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Scilab help >> Polynomials > horner

# horner

polynomial/rational evaluation

### Calling Sequence

`horner(P,x)`

### Arguments

P

polynomial or rational matrix

x

array of numbers or polynomials or rationals

### Description

evaluates the polynomial or rational matrix `P = P(s)` when the variable `s` of the polynomial is replaced by `x`:

`horner(P,x)`=`P(x)`

Example (Bilinear transform): Assume `P = P(s)` is a rational matrix then the rational matrix `P((1+s)/(1-s))` is obtained by `horner(P,(1+s)/(1-s))`.

To evaluate a rational matrix at given frequencies use preferably the `freq` primitive.

### Examples

```//evaluation of a polynomial for a vector of numbers
P=poly(1:3,'x')
horner(P,[1 2 5])
horner(P,[1 2 5]+%i)

//evaluation of a rational
s=poly(0,'s');M=[s,1/s];
horner(M,1)
horner(M,%i)
horner(M,1/s)

//evaluation of a polynomial for a matrix of numbers
X= [1 2;3 4]
p=poly(1:3,'x','c')
m=horner(p, X)
1*X.^0+2*X.^1+3*X.^2```

• freq — frequency response
• repfreq — frequency response
• evstr — evaluation of expressions

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