Glen Whitney
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6 months ago  

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README.md
pocomath
A little proofofconcept for organizing mathjs by module inclusion, avoiding factory functions.
Note this project is packagemanaged by pnpm. I do not expect that a clone can easily be manipulated with npm
.
Defines a class PocomathInstance to embody independent instances of a mathjsstyle CAS. Basically, it keeps track of a collection of implementations (in the sense of typedfunction) for each of the functions to be used in the CAS, rather than just the finalized typedfunctions. It also tracks the dependencies of each implementation (which must form a directed acyclic network). When a method is requested from the instance, it assembles the proper typedfunction (and caches it, of course). Whenever an implementation is added to that function name or any of its dependencies, the previously assembled typedfunction is discarded, so that a new one will be constructed on its next use.
Multiple different instances can coexist and have different collections of operations. Moreover, only the source files for the operations actually desired are ever visited in the import tree, so minimizing a bundle for a specific subset of operations should be quite straightforward.
Hopefully the test cases, especially test/_pocomath.mjs
and test/custom.js
, will show off these aspects in action.
Note that 'subtract' is implemented as a 'generic' operation, that depends only on the 'add' and 'negate' operations (and so doesn't care what types it is operating on). Although it would not be the computationally fastest in a production instance, for the sake of demonstration 'divide' and 'sign' are also so defined.
Furthermore, note that 'Complex' is implemented in a way that doesn't care about the types of the real and imaginary components, so with the 'bigint' type defined here as well, we obtain Gaussian integers for free.
This core could be extended with many more operations, and more types could be defined, and additional subbundles like number/all.mjs
or clever conditional loaders like complex/extendToComplex.mjs
could be defined.
Also see the comments for the public member functions of
core/PocomathInstance.mjs
for further details on the structure and API of this
scheme for organizing a CAS.
Hopefully this shows promise. It is an evolution of the concept first prototyped in picomath. However, picomath depended on typedfunction allowing mutable function entities, which turned out not to be performant. Pocomath, on the other hand, uses typedfunction v3 as it stands, although it does suggest that it would be helpful to extend typedfunction with subtypes, and it could even be reasonable to move the dependency tracking into typedfunction itself (given that typedfunction already supports selfdependencies, it would not be difficult to extend that to interdependencies between different typedfunctions).
Note that Pocomath allows one implementation to depend just on a specific signature of another function, for efficiency's sake (if for example 'bar(Matrix)' knows it will only call 'foo(Matrix)', it avoids another typedispatch). That capability is used in sqrt, for example.
Pocomath also lazily reloads operations that depend on the config when that changes, and if an operation has a signature mentioning an undefined type, that signature is ignored until the type is installed, at which point the function lazily redefines itself to use the additional signature.
Pocomath now also allows template operations and template types, also built on top of typedfunction (but candidates for integration therein). This is used to make many operations more specific, implement a typehomogeneous Tuple type, and make Complex numbers be typehomogeneous (which it seems like it always should be). One of the cutest consequences of this approach is that with careful definitions of the Complex<T>
templates, one gets a working quaternion data type absolutely for free as Complex<Complex<number>>
(and integral quaternions as Complex<Complex<bigint>>
, etc.)
It also now has a facility to adapt a thirdparty numeric class as a type in Pocomath, see src/generic/all.mjs
and src/generic/Types/adapted.mjs
, which it uses by way of example to incorporate fraction.js Fraction objects into Pocomath.