euclid
Syntax
Description
Examples
Euclidean Division of Laurent Polynomials
Create two Laurent polynomials:
cfa = [1 3 5 7]; cfb = [1 2]; lpA = laurentPolynomial(Coefficients=cfa,MaxOrder=2); lpB = laurentPolynomial(Coefficients=cfb);
Perform Euclidean division of by . Use the helper function helperPrintLaurent
to print the quotient and remainder polynomials of each Euclidean division.
dec = euclid(lpA,lpB); numFac = size(dec,1); for k=1:numFac q = helperPrintLaurent(dec(k,1).LP); r = helperPrintLaurent(dec(k,2).LP); fprintf('Euclidean Division #%d\n',k) fprintf('Quotient: %s\n',q) fprintf('Remainder: %s\n \n',r) end
Euclidean Division #1
Quotient: z^(2) + z + 3
Remainder: + z^(-1)
Euclidean Division #2
Quotient: z^(2) + z + 3.5
Remainder: - 0.5
Euclidean Division #3
Quotient: z^(2) + 0.75*z + 3.5
Remainder: + 0.25*z
Euclidean Division #4
Quotient: 1.125*z^(2) + 0.75*z + 3.5
Remainder: - 0.125*z^(2)
For each Euclidean division, confirm that , where and are the quotient and remainder polynomials, respectively, of the ith division.
for k=1:numFac q = dec(k,1).LP; r = dec(k,2).LP; areEqual = (lpA==lpB*q+r); fprintf('Euclidean Division #%d: %d\n',k,areEqual) end
Euclidean Division #1: 1 Euclidean Division #2: 1 Euclidean Division #3: 1 Euclidean Division #4: 1
Input Arguments
A
— Laurent polynomial
laurentPolynomial
object
Laurent polynomial, specified as a laurentPolynomial
object.
B
— Laurent polynomial
laurentPolynomial
object
Laurent polynomial, specified as a laurentPolynomial
object.
Output Arguments
dec
— Euclidean algorithm factors
structure array
Euclidean algorithm factors, returned as a N-by-2 structure
array, where N ≤ 4 is the number of decompositions. The
ith row of dec
contains one Euclidean division
of A
by B
:
A = B*(dec(i,1).LP) +
dec(i,2).LP
where
dec(i,1).LP
is the Laurent polynomial corresponding to the quotient.dec(i,2).LP
is the Laurent polynomial corresponding to the remainder.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced in R2021b
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