Feature Completeness Against SymPy

[ChrisRackauckas]

• Polynomials
  • Factorization
  • Square-free decomposition
  • Grobner bases
  • Partial fraction decomposition
  • Resultants
  • Rootfinding
• Calculus
  • Limits
  • Integration
  • Taylor series helper functions
• Combinatorics
  • Permutations
  • Combinations
  • Partitions
  • Subsets
  • Permutation Groups
  • Prufer and Gray Codes
• Diophantine equations
• Difference operator
• Geometry
• Plot recipes on symbolic equations
• Support for Distributions.jl, expected values and moments

Note that representation and symbolic solving of systems like ODEs, along with physics is left as the domain for ModelingToolkit.jl. Cryptography is out of scope.

┆Issue is synchronized with this Trello card by Unito

[Krastanov]

I would suggest adding an assumption/refine system to this list as well:

• https://docs.sympy.org/latest/modules/assumptions/index.html
• https://docs.sympy.org/latest/modules/assumptions/refine.html
• https://reference.wolfram.com/language/ref/Assumptions.html

Edit: and the opposite direction

Edit: Actually, SymbolicUtils might be a better home for assumptions and refine?

[dpsanders]

Symbolic solution of nonlinear equations seems to be missing from the list.

[ChrisRackauckas]

That's kind of overlapping with ModelingToolkit, though we may want functionality here and then make symbolic_solve(::NonlinearSystem just use it.

[o314]

AFAIK The logic and relational parts of sympy are not mentioned.
Is this intentional or an omission ?

[ChrisRackauckas]

Those should be inherited from Julia?

[o314]

That's clearly done in Julia if we consider the -hacky- reimpl of multidispatch in Simpy

However, I was thinking about their support of boolean algebra with

• normal form (dnf, cnf, anf ...)
• simplify with some interesting rewriting eg. (And(Ge(a, b), Ge(a, c)), Ge(a, Max(b, c))) eg.(a<=b && a<=c) |- a<=max(b,c)
  see https://github.com/sympy/sympy/blob/1.6/sympy/logic/boolalg.py#L2985
• sat via dpll

For the relational part, please note its two meanings

1. Relational as a (chained) combo of equality and/or comparison in language engineering
2. Relational as a mapping in discrete math

Sympy has some support for both

(1) can help to bring piecewise functions, linear programming into declarative symbolic modeling

(2) can help to reconciliate computational vs declarative def of function. there may be some static dispatch optimization good to catch there

More generally

• Sympy allow the processing of mixed model of bool and non-bool input via a mix of booleanfunction and latticeop args
• the assocop / latticeop divide in simpy could help to clarify the computative vs noncommutative cas
• A lot of algo tend to crossover (buchberger, quine-mccluskey, maybe knuth–bendix)

My 2cts
good if some maths guys can have a review before anything serious

[hdavid16]

Support for Boolean algebra (DNF, CNF, etc) would be great to have. Could come be useful for logical constraints in a JuMP extension.

[ChrisRackauckas]

Indeed, the JuMP extension piece is the OptimizationSystem in ModelingToolkit.jl, but it does need some Symbolics love to finish it.

[hdavid16]

Nice to see the optimization systems in ModelToolkit.jl.
If we had good support for symbolic algebra we could use it to reformulate of Boolean logic constraints into algebraic mixed integer constraints for discrete optimization inside of JuMP. We'd convert Boolean constraints into their conjunctive normal form and then into MIP constraints for mathematical programming. GAMS has this capability and it'd be great to bring it over to JuMP (https://www.gams.com/latest/docs/UG_EMP_DisjunctiveProgramming.html)

[ChrisRackauckas]

Seems like a great use case for this.

[AmplitudeGravity]

Do you want to add "Asymptotic solutions of differential equation, Asymptotic Expansion of Integral" in Symbolics?
And something like Pattern selection and replacement (Cases[], Replace[] in Mathematica) also very useful in practice. It would be nice to see them in Symbolics.

[hdavid16]

And something like Pattern selection and replacement (Cases[], Replace[] in Mathematica) also very useful in practice. It would be nice to see them in Symbolics.

Symbolics currently has substitute for replacement: see Docs