`solve_for` gives Float64 instead of rational solutions

[knuesel]

For example the following gives Float64 instead of rational values:

julia> @variables x y;

julia> Symbolics.solve_for([x + y ~ 2, x - y ~ 1], [x, y])
2-element Vector{Float64}:
 1.5
 0.5

julia> Symbolics.solve_for([x + y ~ 2//1, x - y ~ 1//1], [x, y])
2-element Vector{Float64}:
 1.5
 0.5

Here using rational coefficients makes no difference.

Note that the behavior depends on the values of the coefficients. Here's a case where using rational literals results in a mix of Rational and Float64:

julia> Symbolics.solve_for([x + y ~ 3, x - y ~ 1], [x, y])
2-element Vector{Float64}:
 2.0
 1.0

julia> Symbolics.solve_for([x + y ~ 3//1, x - y ~ 1//1], [x, y])
2-element Vector{Real}:
 2
  1.0

And here's one where a rational coefficient gives all-rational output:

julia> Symbolics.solve_for([x + 2y ~ 2, x - y ~ 1], [x, y])
2-element Vector{Float64}:
 1.3333333333333335
 0.3333333333333333

julia> Symbolics.solve_for([x + 2//1*y ~ 2, x - y ~ 1], [x, y])
2-element Vector{Rational{Int64}}:
 4/3
 1/3

┆Issue is synchronized with this Trello card by Unito

[ChrisRackauckas]

@YingboMa you were looking into something around this yesterday?

[YingboMa]

Yeah, I am looking into this problem. The Symbolics.solve_for([x + y ~ 2//1, x - y ~ 1//1], [x, y]) example is arguably a bug.

[hersle]

It seems to me that the issue is that the coefficients of x and y are automatically set to 1 under the hood, and not 1//1. To enforce that the coefficients become rational, multiply one (or both) equation(s) by 2 and make at least one coefficient rational, to "trigger" promotion to rationals during construction of the linear system A*x = B

using Symbolics
@variables x y
Symbolics.solve_for([
    2//1*x + 2*y ~ 4//1,
    x - y ~ 1
], [x, y])

gives

2-element Vector{Rational{Int64}}:
 3//2
 1//2