Examples of using Polynomials in English and their translations into Italian
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Known as the fundamental theorem of symmetric polynomials states that any symmetric polynomial in n variables can be given by a polynomial expression in terms of these elementary symmetric polynomials. .
You can plot any linear combination of the Zernike polynomials, multiplied by the computed Zernike coefficients.
This is just as general as considering polynomials with rational number coefficients because one can multiply by the denominators of rational coefficients to get integer coefficients.
There exist tables in which the coefficients of the polynomials g(p) are reported in octal form.
The set of all integer coefficient polynomials is the union of the set of all such linear equations,
the product rules become even more useful once we start doing derivatives of expressions other than polynomials.
The set of all polynomials with real coefficients which are divisible by the polynomial x2+ 1 is an ideal in the ring of all polynomials.
also known as the Newton-Girard formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials. .
the University of Genova, Italy, used to compute with numbers and polynomials.
denominator are both polynomials.
Thus the cardinality of the set of roots to all integer-coefficient polynomials is at most.
To prove the above assertion let us first consider the set of all polynomials with integer coefficients.
Orthogonal polynomials on the real line===== Positive Hankel matrices and the Hamburger moment problems Orthogonal polynomials on the real line Tridiagonal model of positive Hankel operators Relation between Hankel and Toeplitz matrices===Let formula_14 be the reflection matrix of order formula_15.
Later he introduced the characteristic varieties of the fundamental groups, providing a multivariable extension of Alexander polynomials, and applied these methods to the study of homotopy groups of the complements to hypersurfaces in projective spaces
Note that it is only"possible" that high order polynomials will be lumpy; they could also be smooth, but there is no guarantee of this, unlike with low order polynomial curves.
The degree of the composition of two non-constant polynomials P{\displaystyle P}
The degree of the polynomial curve being higher than needed for an exact fit is undesirable for all the reasons listed previously for high order polynomials, but also leads to a case where there are an infinite number of solutions.
Examples of infinite periodic groups include the additive group of the ring of polynomials over a finite field,
They are orthogonal polynomials with respect to an inner product⟨ f, g⟩∫ 0∞ f( x) g( x)
so now this kind of has the shape of polynomials that hopefully you're used to factoring a little bit.