A method for converting a polynomial expression to a data structure for symbolic computation. One or more variables in the polynomial expression may be determined. The variables may be stored in a first array.
Representation of Polynomial In subject area: Computer Science The 'Representation of Polynomial' refers to a unique way of expressing Boolean and vectorial functions as univariate polynomials over a field, where each function can be represented by a polynomial form of degree not exceeding 2n - 1....
In the single-input, single-output case, the issue of common factors in the scalar numerator and denominator polynomials of G(s) arises at this point. The utility of the polynomial fraction representation begins to emerge from the corresponding concept in the matrix case. Definition 4.2.3 An ...
These can be easily converted to rectangular coordinates, making the Zernike polynomial representation useful for computing the wavefront aberrations. Zernike polynomials can be expressed (referenced) using two indices, one representing the highest order of the radial polynomial term (n), and the other...
The expanded metarule format is Louise's internal representation of metarules, in a form that is more convenient for meta-interpretation. Expanded metarules are encapsulated and have an encapsulation atom in their head, holding the metarule identifier and the existentially quantified variables in the...
Intherecursiverepresentationpolynomialsarerepresentedasunivariatepolynomialsinamainvariable withcoefficientsthatareunivariatepolynomialsinthenextvariable,andsoon.Forexample, f=8x 3 + (9z)y 3 +(−6z+5)y 2x+(−4z 2 )y 3 . Polynomialarithmeticusesunivariatealgorithms(inx)withcoefficientarithmetic(inZ...
It employs the data-driven generalization of polynomial chaos expansion theory known as arbitrary polynomial chaos (aPC: Oladyshkin S. and Nowak W., 2012 and 2018) to construct a corresponding multi-layer representation of a Deep Artificial Neural Network. Doing so, we generalize the convent...
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where Chebyshev polynomials provide a compact representation of the function. In solving delay differential equations, PMCMs use Chebyshev or Legendre polynomials to transform the equation into an algebraic system. Lastly, orthogonal polynomials are applied in least squares fitting for noisy data, providin...
, P). All coefficients obtained via optimization constitute a PCF representation, a sequential point location-dependent global representation of time series. Normally, the complex structure of time series, which has a large amount of abrupt changes along the observed points, would require the higher...