symbolics_to_sympy() and variable constrains

[owiecc]

I'd like to solve a set on nonlinear equations. As this is not implemented yet (JuliaSymbolics/SymbolicUtils.jl#63) I am trying to use SymPy to do that. This is just a MWE, real problem is a bit more complex.

using Symbolics, SymPy

@variables x, y
eqns = [x^2 - y ~ 0, 4*x - 1 ~ 0]

Here I do a conversion to SymPy:

sx = symbols("x")
sy = symbols("y")
sol = nonlinsolve([symbolics_to_sympy(eq.lhs) for eq in eqns], sx, sy)

This solves correctly to {(1/4,1/16)}

However, if I add additional constrains on the variables I get bad results:

sx = symbols("x", positive = True)
sy = symbols("y")
sol = nonlinsolve([symbolics_to_sympy(eq.lhs) for eq in eqns], sx, sy)

This solves to an empty set: ∅

I assume this is because symbolics_to_sympy() creates a variable x without constrains but I add these constrains later, in sx. Any ideas how to solve this problem?

┆Issue is synchronized with this Trello card by Unito

[ChrisRackauckas]

We need to make a constraints system 😅

[owiecc]

I made a small workaround if anyone stumbles on the same problem. I replaced the symbols created with symbolics_to_sympy() with constrained ones from SymPy. It is not pretty but is does work.

sx = symbols("x")
sy = symbols("y")

sa = symbols("a", positive = True)
sb = symbols("b")

subsymbols(ex) = subs(ex, sx=>sa, sy=> sb)

eqns_ab = [subsymbols(symbolics_to_sympy(eq.lhs)) for eq in eqns]

The solve function solves the nonlinear system correctly.

solve(eqns_ab, sa, sb) # (1/4, 1/16)

The nonlinsolve will also solve the system.

nonlinsolve(eqns_ab, sa, sb) # {(1/4, 1/16)}

However, nonlinsolve ignores the constraints. If I change the equations to [x^2 - y ~ 0, 4*x + 1 ~ 0] I get this:

solve(eqns_ab, sa, sb) # Any[]
nonlinsolve(eqns_ab, sa, sb) # {(-1/4, 1/16)}

I guess my original problem can be fixed by passing a list of known, constrained SymPy symbols symbolics_to_sympy(expr, symbols::Vector{Sym}=[]) and using them if necessary.

[ChrisRackauckas]

It would probably be good for those values to be stored in the variable metadata.

@variables x [positive = true]