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Package sympycore :: Package calculus :: Module algebra :: Class Calculus

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Class Calculus

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Represents an element of a symbolic algebra.

The set of a symbolic algebra is a set of expressions.

Nested Classes

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Infinity

Inherited from core.Basic: __metaclass__

Instance Methods

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__divmod__(self, other)

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__eq__(self, other)

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__ge__(self, other)

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__gt__(self, other)

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__le__(self, other)

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__lt__(self, other)

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

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as_polynom(self, cls=None)

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diff(expr, symbol, order=1)
Return derivative of the expression with respect to symbols.

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evalf(self, n=15)

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get_direction(self)

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integrate(expr, x)

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to_Float(self, n=15)

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Inherited from basealgebra.pairs.CommutativeRingWithPairs: __abs__, __add__, __div__, __hash__, __int__, __long__, __mul__, __ne__, __neg__, __nonzero__, __pos__, __pow__, __radd__, __rdiv__, __rmul__, __rsub__, __str__, __sub__, as_Add_args, as_Factors_args, as_Mul_args, as_Pow_args, as_Terms_args, as_primitive, as_tree, copy, expand, has, has_symbol, to_str_data

Inherited from basealgebra.pairs.CommutativeRingWithPairs (private): _get_symbols_data, _subs

Inherited from basealgebra.ring.CommutativeRing: __rpow__, __rtruediv__, __truediv__, as_Log_args

Inherited from basealgebra.ring.CommutativeRing (private): _matches

Inherited from basealgebra.algebra.BasicAlgebra: __repr__, as_primitve, match, matches, subs

Inherited from object: __delattr__, __getattribute__, __init__, __reduce__, __reduce_ex__, __setattr__

Class Methods

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Exp(cls, arg)

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Log(cls, arg, base=None)
Compute logarithm of arg in base.

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Number(cls, num, denom=None)
Construct new number instance as an algebra number.

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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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get_predefined_symbols(cls, name)

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Inherited from basealgebra.pairs.CommutativeRingWithPairs: Add, Factors, Mul, Pow, Sub, Symbol, Terms, callable_to_str_data, coefficient_to_str_data, exponent_to_str_data

Inherited from basealgebra.ring.CommutativeRing: Div

Inherited from basealgebra.algebra.BasicAlgebra: convert

Inherited from basealgebra.algebra.BasicAlgebra (private): _matches_seq

Static Methods

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Inherited from basealgebra.pairs.CommutativeRingWithPairs: __new__

Class Variables

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coefftypes = (<type 'int'>, <type 'long'>, <class 'sympycore.a...

defined_functions = {'cos': <class 'sympycore.calculus.functio...

exptypes = (<type 'int'>, <type 'long'>, <class 'sympycore.ari...

one = Calculus('1')

oo = CalculusInfinity(1)

undefined = CalculusInfinity(0)

zero = Calculus('0')

zoo = CalculusInfinity(CalculusInfinity(0))

Inherited from basealgebra.pairs.CommutativeRingWithPairs: one_c, one_e, zero_c, zero_e

Inherited from basealgebra.pairs.CommutativeRingWithPairs (private): _coeff_terms, _hash, _symbols_data

Inherited from basealgebra.ring.CommutativeRing (private): _symbols

Inherited from basealgebra.algebra.BasicAlgebra (private): _str_value

Properties

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data

head

is_bounded

Inherited from basealgebra.pairs.CommutativeRingWithPairs: args, func, is_Add, is_Mul, is_Number, is_Pow, is_Symbol, symbols

Inherited from basealgebra.pairs.CommutativeRingWithPairs (private): _has_active

Inherited from object: __class__

Method Details

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Log(cls, arg, base=None)
Class Method

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Compute logarithm of arg in base.

Argument arg must be an element of exponent algebra and base is an element of an algebra.

Overrides: basealgebra.ring.CommutativeRing.Log: (inherited documentation)

Number(cls, num, denom=None)
Class Method

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Construct new number instance as an algebra number.

Overrides: basealgebra.pairs.CommutativeRingWithPairs.Number: (inherited documentation)

Convert algebra to another algebra.

Overrides: basealgebra.algebra.BasicAlgebra.as_algebra

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

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Convert obj to coefficient algebra.

Overrides: basealgebra.algebra.BasicAlgebra.convert_coefficient

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

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Convert obj to exponent algebra.

Overrides: basealgebra.algebra.BasicAlgebra.convert_exponent

diff(expr, symbol, order=1)

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Return derivative of the expression with respect to symbols.

Examples:

expr.diff(x,y) - 2nd derivative with respect to x and y
expr.diff(x,4) is equivalent to expr.diff(x,x,x,x).

get_predefined_symbols(cls, name)
Class Method

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Overrides: basealgebra.algebra.BasicAlgebra.get_predefined_symbols

Class Variable Details

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coefftypes

Value:

(<type 'int'>,
 <type 'long'>,
 <class 'sympycore.arithmetic.numbers.FractionTuple'>,
 <class 'sympycore.arithmetic.numbers.Complex'>,
 <class 'sympycore.arithmetic.numbers.Float'>)

defined_functions

Value:

{'cos': <class 'sympycore.calculus.functions.elementary.cos'>,
 'cot': <class 'sympycore.calculus.functions.elementary.cot'>,
 'exp': <class 'sympycore.calculus.functions.elementary.exp'>,
 'log': <class 'sympycore.calculus.functions.elementary.log'>,
 'sign': <class 'sympycore.calculus.functions.elementary.sign'>,
 'sin': <class 'sympycore.calculus.functions.elementary.sin'>,
 'sqrt': <class 'sympycore.calculus.functions.elementary.sqrt'>,
 'tan': <class 'sympycore.calculus.functions.elementary.tan'>}

exptypes

Value:

(<type 'int'>,
 <type 'long'>,
 <class 'sympycore.arithmetic.numbers.FractionTuple'>,
 <class 'sympycore.arithmetic.numbers.Complex'>,
 <class 'sympycore.arithmetic.numbers.Float'>)

Property Details

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is_bounded

Get Method:: unreachable.is_bounded(self)

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Class Calculus

Log(cls, arg, base=None) Class Method

Number(cls, num, denom=None) Class Method

__eq__(self, other) (Equality operator)

__ge__(self, other) (Greater-than-or-equals operator)

__gt__(self, other) (Greater-than operator)

__le__(self, other) (Less-than-or-equals operator)

__lt__(self, other) (Less-than operator)

as_algebra(self, cls)

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

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

diff(expr, symbol, order=1)

get_predefined_symbols(cls, name) Class Method

coefftypes

defined_functions

exptypes

is_bounded

Log(cls, arg, base=None)
Class Method

Number(cls, num, denom=None)
Class Method

eq(self, other)
(Equality operator)

ge(self, other)
(Greater-than-or-equals operator)

gt(self, other)
(Greater-than operator)

le(self, other)
(Less-than-or-equals operator)

lt(self, other)
(Less-than operator)

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

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

get_predefined_symbols(cls, name)
Class Method