plus

Laurent polynomial or Laurent matrix addition

Since R2021b

Syntax

Q = plus(A,B)

Q = A + B

Description

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

Note

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

Q = A + B is equivalent to Q = plus(A,B).

Examples

Laurent Polynomial Addition

Create two Laurent polynomials:

• $$a(z)=z^2+2z+3+5z^{-1}+8z^{-2}+13z^{-3}$$

• $$b(z)=8z+4+2z^{-1}+z^{-2}$$

a = laurentPolynomial(Coefficients=[1 2 3 5 8 13],MaxOrder=2);
b = laurentPolynomial(Coefficients=[8 4 2 1],MaxOrder=1);

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

c = a+b

c = 
  laurentPolynomial with properties:

    Coefficients: [1 10 7 7 9 13]
        MaxOrder: 2

Add $$a(z)$$ and the negative of $$b(z)$$.

d = plus(a,-b)

d = 
  laurentPolynomial with properties:

    Coefficients: [1 -6 -1 3 7 13]
        MaxOrder: 2

Laurent Matrix Addition

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

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

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

Sum the matrices.

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

ans = 
  laurentPolynomial with properties:

    Coefficients: [1 1]
        MaxOrder: 1

lmat.Elements{1,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: 3
        MaxOrder: 0

lmat.Elements{2,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: 4
        MaxOrder: 0

lmat.Elements{2,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: [1 0 0 -1]
        MaxOrder: 2

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 — Sum

laurentPolynomial object | laurentMatrix object

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

Extended Capabilities

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

Version History

Introduced in R2021b