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determinant of a matrix of polynomials


res = determ(W)
res = determ(W, k)



square matrix of real or complex polynomials


integer (upper bound for the degree of the determinant of W)


returns the determinant of a matrix of polynomials.

res=determ(W [,k]) where k is an integer larger than the actual degree of the determinant of W.

The default value of k is the smallest power of 2 which is larger than n*max(degree(W)).

Method (Only if W size is greater than 2*2) : evaluate the determinant of W for the Fourier frequencies and apply inverse FFT to the coefficients of the determinant.


s = %s;
P = [5+3*s, 1-5*s, -4+6*s ; -3+5*s, -3*s, -9 ; 8*s, -6-2*s, 4-6*s]
--> P = [5+3*s, 1-5*s, -4+6*s ; -3+5*s, -3*s, -9 ; 8*s, -6-2*s, 4-6*s]
 P  =
  5 +3s   1 -5s   -4 +6s

  -3 +5s  -3s     -9

  8s      -6 -2s  4 -6s

--> determ(P)
 ans  =
  -330 -278s +380s² -12s³

See also

  • det — determinant of a square matrix
  • detr — determinant of a matrix of rationals
  • coffg — Co-factors of a matrix of polynomials or rationals
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Last updated:
Mon Mar 27 11:52:43 GMT 2023