Roots of a polynomial with variables

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Lewis Fer
Lewis Fer on 15 Jun 2021
Commented: Lewis Fer on 16 Jun 2021
For some problems, we have to to study some notions of stablility and zero polynomials in two variables, my que'stion how we can find the roots or zero polynomials in two variables. for example:
P(x,y)=3*xy -5y^2+7*x^2y
or a nother polynom

Answers (2)

Sulaymon Eshkabilov
Sulaymon Eshkabilov on 15 Jun 2021
One of the viable ways to solve such polynomial type equations is to setp up the solution space within which you are seeking the roots to compute and solve them using fzero(). E.g.:
x=linspace(-2,2): % Choose the necessary solution space
for t=1:100
EQ= @(y)(3*x(t)*y-5*y.^2+7*(x(t)^2)*y);
y_roots = fzero(EQ,0);
end
  1 Comment
Lewis Fer
Lewis Fer on 15 Jun 2021
but this method in reality doesn't making a difference to search and find th pole of some matrices like transfer function in two dimensional case

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Paul
Paul on 15 Jun 2021
Don't know the scope of the actual problems of interest, but for the two examples in the question:
syms x y
sol = solve(3*x*y - 5*y^2 + 7*x^2*y == 0,[x y],'ReturnConditions',true);
[sol.x sol.y sol.conditions]
ans = 
syms z1 z2
sol = solve(1 - z1*z2 - 1/2*z1^2 - 1/2*z2^2 + z1^2*z2^2 == 0,[z1 z2],'ReturnConditions',true);
[sol.z1 sol.z2 sol.conditions]
ans = 
  5 Comments
Lewis Fer
Lewis Fer on 16 Jun 2021
thank', Paul for your answers your idea help me for my work.

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