# How to write equations less redundant

**URL:** <https://discourse.julialang.org/t/how-to-write-equations-less-redundant/105320>\
**Category:** Modelling & Simulations\
**Tags:** question, package, modelingtoolkit\
**Created:** [October 23, 2023, 4:38pm UTC](https://discourse.julialang.org/t/how-to-write-equations-less-redundant/105320 "2023-10-23T16:38:18Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![ufechner7](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ufechner7/32/51363_2.png) [@ufechner7](https://discourse.julialang.org/u/ufechner7)\
**Post date:** [October 23, 2023, 4:38pm UTC](https://discourse.julialang.org/t/how-to-write-equations-less-redundant/105320/1 "2023-10-23T16:38:18Z")

</div>

How can this code be written less redundant?

```julia
    if lin
        @parameters a=eq.a_bar b=eq.b_bar
        eqs = [D(ω) ~ (Pr - Pg) / (J * ω),
            D(Uest) ~ Ku * e_p,
            r_ω ~ Uest * λnom / R,
            e_ω ~ r_ω - ω,
            e_p ~ Pg - Pr_est + J * D(ω) * ω,
            λest ~ ω * R / Uest,
            Pr_est ~ 0.5 * ρ * A * Uest^3 * Γest * (a*λest + b),
            λ ~ ω * R/U,
            Pr ~ 0.5 * ρ * A * U^3 * Γ * (a*λ + b),
            Pg ~ Pgc + Pge]
    else
        eqs = [D(ω) ~ (Pr - Pg) / (J * ω),
            D(Uest) ~ Ku * e_p,
            r_ω ~ Uest * λnom / R,
            e_ω ~ r_ω - ω,
            e_p ~ Pg - Pr_est + J * D(ω) * ω,
            λest ~ ω * R / Uest,
            Pr_est ~ 0.5 * ρ * A * Uest^3 * Γest * Cp(λest),
            λ ~ ω * R/U,
            Pr ~ 0.5 * ρ * A * U^3 * Γ * Cp(λ),
            Pg ~ Pgc + Pge]
    end

```

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<div class="post-metadata">

**Author:** ![contradict](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@contradict](https://discourse.julialang.org/u/contradict)\
**Post date:** [October 23, 2023, 6:11pm UTC](https://discourse.julialang.org/t/how-to-write-equations-less-redundant/105320/2 "2023-10-23T18:11:31Z")

</div>

```julia
eqs = [D(ω) ~ (Pr - Pg) / (J * ω),
       D(Uest) ~ Ku * e_p,
       r_ω ~ Uest * λnom / R,
       e_ω ~ r_ω - ω,
       e_p ~ Pg - Pr_est + J * D(ω) * ω,
       λest ~ ω * R / Uest,
       λ ~ ω * R/U,
       Pg ~ Pgc + Pge]
if lin
    @parameters a=eq.a_bar b=eq.b_bar
    append!(eqs,
            [Pr_est ~ 0.5 * ρ * A * Uest^3 * Γest * (a*λest + b),
             Pr ~ 0.5 * ρ * A * U^3 * Γ * (a*λ + b)])
else
    append!(eqs,
            [Pr_est ~ 0.5 * ρ * A * Uest^3 * Γest * Cp(λest),
             Pr ~ 0.5 * ρ * A * U^3 * Γ * Cp(λ)]_
end

```

Or

```julia
eqs = [D(ω) ~ (Pr - Pg) / (J * ω),
       D(Uest) ~ Ku * e_p,
       r_ω ~ Uest * λnom / R,
       e_ω ~ r_ω - ω,
       e_p ~ Pg - Pr_est + J * D(ω) * ω,
       λest ~ ω * R / Uest,
       Pr_est ~ 0.5 * ρ * A * Uest^3 * Γest * ifelse(lin, (a*λest + b), Cp(λest)),
       λ ~ ω * R/U,
       Pr ~ 0.5 * ρ * A * U^3 * Γ * ifelse(lin, (a*λ + b), Cp(λ)),
       Pg ~ Pgc + Pge]

```

Or even

```julia
eqs = [D(ω) ~ (Pr - Pg) / (J * ω),
       D(Uest) ~ Ku * e_p,
       r_ω ~ Uest * λnom / R,
       e_ω ~ r_ω - ω,
       e_p ~ Pg - Pr_est + J * D(ω) * ω,
       λest ~ ω * R / Uest,
       Cp′ ~ ifelse(lin, (a*λest + b), Cp(λest))
       Pr_est ~ 0.5 * ρ * A * Uest^3 * Γest * Cp′,
       λ ~ ω * R/U,
       Pr ~ 0.5 * ρ * A * U^3 * Γ * Cp′,
       Pg ~ Pgc + Pge]

```

if `lin` is a `Bool`, `ifelse` will be evaluated when the equations are constructed, if `lin` is a symbolic expression then it will be evaluated when the equations are evaluated which may not be what you want.

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<div class="post-metadata">

**Author:** ![ufechner7](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ufechner7/32/51363_2.png) [@ufechner7](https://discourse.julialang.org/u/ufechner7)\
**Post date:** [October 23, 2023, 6:12pm UTC](https://discourse.julialang.org/t/how-to-write-equations-less-redundant/105320/3 "2023-10-23T18:12:21Z")

</div>

lin is Bool

OK, your last version is a little bit wrong, because there is Cp(λ) and Cp(λest), but I get the idea…

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<div class="post-metadata">

**Author:** ![johhell](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/johhell/32/46165_2.png) [@johhell](https://discourse.julialang.org/u/johhell)\
**Post date:** [October 25, 2023, 6:39pm UTC](https://discourse.julialang.org/t/how-to-write-equations-less-redundant/105320/4 "2023-10-25T18:39:57Z")

</div>

It would make sense to have a `Cp()` function for both cases.  
A simplified example:

```julia
using ModelingToolkit, OrdinaryDiffEq
using Plots

lin = true # case distinction

function CpNew(λ::Float64, a::Float64, b::Float64)::Float64
    if lin
        a*λ + b
    else
        λ*λ # your function here
    end
end

@register_symbolic CpNew(λ,a,b)

@variables t x(t)
@parameters a b
D = Differential(t)
eqs = [D(x) ~ CpNew(x, a, b)]
@named sys = ODESystem(eqs)
prob = ODEProblem(sys, [0.1], (0.0,5.0), [0.01, 0.5])
sol = solve(prob, Tsit5())

display(plot(sol))
display(sol)

```