Newton polytope, the Glossary
In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial.[1]
Table of Contents
8 relations: Convex hull, Gröbner basis, Hilbert scheme, Integral polytope, Minkowski addition, Polynomial, Toric variety, Tropical geometry.
- Minkowski spacetime
- Polynomial functions
Convex hull
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it.
See Newton polytope and Convex hull
Gröbner basis
In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring over a field. Newton polytope and Gröbner basis are algebraic geometry.
See Newton polytope and Gröbner basis
Hilbert scheme
In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. Newton polytope and Hilbert scheme are algebraic geometry.
See Newton polytope and Hilbert scheme
Integral polytope
In geometry and polyhedral combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. Newton polytope and integral polytope are polytopes.
See Newton polytope and Integral polytope
Minkowski addition
In geometry, the Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B: The Minkowski difference (also Minkowski subtraction, Minkowski decomposition, or geometric difference) is the corresponding inverse, where (A - B) produces a set that could be summed with B to recover A.
See Newton polytope and Minkowski addition
Polynomial
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.
See Newton polytope and Polynomial
Toric variety
In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety. Newton polytope and toric variety are algebraic geometry.
See Newton polytope and Toric variety
Tropical geometry
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition: So for example, the classical polynomial x^3 + 2xy + y^4 would become \min\. Newton polytope and tropical geometry are algebraic geometry.
See Newton polytope and Tropical geometry
See also
Minkowski spacetime
- De Sitter space
- Electromagnetic tensor
- Four-vector
- Four-vectors
- Hyperbolic orthogonality
- Hyperbolic quaternion
- Hyperboloid model
- Lorentz factor
- Lorentz scalar
- Milne model
- Minkowski space
- Newton polytope
- Proper acceleration
- Proper time
- Proper velocity
- Spacetime algebra
- Squeeze mapping
- World line
Polynomial functions
- Constant function
- Cubic function
- Linear function
- Linear function (calculus)
- Newton polytope
- Quadratic function
- Quartic function
- Quintic function
- Ring of polynomial functions