`clesto.module`: Free modules¶

Module¶

class clesto.module.module.Module_element(data=None, torsion=None)[source]¶

Elements in a free module over \(\mathbb{Z}\) or \(\mathbb{Z}/n \mathbb{Z}\).

Parameters

data (dict or None, default: None) – Dictionary representing a linear cobination of basis elements. Items in the dict correspond with pairs (basis element: coefficient).
torsion (int or 'free', default 'free') – The torsion of the underlying ring \(\mathbb{Z}\) or \(\mathbb{Z}/n \mathbb{Z}\)

torsion¶

The torsion of the underlying ring \(\mathbb{Z}\) or \(\mathbb{Z}/n \mathbb{Z}\)

Type: int or ‘free’, default ‘free’

Example

>>> print(Module_element())
0
>>> print(Module_element({'a': 1, 'b': -1, 'c': 0}))
a - b

default_torsion = 'free'¶

__add__(other)[source]¶

Addition: self + other.

Parameters: other (clesto.basics.module.Module_element object) – The element to add to self.
Returns: The sum of self and other.
Return type: clesto.basics.module.Module_element object

Example

>>> Module_element({'a': 1, 'b': 2}) + Module_element({'a': 1})
Module_element({'a': 2, 'b': 2})

__sub__(other)[source]¶

Diference: self - other.

Parameters: other (clesto.basics.module.Module_element object) – The element to substract from self.
Returns: The difference of self and other.
Return type: clesto.basics.module.Module_element object

Example

>>> Module_element({'a': 1, 'b': 2}) - Module_element({'a': 1})
Module_element({'b': 2})

__rmul__(c)[source]¶

Scaling: c * self.

Parameters: other (int) – The element to scale self. by.
Returns: The scaling of self by other.
Return type: clesto.basics.module.Module_element object

Example

>>> 3 * Module_element({'a':1, 'b':2})
Module_element({'b': 6, 'a': 3})

__neg__()[source]¶

Additive inverse: - self.

Returns: the additive inverse of self.
Return type: clesto.basics.module.Module_element object

Example

>>> - Module_element({'a': 1, 'b': 2})
Module_element({'a': -1, 'b': -2})

__iadd__(other)[source]¶

In place addition: self += other.

Parameters: other (clesto.basics.module.Module_element object) – The element to add to self.

Example

>>> x = Module_element({'a': 1, 'b': 2})
>>> x += Module_element({'a': 3, 'b': 6})
>>> x
Module_element({'b': 8, 'a': 4})

__isub__(other)[source]¶

In place difference: self -= other.

Parameters: other (clesto.basics.module.Module_element object) – The element to substract from self.

Example

>>> x = Module_element({'a': 1, 'b': 2})
>>> x -= Module_element({'a': 3, 'b': 6})
>>> x
Module_element({'a': -2, 'b': -4})

set_torsion(torsion)[source]¶

Sets the torsion of self.

Parameters: torsion (int or 'free') – The new torsion of self

Example

>>> Module_element({'a': 1, 'b': 2}).set_torsion(2)
Module_element({'a': 1})

create(other=None)[source]¶

Instantiates data with same type and attribute values as self.

Parameters: other (dict or None, default: None) – Data to be initialized.
Returns: The initialized object with the given data
Return type: type(self) object

Example

>>> x =  Module_element({'a': 1})
>>> x + x.create({'b': 1})
Module_element({'a': 1, 'b': 1})

zero()[source]¶

Instantiates 0 with same type and attribute values as self.

Returns: The initialized empty object
Return type: type(self) object

Example

>>> x = Module_element({'a': 1})
>>> x + x.zero() == x
True

clesto.module: Free modules¶

Module¶

`clesto.module`: Free modules¶