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Scilab Help >> Polynomials > determ

# determ

determinant of a matrix of polynomials

### Syntax

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

### Arguments

W

square matrix of real or complex polynomials

k

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

### Description

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.

### Examples

```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]
determ(P)```
```--> 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
```

• det — determinant of a square matrix
• detr — determinant of a matrix of rationals
• coffg — Co-factors of a matrix of polynomials or rationals