# Polynomials Composition (G Dataflow)

Computes the composition of two polynomials.

## p(x)

Coefficients, in ascending order of power, of the first polynomial.

This input accepts the following data types:

• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers

## q(x)

Coefficients, in ascending order of power, of the second polynomial.

This input accepts the following data types:

• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers

## 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

## threshold

Level at which the node removes the trailing elements from the composition of two polynomials.

The node removes the trailing elements whose absolute values or relative values are less than or equal to threshold. If all the elements in the composition of two polynomials are less than or equal to threshold, p(q(x)) returns a one-element array.

Default: 0

## threshold type

Method to this node uses to remove the trailing elements from the composition of two polynomials.

Name Value Description
Absolute Value 0 Removes the trailing elements whose absolute values are less than or equal to threshold.
Relative Value 1 Removes the trailing elements whose absolute values are less than or equal to threshold * |a|, where a is the coefficient which has the maximum absolute value in the composition of two polynomials.

Default: Absolute Value

## p(q(x))

Coefficients, in ascending order of power, for the polynomial that results from composing two polynomials.

## 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 Composing Polynomials

The following polynomial defines the nth order polynomial described by the (n + 1) element array P[0...n]:

$\underset{i-0}{\overset{n}{\sum }}P\left[i\right]{x}^{i}$

The following polynomial defines the nth order polynomial described by the (m + 1) element array Q[0...m]:

$\underset{j-0}{\overset{m}{\sum }}P\left[j\right]{x}^{j}$

This node uses the following equation to compose P(x) and Q(x):

$P\left(Q\left(x\right)\right)=P\left[n\right]{\left(Q\left[m\right]{x}^{m}+Q\left[m-1\right]{x}^{m-1}+\dots +Q\left[1\right]x+Q\left[0\right]\right)}^{n}+P\left[n-1\right]{\left(Q\left[m\right]{x}^{m}+Q\left[m-1\right]{x}^{m-1}+\dots +Q\left[1\right]x+Q\left[0\right]\right)}^{n-1}+\dots +P\left[1\right]\left(Q\left[m\right]{x}^{m}+Q\left[m-1\right]{x}^{m-1}+\dots +Q\left[1\right]+Q\left[0\right]\right)+P\left[0\right]$

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices