mtimes

R2026b

Laurent polynomial or Laurent matrix multiplication

Syntax

Q = mtimes(A,B)

Q = A * B

Description

Q = mtimes(A,B) returns the product of the pair of Laurent polynomials or Laurent matrices A and B.

Note

The laurentPolynomial and laurentMatrix objects have their own versions of mtimes. The input data type determines which version is executed.

Q = A * B is equivalent to Q = mtimes(A,B).

Examples

Laurent Polynomial Multiplication

Create three Laurent polynomials:

• $$a(z)=4z+z^{-1}$$

• $$b(z)=2z^2+3z+z^{-1}$$

• $$c(z)=z^3+3z^2+5z+7$$

a = laurentPolynomial(Coefficients=[4 0 1],MaxOrder=1);
b = laurentPolynomial(Coefficients=[2 3 0 1],MaxOrder=2);
c = laurentPolynomial(Coefficients=[1 3 5 7],MaxOrder=3);

Multiply $$a(z)$$ and $$b(z)$$.

ab = mtimes(a,b)

ab = 
  laurentPolynomial with properties:

    Coefficients: [8 12 2 7 0 1]
        MaxOrder: 3

Compute $$a(z)c(z)-b(z)$$.

d = a*c-b

d = 
  laurentPolynomial with properties:

    Coefficients: [4 12 19 28 5 6]
        MaxOrder: 4

Laurent Matrix Multiplication

Create two Laurent polynomials:

• $$a(z)=z+1$$

• $$b(z)=z^2-z^{-1}$$

lpA = laurentPolynomial(Coefficients=[1 1],MaxOrder=1);
lpB = laurentPolynomial(Coefficients=[1 0 0 -1],MaxOrder=2);

Create two Laurent matrices:

• lmatA = $\left[\begin{array}{cc}a\left(z\right)& 1\\ 1& 0\end{array}\right]$

• lmatB = $\left[\begin{array}{cc}0& 2\\ 3& b\left(z\right)\end{array}\right]$

lmatA = laurentMatrix(Elements={lpA,1;1,0});
lmatB = laurentMatrix(Elements={0,2;3,lpB});

Multiply the matrices.

lmat = lmatA*lmatB;
lmat.Elements{1,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: 3
        MaxOrder: 0

lmat.Elements{1,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: [1 2 2 -1]
        MaxOrder: 2

lmat.Elements{2,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: 0
        MaxOrder: 0

lmat.Elements{2,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: 2
        MaxOrder: 0

Input Arguments

A — Laurent polynomial or Laurent matrix

laurentPolynomial object | laurentMatrix object

Laurent polynomial or Laurent matrix, specified as a laurentPolynomial object or a laurentMatrix object, respectively.

B — Laurent polynomial or Laurent matrix

laurentPolynomial object | laurentMatrix object

Laurent polynomial or Laurent matrix, specified as a laurentPolynomial object or a laurentMatrix object, respectively.

Output Arguments

Q — Product

laurentPolynomial object | laurentMatrix object

Product of two Laurent polynomials or two Laurent matrices, returned as a laurentPolynomial object or a laurentMatrix object.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The mtimes function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2021b

R2026b: Use thread-based environments

You can use mtimes in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.