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The sparsevector.py module includes the SparseVector class, which implements basic algebraic operations on sparse representations of vector objects. The class assumes Python 3.3 or greater as it makes use of the yield from syntax.

A prototypical example of a vector is an element in the n-fold set product of the real numbers R, i.e., an n-tuple of real numbers. A sparse vector is a data structure that only records non-zero components of a vector.

One simple way to represent a sparse vector is as an associative array or key-value pairs where the key is a component index and the value is a field element. For example, the vector (0, 1, 0) has a sparse representation {2: 1}.

Despite its name, a SparseVector object can be any elements from a finite product of R-modules for some ring R. If M = M1 x M2 x ... x Mn for R-modules Mi, then a typical element might look something like {Mi1: mi1, ..., Mil: mil}.

The test can be run by issuing python -m test.