# Create Polynomial from PFE (G Dataflow)

Uses partial fraction expansion (PFE) to reconstruct a rational polynomial.

## polynomial

Coefficients, in ascending order of power, for the quotient polynomial.

Use the Partial Fraction Expansion node to obtain polynomial.

## poles

Unique roots of the denominator polynomial.

Use the Partial Fraction Expansion node to obtain poles.

## residues

Numerators of the partial fractions that result for each pole.

Use the Partial Fraction Expansion node to obtain residues.

## multiplicity

Number of times each unique root in the denominator polynomial occurs.

Use the Partial Fraction Expansion node to obtain multiplicity. If multiplicity is empty, this node calculates the number of nonzero elements in each row of residues and regards that number as the multiplicity of the corresponding pole.

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## option

Method this node uses to handle the co-factors of the numerator and denominator polynomials.

Name Value Description
Cancel Co-factors 0 Computes the greatest common denominator (GCD) for the numerator and denominator polynomials before returning the output data.
Reserve Co-factors 1 Keeps the numerator and denominator polynomial unchanged and returns the output data directly.

Default: Cancel Co-factors

## numerator

Numerator coefficients, in ascending order of power, of the rational polynomial.

## denominator

Denominator coefficients, in ascending order of power, of the rational polynomial.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Reconstructing a Rational Polynomial Using Partial Fraction Expansion

The node uses the following equation to reconstruct a rational polynomial:

$\frac{P\left(x\right)}{Q\left(x\right)}=A\left(x\right)+\sum _{k=1}^{{m}_{0}}\frac{{a}_{0k}}{{\left(x-{r}_{0}\right)}^{k}}+\sum _{k=1}^{{m}_{1}}\frac{{a}_{1k}}{{\left(x-{r}_{1}\right)}^{k}}+\sum _{k=1}^{{m}_{2}}\frac{{a}_{2k}}{{\left(x-{r}_{2}\right)}^{k}}+\dots +\sum _{k=1}^{{m}_{n-1}}\frac{{a}_{\left(n-1\right)k}}{{\left(x-{r}_{n-1}\right)}^{k}}$

where

• P(x) is the numerator polynomial
• Q(x) is the denominator polynomial
• A(x) is the quotient polynomial
• n is the number of unique roots in the denominator polynomial
• r i is the i th number of unique roots in the denominator polynomial
• m i is the number of times each unique root in the denominator polynomial occurs
• a i k is the (i, k)th numerator of the partial fractions that result for each pole

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application