CODEWITHSUNDEEP
matlabsymbolic-mathsimplification
dsa42
dsa42

Reputation: 55

Symbolic Algebraic Simplifier

I'm trying to solve this equation for x (or y). Is there some way to do it in Matlab? The "simplify" function (even with "steps",100,"All", true) doesn't do it.

-k+Sqrt[x^2+y^2]+Sqrt[(x-ax)^2+y^2]+Sqrt[(x-bx)^2+(y-by)^2]

Upvotes: 1

Views: 48

Answers (1)

dxiv
dxiv

Reputation: 17638

A symbolic solution does not exist in the general case, because the problem amounts to solving an 8th degree algebraic equation.

Defining the points M(x,y), O(0,0), A(ax,0) and B(bx,by) in the plane, the equation can be written as MO + MA + MB = k. The solution set M is the locus of points with constant sum of distances to 3 fixed points. This is called a 3-ellipse which is a curve of algebraic degree 2^3 = 8 in the general case.

If F is the Fermat point of triangle OAB and f = FO + FA + FB, then no solutions exist for k < f. More material and links related to 3-ellipses can be found on this multiellipse page.

Upvotes: 1

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