Documentation

# laurpoly

Laurent polynomials constructor

## Syntax

```P = laurpoly(C,d) P = laurpoly(C,'dmin',d) P = laurpoly(C,'dmax',d) P = laurpoly(C,d) ```

## Description

`P = laurpoly(C,d)` returns a Laurent polynomial object. `C` is a vector whose elements are the coefficients of the polynomial `P` and `d` is the highest degree of the monomials of `P`.

If `m` is the length of the vector `C`, `P` represents the following Laurent polynomial:

```P(z) = C(1)*z^d + C(2)*z^(d-1) + ... + C(m)*z^(d-m+1) ```

`P = laurpoly(C,'dmin',d)` specifies the lowest degree instead of the highest degree of monomials of `P`. The corresponding output `P` represents the following Laurent polynomial:

```P(z) = C(1)*z^(d+m-1) + ... + C(m-1)*z^(d+1) + C(m)*z^d ```

`P = laurpoly(C,'dmax',d)` is equivalent to `P = laurpoly(C,d)`.

## Examples

```% Define Laurent polynomials. P = laurpoly([1:3],2); P = laurpoly([1:3],'dmax',2) P(z) = + z^(+2) + 2*z^(+1) + 3 P = laurpoly([1:3],'dmin',2) P(z) = + z^(+4) + 2*z^(+3) + 3*z^(+2) % Calculus on Laurent polynomials. Z = laurpoly(1,1) Z(z) = z^(+1) Q = Z*P Q(z) = + z^(+5) + 2*z^(+4) + 3*z^(+3) R = Z^1 - Z^-1 R(z) = + z^(+1) - z^(-1) ```

## References

Strang, G.; T. Nguyen (1996), Wavelets and filter banks, Wellesley-Cambridge Press.

Sweldens, W. (1998), “The Lifting Scheme: a Construction of Second Generation of Wavelets,” SIAM J. Math. Anal., 29 (2), pp. 511–546. 