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searching for System of polynomial equations 22 found (44 total)

alternate case: system of polynomial equations

Approximation property (ring theory) (206 words) [view diff] exact match in snippet view article

approximation property with respect to an ideal I if each finite system of polynomial equations with coefficients in A has a solution in A if and only if it

Tsen rank (560 words) [view diff] exact match in snippet view article find links to article

the Tsen rank of a field describes conditions under which a system of polynomial equations must have a solution in the field. The concept is named for

Jade Mirror of the Four Unknowns (2,089 words) [view diff] exact match in snippet view article find links to article

He showed how to convert a problem stated verbally into a system of polynomial equations (up to the 14th order), by using up to four unknowns: 天 Heaven

Chevalley–Warning theorem (979 words) [view diff] exact match in snippet view article find links to article

theorems are statements about the solutions of the following system of polynomial equations f j ( x 1 , … , x n ) = 0 for j = 1 , … , r . {\displaystyle

Elimination theory (660 words) [view diff] exact match in snippet view article find links to article

considered to belong to elimination theory, as it asserts that a system of polynomial equations does not have any solution if and only if one may eliminate

Comparison of topologies (995 words) [view diff] exact match in snippet view article find links to article

closed if and only if it consists of all solutions to some system of polynomial equations. Since any such V also is a closed set in the ordinary sense

Artin approximation theorem (502 words) [view diff] exact match in snippet view article find links to article

y ) = 0 {\displaystyle f(\mathbf {x} ,\mathbf {y} )=0} be a system of polynomial equations in k [ x , y ] {\displaystyle k[\mathbf {x} ,\mathbf {y} ]}

Zhu Shijie (692 words) [view diff] exact match in snippet view article find links to article

unknowns. He shows how to convert a problem stated verbally into a system of polynomial equations (up to 14th order), by using up to four unknowns: 天 Heaven,

Triangular decomposition (1,610 words) [view diff] exact match in snippet view article find links to article

the corresponding polynomial ring. For F ⊂ R, regarded as a system of polynomial equations, there are two notions of a triangular decomposition over the

Lenore Blum (1,740 words) [view diff] exact match in snippet view article find links to article

any field F, the problem of deciding whether or not a finite system of polynomial equations over F has a common zero is NP-complete over F. (F could be

Hidden Field Equations (2,622 words) [view diff] exact match in snippet view article find links to article

is to use fast algorithm to compute a Gröbner basis of the system of polynomial equations. Faugère broke the HFE challenge 1 in 96 hours in 2002, and

Inequality (mathematics) (3,343 words) [view diff] exact match in snippet view article

decomposition is an algorithm that allows testing whether a system of polynomial equations and inequalities has solutions, and, if solutions exist, describing

Affine variety (4,293 words) [view diff] exact match in snippet view article find links to article

the set of solutions in an algebraically closed field k of a system of polynomial equations with coefficients in k. More precisely, if f 1 , … , f m {\displaystyle

List of Chinese discoveries (5,362 words) [view diff] exact match in snippet view article find links to article

rank: A Tsen rank of a field describes conditions under which a system of polynomial equations must have a solution in the field. It was introduced by mathematician

3D reconstruction from multiple images (3,002 words) [view diff] exact match in snippet view article find links to article

we can obtain the internal parameters of the camera using a system of polynomial equations due to Kruppa, which are derived from a geometric interpretation

Existential Closedness conjecture (1,221 words) [view diff] exact match in snippet view article find links to article

settings) has been proven assuming dominant projection: any system of polynomial equations in the variables z 1 , . . . , z n {\displaystyle z_{1},...

Number theory (12,176 words) [view diff] exact match in snippet view article find links to article

where the task is invariably to find rational solutions to a system of polynomial equations, usually of the form f ( x , y ) = z 2 {\displaystyle f(x,y)=z^{2}}

Cayley–Menger determinant (4,617 words) [view diff] exact match in snippet view article find links to article

the dimension d {\displaystyle d} is fixed, we can solve a system of polynomial equations, one for each inner product entry of Γ {\displaystyle \Gamma

Steven Sperber (1,781 words) [view diff] exact match in snippet view article find links to article

solutions in a finite field of characteristics p of a finite system of polynomial equations defined over such a field. These results were a refinement and

Morphism of schemes (5,034 words) [view diff] exact match in snippet view article find links to article

of X. This notion generalizes the notion of solutions to a system of polynomial equations in classical algebraic geometry. Indeed, let X = Spec(A) with

Steinitz's theorem (5,973 words) [view diff] exact match in snippet view article find links to article

formulated in terms of finding real variables that satisfy a given system of polynomial equations and inequalities. For the algorithmic Steinitz problem, the

Emmy Noether (15,260 words) [view diff] exact match in snippet view article find links to article

is concerned with eliminating one or more variables from a system of polynomial equations, often by the method of resultants. For illustration, a system