asc-community / AngouriMath

New open-source cross-platform symbolic algebra library for C# and F#. Can be used for both production and research purposes.
https://am.angouri.org
MIT License
782 stars 74 forks source link

Support parametric solutions #212

Open Happypig375 opened 4 years ago

Happypig375 commented 4 years ago

2x-4y=12 => x=6+2t and y=t

Happypig375 commented 4 years ago

Especially for EquationSystems where there are infinite solutions.

MomoDeve commented 4 years ago

x = (12 + 4y) / 2 = 6 + 2y y = t => x = 6 + 2t whats the point? Its the same as solving the system for some variable and then replacing it by a new one Please find a better example, I didn't get it

Happypig375 commented 4 years ago

The parameters are the inputs to get solutions. They can be any number, which differentiates them from the original variables in the equation system, where there may be non-free variables.

Happypig375 commented 4 years ago

⎧  𝑥₁ + 2𝑥₂ + 4𝑥₃ +  𝑥₄ -  𝑥₅ =  1
⎨ 2𝑥₁ + 4𝑥₂ + 8𝑥₃ + 3𝑥₄ - 4𝑥₅ =  2
⎩  𝑥₁ + 3𝑥₂ + 7𝑥₃       + 3𝑥₅ = -2
𝑥₁ = 2𝑠 + 3𝑡 + 7
𝑥₂ = -3𝑠 - 2𝑡 - 3
𝑥₃ = 𝑠
𝑥₄ = 2𝑡
𝑥₅ = 𝑡