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Scilab Help >> Polynomials > residu

# residu

residue

### Syntax

`[V]=residu(P,Q1,Q2)`

### Arguments

P, Q1, Q2

polynomials or matrix polynomials with real or complex coefficients.

### Description

`V=residu(P,Q1,Q2)` returns the matrix `V` such that `V(i,j)` is the sum of the residues of the rational fraction `P(i,j)/(Q1(i,j)*Q2(i,j))` calculated at the zeros of `Q1(i,j)`.

`Q1(i,j)` and `Q2(i,j)` must not have any common root.

### Examples

```s=poly(0,'s');
H=[s/(s+1)^2,1/(s+2)];N=numer(H);D=denom(H);
w=residu(N.*horner(N,-s),D,horner(D,-s));  //N(s) N(-s) / D(s) D(-s)
sqrt(sum(w))  //This is H2 norm
h2norm(tf2ss(H))

p=(s-1)*(s+1)*(s+2)*(s+10);a=(s-5)*(s-1)*(s*s)*((s+1/2)**2);
b=(s-3)*(s+2/5)*(s+3);
residu(p,a,b)+531863/4410    //Exact
z=poly(0,'z');a=z^3+0.7*z^2+0.5*z-0.3;b=z^3+0.3*z^2+0.2*z+0.1;
atild=gtild(a,'d');btild=gtild(b,'d');
residu(b*btild,z*a,atild)-2.9488038   //Exact
a=a+0*%i;b=b+0*%i;
real(residu(b*btild,z*a,atild)-2.9488038) //Complex case```

### See also

• pfss — partial fraction decomposition
• bdiag — block diagonalization, generalized eigenvectors
• roots — roots of polynomials
• poly — polynomial definition
• gtild — tilde operation
 Report an issue << rational Polynomials roots >>

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