# Porting challenge for MTK/Symbolics

**URL:** <https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530>\
**Category:** General Usage\
**Created:** [May 4, 2021, 4:52pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530 "2021-05-04T16:52:29Z")\
**Posts on this page:** 9\
**Page:** 1

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**Author:** ![jlperla](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jlperla/32/34332_2.png) [@jlperla](https://discourse.julialang.org/u/jlperla)\
**Post date:** [May 4, 2021, 4:52pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/1 "2021-05-04T16:52:29Z")

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The following SymPy code was given to me by someone who wanted to see if Symbolics/SymbolicUtils/MTK can handle these sorts of situations.

```julia
using SymPy
w_1, w_2 = symbols("w_1, w_2",real=true,positive=true)
pi = symbols("pi")
left = pi*(w_1/2)+(1-pi)w_1
right = pi*w_2+(1-pi)*w_2/2

prob_simp = solve(left-right,pi)[1]
prob = max(min(solve(left-right,pi)[1],1),0)
print(prob)

y_1,y_2 = symbols("y_1,y_2")
profit = (1-(1-prob)^2)*(y_1-w_1)
print(profit)

profit_simp = (1-(1-prob_simp)^2)*(y_1-w_1)
dprofit = diff(profit_simp, w_1)
print(dprofit)
BR = solve(dprofit,w_1)[1]
print(BR)

symmetric_sol = solve(w_2-BR(y_1 => 1))
print(symmetric_sol)

```

Can this be ported directly, and if not what are the missing features/overloads/etc.? By directly I mean that it is the symbolics output that the person cares about. The biggest thing I wasn’t sure about was how to handle the simple 1-D solve.

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**Author:** ![shashi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shashi/32/1824_2.png) [@shashi](https://discourse.julialang.org/u/shashi)\
**Post date:** [May 4, 2021, 5:15pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/2 "2021-05-04T17:15:28Z")

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The solve we have right now can only do linear equations.

So you can pass in `Symbolics.solve_for([left-right ~ 0], [pi])` to try it out.

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**Author:** ![Sukera](https://avatars.discourse-cdn.com/v4/letter/s/ce7236/32.png) [@Sukera](https://discourse.julialang.org/u/Sukera)\
**Post date:** [May 4, 2021, 5:22pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/3 "2021-05-04T17:22:55Z")

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The arrays have to match - so it’d be `solve_for(left-right ~ 0, pi)` or `solve_for([left-right ~ 0], [pi])`, which give

```julia
julia> Symbolics.solve_for(left-right ~ 0, pi)                                                 
(pi*(0.5w1 + 0.5w2) + w1*(1 - pi) + 0.5pi*w1 - (pi*w2) - (0.5w2*(1 - pi)))*((0.5w1 + 0.5w2)^-1)

```

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<div class="post-metadata">

**Author:** ![shashi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shashi/32/1824_2.png) [@shashi](https://discourse.julialang.org/u/shashi)\
**Post date:** [May 4, 2021, 5:27pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/4 "2021-05-04T17:27:35Z")

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Thanks, edited my answer. Well that seems to be a bug ☹

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<div class="post-metadata">

**Author:** ![jlperla](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jlperla/32/34332_2.png) [@jlperla](https://discourse.julialang.org/u/jlperla)\
**Post date:** [May 4, 2021, 5:30pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/5 "2021-05-04T17:30:39Z")

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Thanks guys. I see snippets but do you have the full code you wrote to get to that last stage? If you can throw in a `|> simplify` or whatever at the end of the `solve_for` for good measure. I was hoping to be able to forward this whole post to people as an example of how you can do simple stuff with symbolics (since it is largely focused on the more complicated numerical-symbolic interaction at this point).

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<div class="post-metadata">

**Author:** ![Sukera](https://avatars.discourse-cdn.com/v4/letter/s/ce7236/32.png) [@Sukera](https://discourse.julialang.org/u/Sukera)\
**Post date:** [May 4, 2021, 5:54pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/6 "2021-05-04T17:54:05Z")

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I was just playing around, sorry 😅 I basically just did `@variables w1 w2 pi` and then entered the equations. I didn’t even restrict them to be positive, since I don’t know how.

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**Author:** ![j\_verzani](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/j_verzani/32/8551_2.png) [@j\_verzani](https://discourse.julialang.org/u/j_verzani)\
**Post date:** [May 4, 2021, 6:30pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/7 "2021-05-04T18:30:47Z")

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Here are both approaches written in similar styles:

```julia
using SymPy
@syms pi w[1:2]::(real, positive)
left = sum((pi/2, pi) .* w)
right = sum((pi, (1-pi)/2) .* w)

prob_simp = solve(left-right,pi)[1]
prob = max(min(prob_simp,1),0)
print(prob)

@syms y[1:2]
profit = (1-(1-prob)^2)*(y[1]-w[1]) # (1 - (1 - Max(0, Min(1, -w₂/(w₁ - 3*w₂))))^2)*(-w₁ + y₁)

using Symbolics
@variables pi w[1:2]
left = sum((pi/2, pi) .* w)
right = sum((pi, (1-pi)/2) .* w)

prob_simp = Symbolics.solve_for(left - right ~ 0, pi)
prob = max(min(prob_simp,1),0)
print(prob)

@variables y[1:2]
profit = (1-(1-prob)^2)*(y[1]-w[1]) 

```

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<div class="post-metadata">

**Author:** ![shashi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shashi/32/1824_2.png) [@shashi](https://discourse.julialang.org/u/shashi)\
**Post date:** [May 4, 2021, 11:09pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/8 "2021-05-04T23:09:59Z")

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Oh it works if you call `Symbolics.expand` on the result… @YingboMa take note

```julia
using Symbolics

julia> @variables w1,w2,pi
3-element Vector{Num}:
 w1
 w2
 pi

julia> left = pi*(w1/2)+(1-pi)*w1
w1*(1 - pi) + 0.5pi*w1

julia> right=pi*w2+(1-pi)*w2/2
pi*w2 + 0.5w2*(1 - pi)

julia> Symbolics.expand(Symbolics.solve_for([right-left ~ 0], [pi])[1])
0.5w2*((-0.5w1 - (0.5w2))^-1) - (w1*((-0.5w1 - (0.5w2))^-1))

```

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<div class="post-metadata">

**Author:** ![jlperla](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jlperla/32/34332_2.png) [@jlperla](https://discourse.julialang.org/u/jlperla)\
**Post date:** [May 4, 2021, 11:53pm UTC](https://discourse.julialang.org/t/porting-challenge-for-mtk-symbolics/60530/9 "2021-05-04T23:53:27Z")

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Thanks. What about the `diff` and then solve thing? How to do that with symbolics/mtk and have it simplify correctly?