construct a Convolution matrix of a polynomial
ConvolutionMatrix(F, vars, degree)
ConvolutionMatrix(F, vars, degree, rtableoptions=[options])
set or list of variables
(optional) options that are passed to the Matrix constructor
The ConvolutionMatrix command returns a Matrix that represents polynomial multiplication of F by a polynomial of the given degree (total degree) when the polynomial to multiply is represented as a vector as returned by CoefficientVector.
A Sylvester matrix can be considered to be a block matrix composed of two convolution matrices and the SylvesterMatrix command calls this one.
The approximate polynomial division command Divide solves up a least squares problem on the output of this command.
f ≔ x2+y2−1;g ≔ x2+x⁢y+y+1
fg ≔ sort⁡expand⁡f⁢g,x,y
Cf ≔ ConvolutionMatrix⁡f,x,y,degree⁡g,x,y
vg ≔ PolynomialTools:-CoefficientVector⁡g,x,y
This matrix vector product computes the polynomial product
vfg ≔ `.`⁡Cf,vg
The PolynomialTools:-Approximate:-ConvolutionMatrix command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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