This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.


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.

See Also

Introduced before R2006a

Was this topic helpful?