Laurent polynomials constructor
P = laurpoly(C,d)
P = laurpoly(C,'dmin',d)
P = laurpoly(C,'dmax',d)
P = laurpoly(C,d)
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).
% 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)
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.