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Laurent polynomial or Laurent matrix reflection

Since R2021b



    Q = reflect(P) returns the reflection of the Laurent polynomial or the Laurent matrix specified by P. If P is a Laurent matrix, the function reflects the matrix elements.


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


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    Create a Laurent polynomial a(z)=5z6+4z5+3z4+2z3.

    a = laurentPolynomial(Coefficients=[5 4 3 2],MaxOrder=6)
    a = 
      laurentPolynomial with properties:
        Coefficients: [5 4 3 2]
            MaxOrder: 6

    Obtain the reflection of a(z). Confirm the maximum order of the reflection is –3.

    b = reflect(a)
    b = 
      laurentPolynomial with properties:
        Coefficients: [2 3 4 5]
            MaxOrder: -3

    Create two Laurent polynomials:

    • a(z)=-z3+2z2-3z+4

    • b(z)=5z2-z-z-1+z-2

    lpA = laurentPolynomial(Coefficients=[-1 2 -3 4],MaxOrder=3);
    lpB = laurentPolynomial(Coefficients=[5 -1 0 -1 1],MaxOrder=1);

    Create the Laurent matrix [a(z)01b(z)].

    lmat = laurentMatrix(Elements={lpA,0;1,lpB});

    Obtain the reflection of the matrix. Inspect the diagonal elements of the reflection.

    lmatref = reflect(lmat);
    ans = 
      laurentPolynomial with properties:
        Coefficients: [4 -3 2 -1]
            MaxOrder: 0
    ans = 
      laurentPolynomial with properties:
        Coefficients: [1 -1 0 -1 5]
            MaxOrder: 3

    Input Arguments

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

    Output Arguments

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    Reflection of a Laurent polynomial or a Laurent matrix, returned as a laurentPolynomial object or a laurentMatrix object. The reflection of a Laurent polynomial P(z) is the Laurent polynomial Q(z) = P(1/z).

    Extended Capabilities

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

    Version History

    Introduced in R2021b

    See Also