### Navigation

- index
- modules |
- next |
- previous |
- Combinatorics »

# Pointwise addition of dictionaries

Pointwise addition of dictionaries

Provides function to add dictionaries pointwise with values in a common ring and to compute linear combinations

EXAMPLES:

    sage: from sage.combinat.dict_addition import dict_addition
    sage: D1 = { 0:1, 1:1 }; D2 = { 0:-1, 1:1 }
    sage: dict_addition( [D1,D2] )
    {1: 2}

`sage.combinat.dict_addition.``dict_addition`(dict_iter)

  Returns the pointwise addition of dictionaries with coefficients.

  Parameters: | dict_iter – iterator of dictionaries with values in a common ring.

  OUTPUT:

  - a dictionary containing all keys of dictionaries in `dict_list`, with values being the sum of the values in the different dictionaries (keys with zero value are omitted)

  EXAMPLES:

      sage: from sage.combinat.dict_addition import dict_addition
      sage: D = { 0:1, 1:1 }; D
      {0: 1, 1: 1}
      sage: dict_addition( D for _ in range(5) )
      {0: 5, 1: 5}

      sage: D1 = { 0:1, 1:1 }; D2 = { 0:-1, 1:1 }
      sage: dict_addition( [D1,D2] )
      {1: 2}

`sage.combinat.dict_addition.``dict_linear_combination`(dict_factor_iter, factor_on_left=True)

  Returns the pointwise addition of dictionaries with coefficients.

  Parameters: | dict_factor_iter – iterator of pairs D, coeff, where - the D’s are dictionaries with values in a common ring - the coeff’s are coefficients in this ring factor_on_left (boolean; optional, default `True`) – if True, the coefficients are multiplied on the left, otherwise they are multiplied on the right

  OUTPUT:

  - a dictionary containing all keys of dictionaries in `dict_list`, with values being the sum of the values in the different dictionaries, each one first multiplied by the given factor (keys with zero value are omitted)

  EXAMPLES:

      sage: from sage.combinat.dict_addition import dict_linear_combination
      sage: D = { 0:1, 1:1 }; D
      {0: 1, 1: 1}
      sage: dict_linear_combination( (D,i) for i in range(5) )
      {0: 10, 1: 10}
      sage: dict_linear_combination( [(D,1),(D,-1)] )
      {}

### Navigation

- index
- modules |
- next |
- previous |
- Combinatorics »