Has Exponented terms & an exponent. More...

Inheritance diagram for core.base_calculus.Sum:

Public Member Functions
def	__init__
	Constructor.
def	get_minus_signs_nb
	Returns the number of negative factors of the Sum (i.e.
def	get_numeric_terms
	Returns a raw list of the numeric terms of the Sum.
def	get_literal_terms
	Returns a raw list of the literal terms of the Sum.
def	get_terms_lexicon
	Creates a dict.
def	get_force_inner_brackets_display
	Gets the value of the force_inner_brackets_display field.
def	set_term
	Sets the n-th term to the given arg.
def	set_force_inner_brackets_display
	Sets a value to the force_inner_brackets_display field.
def	into_str
	Creates a string of the given object in the given ML.
def	calculate_next_step
	Returns the next calculated step of a numeric Sum.
def	expand_and_reduce_next_step
	Returns the next step of expansion/reduction of the Sum So, either the Sum of its expanded/reduced terms, or the Sum itself reduced, or None.
def	__cmp__
	Compares two Sums Returns 0 if all terms are the same in the same order and if the exponents are also the same /!\ a + b will be different from de b + a It's not a mathematical comparison, but a "displayable"'s one.
def	operator
	Defines the performed CommutativeOperation as a Sum.
def	next_displayable_term_nb
	Returns the rank of next non-equivalent to 0 term...
def	multiply_symbol_is_required
	True if the usual writing rules require a × between two factors.
def	requires_brackets
	True if the argument requires brackets in a product For instance, a Sum with several terms or a negative Item.
def	requires_inner_brackets
	True if the argument requires inner brackets The reason for requiring them is having an exponent different from 1 and several terms or factors (in the case of Products & Sums)
def	numeric_terms_require_to_be_reduced
	True if a gathering of numeric terms must be reduced It is True if at least two consecutive numeric Items are in the list and no other numeric term elsewhere.
def	intermediate_reduction_line
	Creates the intermediate reduction line.
def	reduce_
	Returns the reduced Sum For instance, giving the Sum 5x + 7x³ - 3x + 1, this method would return -2x + 7x³ + 1.
def	is_null
	True if the result of the Sum is null.
def	is_displ_as_a_single_1
	True if the Sum contains only 0s and one 1.
def	is_displ_as_a_single_minus_1
	True if the Sum can be displayed as a single -1 So, if it only contains 0s and a single -1.
def	is_displ_as_a_single_0
	True if the object can be displayed as a single 0 For instance, 0 + 0 + 0 but NOT - 1 + 0 + 1 (it's a matter of display)
def	is_reducible
	True if the Sum is reducible This is based on the result of the get_term_lexicon method.
Public Attributes
	str_openmark
	str_closemark
Properties
	term
	force_inner_brackets_display

Detailed Description

Has Exponented terms & an exponent.

Iterable. Two display modes.

Definition at line 5971 of file base_calculus.py.

Constructor & Destructor Documentation

def core.base_calculus.Sum.__init__	(	self,
		arg
	)

Constructor.

Warning:: Might raise an UncompatibleType exception.

Parameters:

arg None|Sum|Number|String|Exponented|[Number|String|Exponented] In the case of the list, the Sums having an exponent equal to 1 will be treated before the Exponenteds so that their terms are inserted in the current Sum instead of inserting a term as a Sum. If the exponent is greater than 1, then it will be the case. If the argument isn't of the kinds listed above, an exception will be raised. Giving None or an empty list is equivalent to giving 0

Returns:: One instance of Sum

Reimplemented in core.base_calculus.Polynomial.

Definition at line 5990 of file base_calculus.py.

Referenced by core.calculus.Equation.__init__(), and core.root_calculus.Value.substitute().

Member Function Documentation

def core.base_calculus.Sum.__cmp__	(	self,
		objct
	)

Compares two Sums Returns 0 if all terms are the same in the same order and if the exponents are also the same /!\ a + b will be different from de b + a It's not a mathematical comparison, but a "displayable"'s one.

Returns:: 0 if all terms are the same in the same order & the exponent

Definition at line 7078 of file base_calculus.py.

References core.base_calculus.Item.exponent, core.root_calculus.Exponented.exponent, core.base_calculus.Fraction.exponent, and core.base_calculus.Sum.term.

def core.base_calculus.Sum.calculate_next_step	(	self,
		options
	)

Returns the next calculated step of a *numeric* Sum.

Todo:

This method may be only partially implemented (see source)

the inner '-' signs (±(-2)) are not handled by this method so far

Reimplemented from core.root_calculus.Calculable.

Definition at line 6540 of file base_calculus.py.

Referenced by core.base_calculus.CommutativeOperation.evaluate(), and core.base_calculus.Sum.expand_and_reduce_next_step().

def core.base_calculus.Sum.expand_and_reduce_next_step	(	self,
		options
	)

Returns the next step of expansion/reduction of the Sum So, either the Sum of its expanded/reduced terms, or the Sum itself reduced, or None.

Returns:: Exponented

Reimplemented from core.root_calculus.Calculable.

Definition at line 6885 of file base_calculus.py.

Referenced by core.base_calculus.Sum.calculate_next_step().

def core.base_calculus.Sum.get_minus_signs_nb ( self )

Returns the number of negative factors of the Sum (i.e.

0)

Reimplemented from core.root_calculus.Signed.

Definition at line 6073 of file base_calculus.py.

def core.base_calculus.Sum.get_terms_lexicon ( self )

Creates a dict.

of couples (literal object):(numeric coeffs sum) Two objects are in fact created : a dictionary + an index which is a list containing the objects in the order they appear. The dictionary loses this order in general and the Sums created after that would never be in the same order without this index. Numeric Items are labeled NUMERIC in the index. For ex. giving the expression 6 + 2x² + 3x - 9 + x³ - 5x as an argument should return ({NUMERIC:(6-9), x²:2, x:(3-5), x³:1}, [NUMERIC, x², x, x³]). This method is fundamental to reduce Sums correctly, it is most important that it returns an object of the kind mentionned here above.

Parameters:

provided_sum The Sum to examine...

Returns:: A tuple (dic, index).

Definition at line 6135 of file base_calculus.py.

References core.base_calculus.Operation.element, and core.base_calculus.Operation.is_literal().

Referenced by core.base_calculus.Sum.intermediate_reduction_line(), core.base_calculus.Sum.is_reducible(), and core.base_calculus.Sum.reduce_().

def core.base_calculus.Sum.intermediate_reduction_line ( self )

Creates the intermediate reduction line.

For instance, giving the Sum 5x + 7x³ - 3x + 1, this method would return (5 - 3)x + 7x³ + 1. No intermediate expansion will be done, though. For instance, the expression a + b + (a + b) will be reduced in 2a + 2b (provided the (a+b) is given as a Sum and not, for instance, as this Product : 1×(a + b) ; but the expression a + b + 5(a + b) won't be reduced in 6a + 6b. It has to be expanded first (there's a Expandable term there !). This method is the base to process the reduction of a Sum. It is therefore important that it returns the described kind of result.

Returns:: A Products' Sum : (coefficients Sum)×(literal factor)

Definition at line 7286 of file base_calculus.py.

References core.base_calculus.Sum.force_inner_brackets_display, core.base_calculus.Sum.get_terms_lexicon(), core.base_calculus.Sum.is_displ_as_a_single_1(), and core.base_calculus.Sum.numeric_terms_require_to_be_reduced().

def core.base_calculus.Sum.into_str	(	self,
		options
	)

Creates a string of the given object in the given ML.

Parameters:

options Any options

Returns:: The formated string

Reimplemented from core.base.Printable.

Definition at line 6338 of file base_calculus.py.

References core.base_calculus.CommutativeOperation.compact_display, core.base_calculus.CommutativeOperation.dbg_str(), core.root_calculus.Exponented.exponent_must_be_displayed(), core.base_calculus.Sum.force_inner_brackets_display, core.base_calculus.CommutativeOperation.get_sign(), core.base_calculus.CommutativeOperation.info, core.base_calculus.Sum.is_displ_as_a_single_0(), core.base_calculus.Sum.next_displayable_term_nb(), core.base_calculus.Sum.requires_brackets(), core.base_calculus.Sum.requires_inner_brackets(), core.base_calculus.Sum.term, and core.base_calculus.CommutativeOperation.throw_away_the_neutrals().

def core.base_calculus.Sum.is_displ_as_a_single_1 ( self )

True if the Sum contains only 0s and one 1.

For instance, 1+0+0

Reimplemented from core.root_calculus.Calculable.

Definition at line 7428 of file base_calculus.py.

References core.base_calculus.Operation.element, and core.base_calculus.Sum.term.

Referenced by core.base_calculus.Sum.intermediate_reduction_line(), core.base_calculus.Sum.is_reducible(), core.base_calculus.Sum.reduce_(), and core.base_calculus.Sum.requires_inner_brackets().

def core.base_calculus.Sum.is_displ_as_a_single_minus_1 ( self )

True if the Sum can be displayed as a single -1 So, if it only contains 0s and a single -1.

For instance, 0+0+(-1)+0

Reimplemented from core.root_calculus.Calculable.

Definition at line 7457 of file base_calculus.py.

References core.base_calculus.Operation.element.

Referenced by core.base_calculus.Sum.is_reducible().

def core.base_calculus.Sum.is_reducible ( self )

True if the Sum is reducible This is based on the result of the get_term_lexicon method.

Returns:: True|False

Definition at line 7494 of file base_calculus.py.

def core.base_calculus.Sum.multiply_symbol_is_required	(	self,
		objct,
		position
	)

True if the usual writing rules require a × between two factors.

Parameters:

objct	The other one
position	The position (integer) of self in the Product

Returns:: True if the writing rules require × between self & obj

Reimplemented from core.root_calculus.Calculable.

Definition at line 7129 of file base_calculus.py.

References core.base_calculus.Item.multiply_symbol_is_required(), core.base_calculus.SquareRoot.multiply_symbol_is_required(), core.base_calculus.Quotient.multiply_symbol_is_required(), core.base_calculus.Product.multiply_symbol_is_required(), core.base_calculus.Sum.multiply_symbol_is_required(), and core.base_calculus.Sum.term.

Referenced by core.base_calculus.Sum.multiply_symbol_is_required().

def core.base_calculus.Sum.next_displayable_term_nb	(	self,
		position
	)

Returns the rank of next non-equivalent to 0 term...

Parameters:

position The point where to start from to search

Returns:: The rank of next non-equivalent to 0 term (or None)

Definition at line 7113 of file base_calculus.py.

References core.base_calculus.Sum.is_displ_as_a_single_0(), and core.base_calculus.Sum.term.

Referenced by core.base_calculus.Sum.into_str().

def core.base_calculus.Sum.numeric_terms_require_to_be_reduced ( self )

True if a gathering of numeric terms must be reduced It is True if at least two consecutive numeric Items are in the list and no other numeric term elsewhere.

Examples where it's True : 3x - 5 + 2 + 5x -2 + 4 + 9 - 2x + 3x² When it's False : 3 - 5 + 2x + 6 4 + x - 2 -7 + 2×5 + 4 + 2x

Returns:: True if a gathering of numeric terms must be reduced

Definition at line 7248 of file base_calculus.py.

References core.base_calculus.CommutativeOperation.is_displ_as_a_single_numeric_Item(), and core.base_calculus.Sum.term.

Referenced by core.base_calculus.Sum.intermediate_reduction_line().

def core.base_calculus.Sum.reduce_ ( self )

Returns the reduced Sum For instance, giving the Sum 5x + 7x³ - 3x + 1, this method would return -2x + 7x³ + 1.

No intermediate expandment will be done, though. For instance, the expression a + b + (a + b) will be reduced in 2a + 2b (provided the (a+b) is given as a Sum and not, for instance, as this Product : 1×(a + b) ; but the expression a + b + 5(a + b) won't be reduced in 6a + 6b. It has to be expanded first (there's a Expandable term there !).

Todo:: support for Fractions (evaluation...)

Returns:: One instance of Sum (reduced) [?] or of the only remaining term

Definition at line 7349 of file base_calculus.py.

Referenced by core.base_calculus.Sum.calculate_next_step().

def core.base_calculus.Sum.requires_brackets	(	self,
		position
	)

True if the argument requires brackets in a product For instance, a Sum with several terms or a negative Item.

Parameters:

position The position of the object in the Product

Returns:: True if the object requires brackets in a Product

Reimplemented from core.root_calculus.Calculable.

Definition at line 7176 of file base_calculus.py.

References core.base.Clonable.clone(), machine.Structure.Structure.clone(), core.base_calculus.CommutativeOperation.compact_display, and core.base_calculus.CommutativeOperation.throw_away_the_neutrals().

Referenced by core.base_calculus.Sum.into_str().

def core.base_calculus.Sum.requires_inner_brackets ( self )

True if the argument requires inner brackets The reason for requiring them is having an exponent different from 1 and several terms or factors (in the case of Products & Sums)

Returns:: True if the object requires inner brackets

Reimplemented from core.root_calculus.Calculable.

Definition at line 7217 of file base_calculus.py.

Referenced by core.base_calculus.Sum.into_str().

def core.base_calculus.Sum.set_force_inner_brackets_display	(	self,
		arg
	)

Sets a value to the force_inner_brackets_display field.

Parameters:

arg	Assumed to be True or False (not tested)

Definition at line 6326 of file base_calculus.py.

References core.base_calculus.Sum._force_inner_brackets_display.

Property Documentation

core::base_calculus.Sum::force_inner_brackets_display [static]

Initial value:

property(get_force_inner_brackets_display,
                    doc = "force_inner_brackets_display field of a Sum")

Definition at line 6306 of file base_calculus.py.

Referenced by core.base_calculus.Sum.intermediate_reduction_line(), core.base_calculus.Sum.into_str(), and core.base_calculus.Sum.reduce_().

core::base_calculus.Sum::term [static]

Initial value:

property(CommutativeOperation.get_element,
                    doc = "To access the terms of the Sum.")

Definition at line 6303 of file base_calculus.py.

Referenced by core.base_calculus.Sum.__cmp__(), core.base_calculus.Polynomial.dbg_str(), core.base_calculus.Polynomial.get_degree(), core.base_calculus.Polynomial.get_max_degree(), core.base_calculus.Sum.into_str(), core.base_calculus.Sum.is_displ_as_a_single_1(), core.base_calculus.Sum.multiply_symbol_is_required(), core.base_calculus.Sum.next_displayable_term_nb(), core.base_calculus.Sum.numeric_terms_require_to_be_reduced(), and core.base_calculus.Sum.requires_inner_brackets().

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

mathmaker_dev/core/base_calculus.py

Public Member Functions

Public Attributes

Properties

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Property Documentation