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0 pointszozbot2342y ago0 comments

Typically, there are 'group', 'ring' and 'field' tactics that will perform simplification in the relevant algebraic structures. Going from that to solving sin^2 x + cos^2 x is simply a matter of writing more such tactics, operating on e.g. real fields or whatever is applicable in any given case.

This is a lot less ad-hoc than whatever CAS's do, but it's also less error prone.

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westurner2y ago

Do any existing CAS systems have configurable axioms? OTOH: Conway's surreal infinities, Do not early eliminate terms next to infinity, Each instance of infinity might should have a unique identity, configurable Order of operations,

All of the axiomatic transformations applied by a CAS like SymPy should/must be in Lean Mathlib somewhere? If nothing else, a lookup_lean_mathlib_definition(expr, 'path/to/mathlib-v0.0.2') or find_similar(expr, AxiomDB) would be useful.

How do CAS differ from Production Rule Systems? https://en.wikipedia.org/wiki/Production_system_(computer_sc...

CAS > Simplification: https://en.wikipedia.org/wiki/Computer_algebra#Simplificatio...

Rewriting: https://en.wikipedia.org/wiki/Rewriting

Because the rulesets are expected to change, rules engines have functionality to compile rules into a tree or better for performance.

eBPF is not a rules engine, but it does optimize filter sets IIRC?

staunton2y ago

Julia's Symbolics.jl allows users to easily add custom rewrite rules. However, it's not a state-of-the-art CAS. I don't have that much experience with others. Mathematica doesn't allow it, I think.

westurner2y ago

FWIU Wolfram's searching for a unified model with the Wolfram Physics Project, too; e.g. "The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics" (2022) https://www.wolframscience.com/metamathematics/ https://www.wolframphysics.org/bulletins/

Are fundamental constants other-valued in any Many Worlds interpretations, or are e, i, and Pi always e, i, and pi with the same relations?

Countability and continuua (in a Hilbert space of degree n, where n is or is not inconstant like the many forms of [quantum discord] entropy and the energy that represents them)

TIL the separable states problem is considered NP-hard, and many models specify independence of observation as necessary.

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westurner2y ago

How do CAS differ from Production Rule Systems? https://en.wikipedia.org/wiki/Production_system_(computer_sc...

CAS > Simplification: https://en.wikipedia.org/wiki/Computer_algebra#Simplificatio...

Rewriting: https://en.wikipedia.org/wiki/Rewriting

Because the rulesets are expected to change, rules engines have functionality to compile rules into a tree or better for performance.

eBPF is not a rules engine, but it does optimize filter sets IIRC?

staunton2y ago

Julia's Symbolics.jl allows users to easily add custom rewrite rules. However, it's not a state-of-the-art CAS. I don't have that much experience with others. Mathematica doesn't allow it, I think.

westurner2y ago

Are fundamental constants other-valued in any Many Worlds interpretations, or are e, i, and Pi always e, i, and pi with the same relations?

Countability and continuua (in a Hilbert space of degree n, where n is or is not inconstant like the many forms of [quantum discord] entropy and the energy that represents them)

TIL the separable states problem is considered NP-hard, and many models specify independence of observation as necessary.

1 more reply

j / k navigate · click thread line to collapse