Originally, Galois used permutation groups to describe how the various roots of a given polynomial equation are related to each other.
42.
Khi is designed to reflect arterial resistance; compliance is a multivariate polynomial equation that continuously quantifies arterial compliance and vascular resistance.
43.
This is defined in analogy with the classical Zariski topology, where closed sets in affine space are those defined by polynomial equations.
44.
The concept can also be applied to more general systems of equations, such as systems of polynomial equations or partial differential equations.
45.
Resultants were introduced for solving systems of polynomial equations and provides the oldest proof that there exist algorithms for solving such systems.
46.
A Diophantine equation is a ( usually multivariate ) polynomial equation with integer coefficients for which one is interested in the integer solutions.
47.
For a set of polynomial equations in several unknowns, there are algorithms to decide whether they have a finite number of complex solutions.
48.
The elements of a number field are usually represented as polynomials in a generator of the field which satisfies some univariate polynomial equation.
49.
The search for roots of Galois ( 1832 ) linked polynomial equations to group theory giving rise to the field of Galois theory.
50.
A proof exists to demonstrate that any Euclidean number is an algebraic number a number that is the solution to some polynomial equation.
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