reg_eq_solver.rb

require 'matrix'
module RegEqSolver
  class RHS
    alias ~ binding
    public :~
  end
  [Integer, Float, Rational, Complex].each do |klass|
    refine klass do
      def ~
        $rhs = self
        RHS.new
      end
    end
  end
  refine Regexp do
    def =~ binding
      params = source.scan(/(-?[\d.]+)\(\?<([a-z]+)>\)/)
      [params, binding, $rhs]
    end
  end
  refine Kernel do
    def solve(*param_bind_rhs)
      bind = nil
      params = param_bind_rhs.map do |ps,b|
        bind ||= b
        ps.map(&:last)
      end.flatten.uniq
      rhs = []
      matrix = param_bind_rhs.map do |ps,_b,r|
        rhs << r
        v = [0] * params.size
        ps.each do |p|
          v[params.index(p.last)] = p.first.to_f
        end
        v
      end
      ans = Matrix[*matrix].lup.solve(rhs)
      params.zip(ans).each do |p,a|
        bind.local_variable_set(p, a)
      end
    end
  end
end

using RegEqSolver
solve(
  /2(?<x>)+3(?<y>)/ =~~~ 8,
  /5(?<x>)+2(?<y>)/ =~~~ 9,
  /8(?<y>)-3(?<z>)/ =~~~ 7
)
p(x:, y:, z:)