# Using JuMP for solving a symbolic algebraic system
**URL:** https://discourse.julialang.org/t/using-jump-for-solving-a-symbolic-algebraic-system/130153
**Category:** Optimization (Mathematical)
**Tags:** question, jump
**Created:** [June 24, 2025, 3:23am UTC](https://discourse.julialang.org/t/using-jump-for-solving-a-symbolic-algebraic-system/130153 "2025-06-24T03:23:07Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@jonlym](https://discourse.julialang.org/u/jonlym)
#### Post date: [June 24, 2025, 3:23am UTC](https://discourse.julialang.org/t/using-jump-for-solving-a-symbolic-algebraic-system/130153/1 "2025-06-24T03:23:07Z")
Hi All,
I’d like to solve a system of algebraic equations with the flexibility to specify one variable as independent and one as the dependent variable. In the toy example below, I am calculating the [Reynolds number](https://en.wikipedia.org/wiki/Reynolds_number), `Re` but as shown in the output below, the solver did not converge.
**Questions:**
1. Is JuMP the best package for this? I tried Symbolics.jl previously but I received an error indicating the solver is only compatible with integers and rational values, which is not applicable to my system.
2. Is there a way I can see more information about the termination status?
3. Did the model not solve because the equations are non-linear and I need to use a different type of optimizer?
Thank you!
**Code**
```julia
# Sample problem to solve for variables associated with Reynolds number
using JuMP, Optim
# Set up actual values
ρ_val = 1000.0;
u_val = 1.0;
L_val = 1.0;
μ_val = 1.67e-3;
Re_val = 5.98e+5; # Expected answer
model = Model(Optim.Optimizer)
@variable(model, Re >= 0)
@variable(model, ρ == ρ_val)
@variable(model, u == u_val)
@variable(model, L == L_val)
@variable(model, μ == μ_val)
@objective(model, Min, 0)
@constraint(model, c1, Re == ρ * u * L / μ)
println(model)
optimize!(model)
if !is_solved_and_feasible(model)
error("Solver did not find an optimal solution. Termination status: $(termination_status(model))")
end
println("Solver found an optimal solution")
println("Objective value: $(objective_value(model))")
println("Re: $(value.(Re))")
```
Output
```julia
ERROR: Solver did not find an optimal solution. Termination status: OTHER_ERROR
Stacktrace:
[1] error(s::String)
@ Base .\error.jl:35
[2] top-level scope
@ c:\Users\jlym\ReynoldsNumberToy\ReynoldsNumberToy.jl:28
```
---
### Author:  [@jonlym](https://discourse.julialang.org/u/jonlym)
#### Post date: [June 24, 2025, 3:51pm UTC](https://discourse.julialang.org/t/using-jump-for-solving-a-symbolic-algebraic-system/130153/2 "2025-06-24T15:51:37Z")
FYI, I solved the issue by switching to Ipopt.jl. For my understanding, I would still be interested to learn why I received the error above from Optim.jl.
Updated Code
```julia
# Sample problem to solve for variables associated with Reynolds number
using JuMP, Ipopt
# Set up actual values
ρ_val = 1000.0;
u_val = 1.0;
L_val = 1.0;
μ_val = 1.67e-3;
Re_val = 5.98e+5; # Expected answer
model = Model(Ipopt.Optimizer)
@variable(model, Re >= 0)
@variable(model, ρ == ρ_val)
@variable(model, u == u_val)
@variable(model, L == L_val)
@variable(model, μ == μ_val)
@objective(model, Min, 0)
@constraint(model, c1, Re == ρ * u * L / μ)
println(model)
optimize!(model)
if !is_solved_and_feasible(model)
error("Solver did not find an optimal solution. Termination status: $(termination_status(model))")
end
println("Solver found an optimal solution")
println("Objective value: $(objective_value(model))")
println("Re: $(value.(Re))")
```
Output
```julia
Min 0
Subject to
c1 : Re - (((ρ*u) * L) / μ) == 0
ρ == 1000
u == 1
L == 1
μ == 0.00167
Re >= 0
This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.
Number of nonzeros in equality constraint Jacobian...: 1
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 0
Total number of variables............................: 1
variables with only lower bounds: 1
variables with lower and upper bounds: 0
variables with only upper bounds: 0
Total number of equality constraints.................: 1
Total number of inequality constraints...............: 0
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 0.0000000e+00 5.99e+05 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 0.0000000e+00 0.00e+00 0.00e+00 -1.0 5.99e+05 - 1.65e-08 1.00e+00f 1
Number of Iterations....: 1
(scaled) (unscaled)
Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
Dual infeasibility......: 0.0000000000000000e+00 0.0000000000000000e+00
Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 0.0000000000000000e+00 0.0000000000000000e+00
Number of objective function evaluations = 2
Number of objective gradient evaluations = 2
Number of equality constraint evaluations = 2
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 2
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 1
Total seconds in IPOPT = 0.026
EXIT: Optimal Solution Found.
Solver found an optimal solution
Objective value: 0.0
Re: 598802.3952095808
```
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [June 24, 2025, 7:00pm UTC](https://discourse.julialang.org/t/using-jump-for-solving-a-symbolic-algebraic-system/130153/3 "2025-06-24T19:00:05Z")
Ipopt is probably the recommended option here. There are many reasons why Optim failed; it is less robust, particularly with a bunch of fixed variables like this.