laurpoly
(To be removed) Laurent polynomials constructor
laurpoly
will be removed in a future release. Use laurentPolynomial
instead. For more information, see Compatibility Considerations.
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.