Support for SparseArray

[Li-Xiang-Ideal]

Summary of previous discussion in #946

Correct result of Part,Equal,ArrayQ, etc. on SparseArray is expected.

• SparseArray[{{1, 2} -> 3}, {3, 3}][[1]] === SparseArray[{{2} -> 3}, {3}]
• SparseArray[{{1, 2} -> 1, {2, 1} -> -1}] == {{0, 1}, {-1, 0}}
• ArrayQ[SparseArray[{{1, 2} -> 1, {2, 1} -> -1}]] === True
• ArrayQ[SparseArray[3, Pi]] === False
• ArrayQ[SparseArray[{{1, 8} -> 3}, {3, 3}]] === False

To be continued...

Methods to implement SparseArray

• SparseArrayExpression as special type of Expression (like ListExpression)
• Use existing libraries like SymPy or SciPy

Things to keep in mind

• we are not experts in how to implement sparse arrays, there are others who are
• we don't have the resources to do a good job, and in the past when this has been tried the results have been a bit lacking to the point of ripping out that code and replacing it with someone else's library; this has generally been a win in terms of functionality, speed, and reduced maintenance.
• to a limited extent, we sometimes do have to provide fallback code, but we shouldn't go too deep down here without good reason and justification
• if other libraries and packages are lacking, we should be working with those folks to improve things.

Current status

• SciPy is not particularly designed to work with symbolic expressions
• SymPy supports SparseMatrix only (not SparseArray)

To be continued...

Issues to be discussed

• How to implement SparseArray? Use as many existing packages as possible, or define our new type of SparseArrayExpression while leaving specific evaluations like RowReduce and SingularValueDecomposition to SymPy or SciPy, or any other approaches?
• Which existing packages can help implement SparseArray? SymPy, SciPy, and?
• If SparseArrayExpression is needed, how to organize the code? Can we implement it in mathics.core without being too entangled with the rest of the code (which means a new branch is preferred), or shall we use Pymathics module?

To be continued...

Conclusions from new discussions

To be continued...