WIP: Extend factorial #3568
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WIP: Extend factorial #3568
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With this commit, Range is now a full-fledged implementation of Matrix,
representing an arbitrary arithmetic sequence (of any type supported
by mathjs) in a "lazy" way, i.e. its entries are generated on demand.
(Thus, even infinite Ranges are supported.)
Note that Range therefore has many new dependencies, and the `matrix()`
convertor/constructor function must be able to create Ranges. Therefore,
to avoid a circular dependency on `matrix`, many mathjs methods have
their dependence on `matrix()` removed. Often this dependence was
very superficial, and removing it was essentially trivial; in all other
cases, the dependence could be shifted to DenseMatrix rather than matrix,
removing the possibility of circularity.
In addition, as it seemed very confusing (almost to the point of a bug)
that `math.parse('2:5')` produced a representation of 2, 3, 4, 5 while
`Range.parse('2:5')` produced a representation of 2, 3, 4. Therefore, this
commit changes the interpretation so that both `parse` command include the
endpoint.
Finally, this commit fixes the remaining doc examples tests in the
src/type directory.
…et()
* A single number is now interpreted as the entire "layer" at that position;
adds `layer` method to Matrix for efficient support of this convention.
* An array is just passed to index
* A string form of a Range is now allowed in the index; the lower and upper
limits may be elided, allowing `':'` as a wildcard for an entire dimension.
* Also removes unnecessary dependence of set functions on Index.
* Now passes all doc example testing for `subset`
The prod function now first reduces its argument to a 1d vector, then uses binary splitting without allocating any new matrices or arrays. Also implements the previously unimplemented second "dimension" argument to prod (albeit not as efficiently). As these changes added new dependencies to `prod`, some other minor refactors were necessary to avoid circular dependencies and/or keep unwanted dependencies from the number bundle. Also fixes a couple more instances of doc example tests.
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The most "controversial" change in this PR is that I couldn't wrap my mind around the following: previously, if you took the exact same string, say On the other hand, I left |
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This is a work-in-progress, proof-of-concept PR that allows one to calculate e.g. the 10th rising factorial of bignumber 8.5 by
math.prod(math.range(math.bignumber(8.5), math.bignumber(19.5)). The major highlights include:Making Range an implementation of Matrix. (This change breaks important ground to pave the way for alternate Matrix implementations besides DenseMatrix and SparseMatrix, given that there have been discussions of flat matrices and ones based on JavaScript's type arrays.)
Allowing Range to encode arbitrary arithmetic progressions of arbitrary mathjs entities.
Complete reimplementation of prod.
Several indexing extensions, and addition of new scalarDivide(V, W), one(x), and zero(x) methods.
In addition, there is a significant reduction in the number of failing doc example tests.
This PR is being submitted for feedback on the approach and scope. It needs at least extensive addition of tests and documentation before being merge-ready.