# residue (MathScript RT Module Function)

LabVIEW 2012 MathScript RT模块帮助

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Owning Class: polynomials

Requires: MathScript RT Module

## Syntax

[b, a] = residue(r, p, k)

[r2, p2, k2] = residue(b2, a2)

## Description

Computes the partial fraction expansion of two polynomials or transforms a given partial fraction expansion into the original polynomial representation.

Details

Examples

## Inputs

Name Description
r Specifies the residues of the partial fraction expansion. r is a real or complex vector.
p Specifies the poles of the partial fraction expansion. p is a real or complex vector.
k Specifies the coefficients in descending order of power of the quotient polynomial of a and b.
b2 Specifies the coefficients in descending order of power of the numerator polynomial.
a2 Specifies the coefficients in descending order of power of the denominator polynomial.

## Outputs

Name Description
b Returns the coefficients in descending order of power of the numerator polynomial.
a Returns the coefficients in descending order of power of the denominator polynomial.
r2 Returns the residues of the partial fraction expansion. r2 is a real or complex vector.
p2 Returns the poles of the partial fraction expansion. p2 is a real or complex vector.
k2 Returns the coefficients in descending order of power of the quotient polynomial of a2 and b2.

## Details

LabVIEW computes a and b using the following equation if no multiple roots exist:
bs/as = (r1/(s-p1)) + (r2/(s-p2)) + ... + (rn/(s-pn)) + ks
where s is the power and n is the number of elements in the partial fraction expansion.

If multiple poles exist, that is, if pj = ... = pj+m-1 where j is the element index and m is the multiple, then the partial fraction expansion includes the following terms: (rj/(s-pj)) + (rj+1/(s-pj))2 + ... + (rj+m-1/(s-pj))m.

The following table lists the support characteristics of this function.

 Supported in the LabVIEW Run-Time Engine Yes Supported on RT targets Yes Suitable for bounded execution times on RT Not characterized

## Examples

B = [1, 2, 3, 4]
A = [1, 1]
[R, P, K] = residue(B, A)

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