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Package sympycore :: Package basealgebra :: Module algebra :: Class Algebra

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Class Algebra

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Represents an element of an algebraic structure.

This class collects implementation specific methods of algebra classes.

For implemented algebras, see:

Verbatim CollectingField

New algebras may need to redefine the following methods:

__new__(cls, ...)
convert(cls, obj, typeerror=True)
convert_coefficient(cls, obj, typeerror=True)
convert_exponent(cls, obj, typeerror=True)
as_verbatim(self)
as_algebra(self, cls)

and the following properties:

args(self)
func(self)

Instance Methods

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__nonzero__(self)

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__repr__(self)

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__str__(self)
str(x)

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_matches(pattern, expr, repl_dict, wild_info)

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_subs(self, subexpr, newexpr)

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as_algebra(self, cls)
Convert algebra to another algebra.

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as_tree(self, tab='', level=0) source code

as_verbatim(self)

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has(self, obj)
Return True if self contains atomic expression obj.

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match(self, pattern, *wildcards)
Pattern matching.

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matches(pattern, expr, repl_dict={}, wild_info=None) source code
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subs(self, subexpr, newexpr=None)
Substitute a sub-expression with new expression.

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Inherited from expr.Expr: __eq__, __ge__, __gt__, __hash__, __init__, __le__, __lt__, __ne__, __reduce__, as_lowlevel

Inherited from expr.Expr (private): _sethash

Inherited from object: __delattr__, __getattribute__, __new__, __reduce_ex__, __setattr__

Class Methods

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Number(cls, num, denom=None)
Construct algebra number directly from obj.

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Symbol(cls, obj)
Construct algebra symbol directly from obj.

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_matches_seq(cls, pattern_seq, expr_seq, repl_dict, wild_info)

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convert(cls, obj, typeerror=True)
Convert obj to algebra element.

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convert_coefficient(cls, obj, typeerror=True)
Convert obj to coefficient algebra.

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convert_exponent(cls, obj, typeerror=True)
Convert obj to exponent algebra.

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disable_symbolic_comparison(cls, name='equality')
Disable returning Logic instances from relational methods. source code

enable_symbolic_comparison(cls, name='equality')
Enable returning Logic instances from relational methods. source code

get_predefined_symbols(cls, name)

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Class Variables

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_str_value = None

coefftypes = (<type 'int'>, <type 'long'>)

exptypes = (<type 'int'>, <type 'long'>)

Properties

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args
Returns a sequence such that self.func(*self.args) == self.

func
Returns a callable such that self.func(*self.args) == self.

symbols
Return a set of atomic subexpressions in a symbolic object.

Inherited from expr.Expr: data, head, is_writable, pair

Inherited from expr.Expr (private): _hash

Inherited from object: __class__

Method Details

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str(x)

Overrides: object.__str__: (inherited documentation)

as_algebra(self, cls)

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Convert algebra to another algebra.

This method uses default conversation via verbatim algebra that might not be the most efficient. For efficiency, algebras should redefine this method to implement direct conversation.

convert(cls, obj, typeerror=True)
Class Method

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Convert obj to algebra element.

Set typeerror=False when calling from operation methods like __add__, __mul__, etc.

match(self, pattern, *wildcards)

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Pattern matching.

Return None when expression (self) does not match with pattern. Otherwise return a dictionary such that

pattern.subs_dict(self.match(pattern, *wildcards)) == self

Don't redefine this method, redefine matches(..) method instead.

subs(self, subexpr, newexpr=None)

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Substitute a sub-expression with new expression.

There are two usage forms:

obj.subs(subexpr, newexpr)
obj.subs([(subexpr1, newexpr1), (subexpr2, newexpr2), ..])

Property Details

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args

Returns a sequence such that self.func(*self.args) == self.

Get Method:: unreachable.args(self) - Returns a sequence such that self.func(*self.args) == self.

func

Returns a callable such that self.func(*self.args) == self.

Get Method:: unreachable.func(self) - Returns a callable such that self.func(*self.args) == self.

symbols

Return a set of atomic subexpressions in a symbolic object.

Get Method:: unreachable.symbols(self) - Return a set of atomic subexpressions in a symbolic object.

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Class Algebra

__nonzero__(self) (Boolean test operator)

__repr__(self) (Representation operator)

__str__(self) (Informal representation operator)

as_algebra(self, cls)

convert(cls, obj, typeerror=True) Class Method

match(self, pattern, *wildcards)

subs(self, subexpr, newexpr=None)

args

func

symbols

nonzero(self)
(Boolean test operator)

repr(self)
(Representation operator)

str(self)
(Informal representation operator)

convert(cls, obj, typeerror=True)
Class Method