definition
(strict sense) An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as a_n x^n + a_{n-1}x^{n-1} + ... + a_0 x^0.
definition
A taxonomic designation (such as of a subspecies) consisting of more than two terms.
It is practically identical with that of finding the greatest common measure of two polynomials.
Lower order polynomials are trivial to solve while higher order polynomials require iterative algorithms to solve them.
Thus we don't ever need to compute the Bezier polynomials, we simply depth reduce the control points recursively until d =0.
These methods are based on a discontinuous Galerkin approach, where the unknowns are approximated by completely discontinuous piecewise polynomials.
To calculate the greatest common divisor of two integers and of two polynomials over a field.
Here, orthogonal polynomials play an important role in the analysis.
I shall discuss recent developments in the ' transfer matrix ' method for calculating chromatic polynomials of families of graphs.
Clearly writing a class hierarchy starting with multivariate polynomials in order to derive integers makes no sense!
Examples of polynomials which are not solvable by radicals.
It is the resultant of k polynomials each of degree m-I, and thus contains the coefficients of each form to the degree (m-I)'-1; hence the total degrees in the coefficients of the k forms is, by addition, k (m - 1) k - 1; it may further be shown that the weight of each term of the resultant is constant and equal to m(m-I) - (Salmon, l.c. p. loo).
Discriminants.-The discriminant of a homogeneous polynomial in k variables is the resultant of the k polynomials formed by differentiations in regard to each of the variables.
Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.
Case of Three Variables.-In the next place we consider the resultants of three homogeneous polynomials in three variables.
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