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2017-05-12 01:50:21 +0100 commented answer solve with many variables

thanks you for your time may be i didnt understand you'r answer so we start with my matrix k which contains many variables im asking if i can compute all eigenvalues of this matrix such that if we suppose that x is an eigenvalue of this matrix i want to find some function f such that x=f(a,b,c,s1,..s6) and i need that this function must be sumbolic exxample

let A=matrix([[a,0];[0 b]]) f(a,b)=A.charpoly()=(a-x)*(b-x) f(a,b)=0 thats mean x=a or x=b what is a simple example but with my metrics I can't get some results in this forme

2017-05-11 12:04:33 +0100 asked a question solve with many variables

hi please i have a problem i have a MATRIX contains many variables, and i want to find the eigenvalues of this matrix in function of this variables i let you my matrix here and my code

x,a,b,c,s1,s2,s3,s4,s5,s6=var('x a b c s1 s2 s3 s4 s5 s6')
k=matrix([[-3*a-b+c*s1,a,a,0,a,0],
[a,-2*a-b+c*s2,a,0,0,0],
[a,a,-4*a-b+c*s3,a,a,0],
[0,0,a,-2*a-b+c*s4,a,0],
[a,0,a,a,-4*a-b+c*s5,a],
[0,0,0,0,a,-a-b+c*s6]]
)
B=matrix(k- x*matrix.identity(6))
eq(a,b,c,s1,s2,s3,s4,s5,s6)=det(B)
solve(eq==0,x)

but i can get the solution but if i give to the variable c=0 or b=0 i get the solution so please can you help me