the replacement_map logic in Compare.cc.

reset_state()

void cadabra::Ex::reset_state

(

)

state()

Ex::result_t cadabra::Ex::state

(

)

const

to_integer()

long cadabra::Ex::to_integer

(

)

const

to_rational()

multiplier_t cadabra::Ex::to_rational

(

)

const

update_state()

void cadabra::Ex::update_state

(

Ex::result_t

newstate

)

Member Data Documentation

history

std::vector<tree<str_node> > cadabra::Ex::history

private

state_

result_t cadabra::Ex::state_

private

terms

std::vector<std::vector<Ex::path_t> > cadabra::Ex::terms

private

Patterns which describe how to get from one history step to the next.

---

The documentation for this class was generated from the following files:

• core/Storage.hh
• core/Storage.cc