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MONOMIAL ORDER

  • Monomial order
  • Order for the terms of a polynomial

    mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all (monic) monomials in a given polynomial

    Monomial order

    Monomial_order

  • Lexicographic order
  • Generalised alphabetical order

    number of variables, every monomial order is thus the restriction to N n {\displaystyle \mathbb {N} ^{n}} of a monomial order of Z n {\displaystyle \mathbb

    Lexicographic order

    Lexicographic_order

  • Gröbner basis
  • Mathematical construct in computer algebra

    sequence of monomials is finite. Although Gröbner basis theory does not depend on a particular choice of an admissible monomial ordering, three monomial orderings

    Gröbner basis

    Gröbner_basis

  • Monomial
  • Polynomial with only one term

    mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: A monomial, also called

    Monomial

    Monomial

  • Monomial basis
  • Basis of polynomials consisting of monomials

    consists of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an

    Monomial basis

    Monomial_basis

  • Monomial ideal
  • Ideal generated by one-term polynomials

    In abstract algebra, a monomial ideal is an ideal generated by monomials in a multivariate polynomial ring over a field. Let K {\displaystyle \mathbb

    Monomial ideal

    Monomial_ideal

  • Monic polynomial
  • Polynomial with 1 as leading coefficient

    monomial order is generally fixed. In this case, a polynomial may be said to be monic if it has 1 as its leading coefficient (in the monomial order)

    Monic polynomial

    Monic_polynomial

  • Order of operations
  • Performing order of mathematical operations

    extends to monomials; thus, sin 3x = sin(3x) and even sin ⁠1/2⁠xy = sin(⁠1/2⁠xy), but sin x + y = sin(x) + y, because x + y is not a monomial. However,

    Order of operations

    Order_of_operations

  • FGLM algorithm
  • Algorithm in computer algebra

    respect to a monomial order and a second monomial order. As its output, it returns a Gröbner basis of the ideal with respect to the second ordering. The algorithm

    FGLM algorithm

    FGLM_algorithm

  • List of order theory topics
  • Linearly ordered group Monomial order Weak order of permutations Bruhat order on a Coxeter group Incidence algebra Monotonic Pointwise order of functions Galois

    List of order theory topics

    List_of_order_theory_topics

  • Binomial (polynomial)
  • In mathematics, a polynomial with two terms

    For every admissible monomial ordering, the minimal Gröbner basis of a toric ideal consists only of differences of monomials. (This is an immediate

    Binomial (polynomial)

    Binomial_(polynomial)

  • Coefficient
  • Multiplicative factor in a mathematical expression

    multivariate polynomials with respect to a monomial order, see Gröbner basis § Leading term, coefficient and monomial. In linear algebra, a system of linear

    Coefficient

    Coefficient

  • Hilbert's Nullstellensatz
  • Relation between algebraic varieties and polynomial ideals

    any monomial ordering) is 1. The number of the common zeros of the polynomials in a Gröbner basis is strongly related to the number of monomials that

    Hilbert's Nullstellensatz

    Hilbert's_Nullstellensatz

  • Differential algebra
  • Algebraic study of differential equations

    }p\geq \theta _{\mu }q.} Each derivative has an integer tuple, and a monomial order ranks the derivative by ranking the derivative's integer tuple. The

    Differential algebra

    Differential_algebra

  • Elementary symmetric polynomial
  • Mathematical function

    terms of each factor (this is true whenever one uses a monomial order, like the lexicographic order used here), and the leading term of the factor ei (X1

    Elementary symmetric polynomial

    Elementary_symmetric_polynomial

  • Bergman's diamond lemma
  • Gröbner bases for non-commutative algebra

    (after George Bergman) is a method for confirming whether a given set of monomials of an algebra forms a k {\displaystyle k} -basis. It is an extension of

    Bergman's diamond lemma

    Bergman's_diamond_lemma

  • Gaussian elimination
  • Algorithm for solving systems of linear equations

    This generalization depends heavily on the notion of a monomial order. The choice of an ordering on the variables is already implicit in Gaussian elimination

    Gaussian elimination

    Gaussian elimination

    Gaussian_elimination

  • Tropical geometry
  • Skeletonized version of algebraic geometry

    that can be expressed as the tropical sum of a finite number of monomial terms. A monomial term is a tropical product (and/or quotient) of a constant and

    Tropical geometry

    Tropical geometry

    Tropical_geometry

  • Algebraic geometry
  • Branch of mathematics

    extension of the basis field) if and only if the Gröbner basis for any monomial ordering is reduced to {1}. By means of the Hilbert series, one may compute

    Algebraic geometry

    Algebraic geometry

    Algebraic_geometry

  • Dimension of an algebraic variety
  • Measure of a mathematical object studied in the field of algebraic geometry

    {\displaystyle I} for any admissible monomial ordering (the initial ideal of I {\displaystyle I} is the set of all leading monomials of elements of I {\displaystyle

    Dimension of an algebraic variety

    Dimension_of_an_algebraic_variety

  • Buchberger's algorithm
  • Algorithm for computing Gröbner bases

    G, denote by gi the leading term of fi with respect to the given monomial ordering, and by aij the least common multiple of gi and gj. Choose two polynomials

    Buchberger's algorithm

    Buchberger's_algorithm

  • Generalized permutation matrix
  • Matrix with one nonzero entry in each row and column

    In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is

    Generalized permutation matrix

    Generalized_permutation_matrix

  • Cyclic order
  • Alternative mathematical ordering

    symmetric functions, for example as in xy + yz + zx where writing the final monomial as xz would distract from the pattern. A substantial use of cyclic orders

    Cyclic order

    Cyclic order

    Cyclic_order

  • Algebraic variety
  • Mathematical object studied in the field of algebraic geometry

    (not always needed); then a Gröbner basis computation for another monomial ordering to compute the projection and to prove that it is generically injective

    Algebraic variety

    Algebraic variety

    Algebraic_variety

  • Order of a polynomial
  • Topics referred to by the same term

    polynomial) in any of its monomials; the multiplicative order, that is, the number of times the polynomial is divisible by some value; the order of the polynomial

    Order of a polynomial

    Order_of_a_polynomial

  • Normal order
  • Type of operator ordering in quantum field theory

    {b}}^{4}.} 4. A simple example shows that normal ordering cannot be extended by linearity from the monomials to all operators in a self-consistent way. Assume

    Normal order

    Normal_order

  • Gauss's lemma (polynomials)
  • About products of primitive polynomials

    highest-degree terms of f , g {\displaystyle f,g} in terms of lexicographical monomial ordering. Then f 0 g 0 {\displaystyle f_{0}g_{0}} is precisely the leading

    Gauss's lemma (polynomials)

    Gauss's_lemma_(polynomials)

  • Monomial group
  • that is not monomial: since the abelianization of this group has order three, its irreducible characters of degree two are not monomial. Isaacs (1994)

    Monomial group

    Monomial_group

  • Residue (complex analysis)
  • Attribute of a mathematical function

    point corresponding to ⁠ x {\displaystyle x} ⁠. Computing the residue of a monomial ∮ C z k d z {\displaystyle \oint _{C}z^{k}\,dz} makes most residue computations

    Residue (complex analysis)

    Residue (complex analysis)

    Residue_(complex_analysis)

  • System of polynomial equations
  • Roots of multiple multivariate polynomials

    is a leading monomial of some element of the Gröbner basis which is a pure power of this variable. For this test, the best monomial order (that is the

    System of polynomial equations

    System_of_polynomial_equations

  • Hilbert series and Hilbert polynomial
  • Tool in mathematical dimension theory

    of I for a monomial ordering refining the total degree partial ordering and G the (homogeneous) ideal generated by the leading monomials of the elements

    Hilbert series and Hilbert polynomial

    Hilbert_series_and_Hilbert_polynomial

  • Conway group
  • Four finite groups derived from the Leech lattice

    suspected that Co0 was transitive on Λ2, and indeed he found a new matrix, not monomial and not an integer matrix. Let η be the 4-by-4 matrix 1 2 ( 1 − 1 − 1 −

    Conway group

    Conway group

    Conway_group

  • Glossary of commutative algebra
  • given monomial ordering is the set of all leading monomials of the elements in I (this is an ideal of the multiplicative monoid of the monomials). injective

    Glossary of commutative algebra

    Glossary_of_commutative_algebra

  • Dominance order
  • Discrete math concept

    Similarly, there is a dominance order on the set of standard Young bitableaux, which plays a role in the theory of standard monomials. Young's lattice Majorization

    Dominance order

    Dominance_order

  • Buchberger
  • Topics referred to by the same term

    generators for a polynomial ideal into a Gröbner basis with respect to some monomial order This disambiguation page lists articles associated with the title Buchberger

    Buchberger

    Buchberger

  • Index of combinatorics articles
  • MacMahon's master theorem Magic square Matroid embedding Monge array Monomial order Moreau's necklace-counting function Motzkin number Multiplicities of

    Index of combinatorics articles

    Index_of_combinatorics_articles

  • Power series
  • Infinite sum of monomials

    series. Let α be a multi-index for a power series f(x1, x2, …, xn). The order of the power series f is defined to be the least value r {\displaystyle

    Power series

    Power_series

  • Polynomial
  • Type of mathematical expression

    bi- with the Greek poly-. That is, it means a sum of many terms (many monomials). The word polynomial was first used in the 17th century. The x {\displaystyle

    Polynomial

    Polynomial

  • Poincaré–Birkhoff–Witt theorem
  • Explicitly describes the universal enveloping algebra of a Lie algebra

    basis of L. A canonical monomial over X is a finite sequence (x1, x2 ..., xn) of elements of X which is non-decreasing in the order ≤, that is, x1 ≤x2 ≤

    Poincaré–Birkhoff–Witt theorem

    Poincaré–Birkhoff–Witt_theorem

  • Newton polytope
  • {\displaystyle \mathbb {N} ^{n}} each encoding the exponents within a monomial, consider the multivariate polynomial f ( x ) = ∑ k c k x a k {\displaystyle

    Newton polytope

    Newton polytope

    Newton_polytope

  • Patrizia Gianni
  • Italian mathematician (born 1952)

    bases including her discovery of the FGLM algorithm for changing monomial orderings in Gröbner bases, and for her development of the components of the

    Patrizia Gianni

    Patrizia_Gianni

  • Differential operator
  • Typically linear operator defined in terms of differentiation of functions

    also called the homogeneity operator, because its eigenfunctions are the monomials in z: Θ ( z k ) = k z k , k = 0 , 1 , 2 , … {\displaystyle \Theta (z^{k})=kz^{k}

    Differential operator

    Differential operator

    Differential_operator

  • Cycle index
  • Polynomial in combinatorial mathematics

    of objects partitions that set into cycles; the cycle index monomial of π is a monomial in variables a1, a2, … that describes the cycle type of this

    Cycle index

    Cycle_index

  • Ring of symmetric functions
  • for every i > 1 in order to be symmetric. Unlike the whole power series ring, the subring ΛR is graded by the total degree of monomials: due to condition 2

    Ring of symmetric functions

    Ring_of_symmetric_functions

  • Log–log plot
  • 2D graphic with logarithmic scales on both axes

    logarithm, though most commonly base 10 (common logs) are used. Given a monomial equation y = a x k , {\displaystyle y=ax^{k},} taking the logarithm of

    Log–log plot

    Log–log plot

    Log–log_plot

  • Supersolvable group
  • Group with series of normal subgroups where all factors are cyclic

    supersolvable group is monomial, that is, induced from a linear character of a subgroup. In other words, every finite supersolvable group is a monomial group. Every

    Supersolvable group

    Supersolvable_group

  • Moment matrix
  • rows and columns are indexed by monomials. The entries of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices.) Moment

    Moment matrix

    Moment_matrix

  • Boolean function
  • Function returning one of only two values

    completeness) The algebraic degree of a function is the order of the highest order monomial in its algebraic normal form Circuit complexity attempts

    Boolean function

    Boolean function

    Boolean_function

  • Hyperoctahedral group
  • Group of symmetries of an n-dimensional hypercube

    273, JFM 56.0135.02 Yu, Houyi (2024), "The weak order on the hyperoctahedral group and the monomial basis for the Hopf algebra of signed permutations"

    Hyperoctahedral group

    Hyperoctahedral group

    Hyperoctahedral_group

  • Algebraic normal form
  • Boolean polynomials as sums of monomials

    Zhegalkin monomials, with the empty set denoted by 0. A given monomial's presence or absence in a polynomial corresponds to that monomial's coefficient

    Algebraic normal form

    Algebraic_normal_form

  • Bracket algebra
  • any monomials in Super[L]: {w} = 0 if length(w) ≠ n {w}{w'}...{w"} = 0 whenever any positive letter a of L occurs more than n times in the monomial {w}{w'}

    Bracket algebra

    Bracket_algebra

  • Complete homogeneous symmetric polynomial
  • Expression in commutative algebra

    variables X1, ..., Xn, written hk for k = 0, 1, 2, ..., is the sum of all monomials of total degree k in the variables. Formally, h k ( X 1 , X 2 , … , X

    Complete homogeneous symmetric polynomial

    Complete_homogeneous_symmetric_polynomial

  • Weyl algebra
  • Differential algebra

    at least one nonzero monomial that has degree deg ⁡ ( g ) + deg ⁡ ( h ) {\displaystyle \deg(g)+\deg(h)} . To find such a monomial, pick the one in g {\displaystyle

    Weyl algebra

    Weyl_algebra

  • Cumulant
  • Set of quantities in probability theory

    which the set is partitioned; and |B| is the size of the set B. Thus each monomial is a constant times a product of cumulants in which the sum of the indices

    Cumulant

    Cumulant

  • Algebra tile
  • Type of mathematical manipulative

    to multiply a monomial by a monomial, the student must first set up a rectangle where the length of the rectangle is the one monomial and then the width

    Algebra tile

    Algebra_tile

  • Kostka number
  • polynomial s λ {\displaystyle s_{\lambda }} as a linear combination of monomial symmetric functions m μ {\displaystyle m_{\mu }} : s λ = ∑ μ K λ μ m μ

    Kostka number

    Kostka number

    Kostka_number

  • Degree of a polynomial
  • Mathematical concept

    degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is

    Degree of a polynomial

    Degree_of_a_polynomial

  • Sequence
  • Finite or infinite ordered list of elements

    elements of a sequence can be functions instead of numbers. For example, the monomial basis for polynomials of a single variable forms the sequence ( x ↦ 1

    Sequence

    Sequence

    Sequence

  • Keldysh formalism
  • Concept in non-equilibrium physics

    organize this perturbation series into monomial terms and apply all possible Wick pairings to the fields in each monomial, obtaining a summation of Feynman

    Keldysh formalism

    Keldysh formalism

    Keldysh_formalism

  • Polynomial ring
  • Algebraic structure

    in J (usual sum of vectors). In particular, the product of two monomials is a monomial whose exponent vector is the sum of the exponent vectors of the

    Polynomial ring

    Polynomial_ring

  • List of unsolved problems in mathematics
  • it has no nil one-sided ideal other than { 0 } {\displaystyle \{0\}} . Monomial conjecture on Noetherian local rings Existence of perfect cuboids and associated

    List of unsolved problems in mathematics

    List_of_unsolved_problems_in_mathematics

  • Convex cone
  • Mathematical set closed under positive linear combinations

    Business Media. p. 61. ISBN 9783662217115. Villarreal, Rafael (2015-03-26). Monomial Algebras, Second Edition. CRC Press. p. 9. ISBN 9781482234701. Dhara, Anulekha;

    Convex cone

    Convex cone

    Convex_cone

  • Chebyshev polynomials
  • Pair of polynomial sequences

    )}^{\mp 1}.} An explicit form of the Chebyshev polynomial in terms of monomials x k {\displaystyle \textstyle x^{k}} can be obtained as follows. Letting

    Chebyshev polynomials

    Chebyshev polynomials

    Chebyshev_polynomials

  • Partition function (number theory)
  • Number of partitions of an integer

    distributive law to the product. This expands the product into a sum of monomials of the form x a 1 x 2 a 2 x 3 a 3 ⋯ {\displaystyle x^{a_{1}}x^{2a_{2}}x^{3a_{3}}\cdots

    Partition function (number theory)

    Partition function (number theory)

    Partition_function_(number_theory)

  • Schwartz–Zippel lemma
  • Tool used in probabilistic polynomial identity testing

    can multiply all the terms and check whether the coefficient of every monomial is nonzero. However, this can take exponential time in the number of variables

    Schwartz–Zippel lemma

    Schwartz–Zippel_lemma

  • Formal power series
  • Infinite sum that is considered independently from any notion of convergence

    defined similarly by replacing the powers of a single indeterminate by monomials in several indeterminates. Formal power series are widely used in combinatorics

    Formal power series

    Formal_power_series

  • FOIL method
  • Mnemonic for finding the product of two binomial functions

    binomials into a sum of four (or fewer, if like terms are then combined) monomials. The reverse process is called factoring or factorization. In particular

    FOIL method

    FOIL method

    FOIL_method

  • Muirhead's inequality
  • Mathematical inequality

    are nonnegative integers, the a-mean can be equivalently defined via the monomial symmetric polynomial m a ( x 1 , … , x n ) {\displaystyle m_{a}(x_{1},\dots

    Muirhead's inequality

    Muirhead's_inequality

  • Non-negative matrix factorization
  • Algorithms for matrix decomposition

    time algorithm for solving nonnegative rank factorization if V contains a monomial sub matrix of rank equal to its rank was given by Campbell and Poole in

    Non-negative matrix factorization

    Non-negative_matrix_factorization

  • Hall–Littlewood polynomials
  • parameter t and a partition λ. They are Schur functions when t is 0 and monomial symmetric functions when t is 1 and are special cases of Macdonald polynomials

    Hall–Littlewood polynomials

    Hall–Littlewood_polynomials

  • Q-derivative
  • Q-analog of the ordinary derivative

    differentiation, with curious differences. For example, the q-derivative of the monomial is: ( d d z ) q z n = 1 − q n 1 − q z n − 1 = [ n ] q z n − 1 {\displaystyle

    Q-derivative

    Q-derivative

  • Finite difference
  • Discrete analog of a derivative

    finite-difference analogs involving f( x T−1 h ). For instance, the umbral analog of a monomial xn is a generalization of the above falling factorial (Pochhammer k-symbol)

    Finite difference

    Finite_difference

  • Indefinite sum
  • Inverse of a finite difference

    Euler–Maclaurin formula, it is convenient to identify the indefinite sum of a monomial with the corresponding Bernoulli polynomial. The Bernoulli polynomials

    Indefinite sum

    Indefinite sum

    Indefinite_sum

  • Newton's identities
  • Relations between power sums and elementary symmetric functions

    if the coefficients of any monomial match. Because no individual monomial involves more than k of the variables, the monomial will survive the substitution

    Newton's identities

    Newton's_identities

  • Loewy decomposition
  • term orderings g r l e x {\displaystyle grlex} are applied. For partial derivatives of a single function their definition is analogous to the monomial orderings

    Loewy decomposition

    Loewy_decomposition

  • Eilenberg–Niven theorem
  • Algebraic theorem

    octonionic polynomials with a unique monomial of highest degree have at least one solution, independent of the order of the parentheses (the octonions are

    Eilenberg–Niven theorem

    Eilenberg–Niven_theorem

  • Continued fraction
  • Mathematical expression

    area is to quantify the mathematical coincidence idea; for example, for monomials in several real numbers, take the logarithmic form and consider how small

    Continued fraction

    Continued_fraction

  • Critical dimension
  • Dimensionality of space at which the character of the phase transition changes

    may be written as a sum of terms, each consisting of an integral over a monomial of coordinates x i {\displaystyle x_{i}} and fields ϕ i {\displaystyle

    Critical dimension

    Critical_dimension

  • Newton polygon
  • Tool for solving polynomial equations

    {\displaystyle i} , denote by f i {\displaystyle f_{i}} the product of the monomials ( X − α ) {\displaystyle (X-\alpha )} such that α {\displaystyle \alpha

    Newton polygon

    Newton_polygon

  • Riemann–Liouville integral
  • Integral transform

    }f}{dx^{\lceil \alpha \rceil }}}\right).} Let us assume that f(x) is a monomial of the form f ( x ) = x k . {\displaystyle f(x)=x^{k}\,.} The first derivative

    Riemann–Liouville integral

    Riemann–Liouville_integral

  • Precalculus
  • Course designed to prepare students for calculus

    This part of precalculus prepares the student for integration of the monomial x p {\displaystyle x^{p}} in the instance of p = − 1 {\displaystyle p=-1}

    Precalculus

    Precalculus

    Precalculus

  • Dessin d'enfant
  • Graph drawing used to study Riemann surfaces

    after George Shabat. For example, take p {\displaystyle p} to be the monomial p ( x ) = x d {\displaystyle p(x)=x^{d}} having only one finite critical

    Dessin d'enfant

    Dessin_d'enfant

  • Absolutely and completely monotonic functions and sequences
  • {\displaystyle n} -th Bell polynomial. Each Bell polynomial is a finite sum of monomials of the form ∏ i = 1 n ( g ( i ) ) k i {\displaystyle \prod _{i=1}^{n}(g^{(i)})^{k_{i}}}

    Absolutely and completely monotonic functions and sequences

    Absolutely_and_completely_monotonic_functions_and_sequences

  • Arithmetic circuit complexity
  • Standard model in theoretical computer science

    polynomials f {\displaystyle f} of polynomial degree such that given a monomial we can determine its coefficient in f {\displaystyle f} efficiently, with

    Arithmetic circuit complexity

    Arithmetic_circuit_complexity

  • Orthonormal basis
  • Specific linear basis (mathematics)

    (an orthonormal basis), but not necessarily as an infinite sum of the monomials x n . {\displaystyle x^{n}.} A different generalisation is to pseudo-inner

    Orthonormal basis

    Orthonormal_basis

  • Horner's method
  • Algorithm for polynomial evaluation

    {f_{1}(x)}{f_{2}(x)}}=2x^{3}-2x^{2}-x+1-{\frac {4}{2x-1}}.} Evaluation using the monomial form of a degree n {\displaystyle n} polynomial requires at most n {\displaystyle

    Horner's method

    Horner's_method

  • Legendre polynomials
  • System of complete and orthogonal polynomials

    from the recursion formula, expresses the Legendre polynomials by simple monomials and involves the generalized form of the binomial coefficient. The reversal

    Legendre polynomials

    Legendre polynomials

    Legendre_polynomials

  • Conway group Co1
  • Sporadic simple group

    known as group theory, the Conway group Co1 is a sporadic simple group of order    4,157,776,806,543,360,000 = 221 · 39 · 54 · 72 · 11 · 13 · 23 ≈ 4×1018

    Conway group Co1

    Conway group Co1

    Conway_group_Co1

  • CMF
  • Topics referred to by the same term

    vision modeling. See CIE 1931 color space#Color matching functions Common Monomial Factor, the factored form of a polynomial, also known as the greatest common

    CMF

    CMF

  • Pólya enumeration theorem
  • Formula for number of orbits of a group action

    \omega } , let x ω {\displaystyle x^{\omega }} denote the corresponding monomial term of f. Applying Burnside's lemma to orbits of weight ω {\displaystyle

    Pólya enumeration theorem

    Pólya_enumeration_theorem

  • Homogeneous function
  • Function with a multiplicative scaling behaviour

    {\displaystyle v_{1}\in V_{1},v_{2}\in V_{2},\ldots ,v_{n}\in V_{n}.} Monomials in n {\displaystyle n} variables define homogeneous functions f : F n

    Homogeneous function

    Homogeneous_function

  • Binomial coefficient
  • Number of subsets of a given size

    {\displaystyle {\tbinom {n}{k}}} can be defined as the coefficient of the monomial Xk in the expansion of (1 + X)n. The same coefficient also occurs (if k

    Binomial coefficient

    Binomial coefficient

    Binomial_coefficient

  • Reed–Muller code
  • Error-correcting codes used in wireless communication

    update the code to remove the monomial μ {\textstyle \mu } from the input code and continue to next monomial, in reverse order of their degree. Let's consider

    Reed–Muller code

    Reed–Muller_code

  • Abstract simplicial complex
  • Mathematical object

    example of a flag complex. 6. Let I {\displaystyle I} be a square-free monomial ideal in a polynomial ring S = K [ x 1 , … , x n ] {\displaystyle S=K[x_{1}

    Abstract simplicial complex

    Abstract simplicial complex

    Abstract_simplicial_complex

  • Alexander polynomial
  • Knot invariant

    the knot. Since this is only unique up to multiplication by the Laurent monomial ± t n {\displaystyle \pm t^{n}} , one often fixes a particular unique form

    Alexander polynomial

    Alexander_polynomial

  • Z-group
  • character theory of Z-groups is well understood (Çelik 1976), as they are monomial groups. The derived length of a Z-group is at most 2, so Z-groups may be

    Z-group

    Z-group

  • Root locus analysis
  • Stability criterion in control theory

    divide magnitudes. The vector formulation arises from the fact that each monomial term ( s − a ) {\displaystyle (s-a)} in the factored G ( s ) H ( s ) {\displaystyle

    Root locus analysis

    Root locus analysis

    Root_locus_analysis

  • Discriminant
  • Function of the coefficients of a polynomial that gives information on its roots

    +a_{0}.} It follows from what precedes that the exponents in every monomial a 0 i 0 , … , a n i n {\displaystyle a_{0}^{i_{0}},\dots ,a_{n}^{i_{n}}}

    Discriminant

    Discriminant

  • Lindemann–Weierstrass theorem
  • Theorem in transcendental number theory

    product is symmetric, for any τ ∈ S N {\displaystyle \tau \in S_{N}} the monomials x τ ( 1 ) h 1 ⋯ x τ ( N ) h N {\displaystyle x_{\tau (1)}^{h_{1}}\cdots

    Lindemann–Weierstrass theorem

    Lindemann–Weierstrass theorem

    Lindemann–Weierstrass_theorem

  • Bernstein polynomial
  • Type of polynomial used in Numerical Analysis

    coefficients. The first few Bernstein basis polynomials from above in monomial form are: b 0 , 0 ( x ) = 1   , b 0 , 1 ( x ) = 1 − 1 x   , b 1 , 1 ( x

    Bernstein polynomial

    Bernstein polynomial

    Bernstein_polynomial

AI & ChatGPT searchs for online references containing MONOMIAL ORDER

MONOMIAL ORDER

AI search references containing MONOMIAL ORDER

MONOMIAL ORDER

  • Herod
  • Surname or Lastname

    English (chiefly Nottinghamshire)

    Herod

    English (chiefly Nottinghamshire) : nickname from the personal name Herod (Greek Hērōdēs, apparently derived from hērōs ‘hero’), borne by the king of Judea (died ad 4) who at the time of the birth of Christ ordered that all male children in Bethlehem should be slaughtered (Matthew 2: 16–18). In medieval mystery plays Herod was portrayed as a blustering tyrant, and the name was therefore given to someone one who had played the part, or who had an overbearing temper.English : variant of Harold (1 or 2).Greek : shortened form of Herodiadis, a patronymic from the classical personal name Hērodiōn. This was the name of a relative of St. Paul and an early Bishop of Patras, venerated in the Orthodox Church. Hērodēs ‘Herod’ is also found in Greek as a nickname for a violent man, but this is less likely to be the source of the surname.

    Herod

  • Lambeth
  • Surname or Lastname

    English

    Lambeth

    English : habitational name from Lambeth, now part of Greater London, named in Old English as ‘lamb hithe’, from Old English lamb ‘lamb’ + h̄th ‘hithe’, ‘landing place’, i.e. a place where lambs were put on board boat or taken ashore, no doubt in order to supply the meat markets of London on the other side of the river Thames.

    Lambeth

  • Farman
  • Surname or Lastname

    English and French

    Farman

    English and French : from an Old Norse personal name, Farmaðr, denoting a seafarer or traveling merchant.English : occupational name for a peddler or itinerant merchant, Middle English far(e)man, from an Old Norse word meaning ‘traveling man’ (see 1).Muslim : from the Arabic personal name based on faraman ‘command’, ‘order’, ‘decree’. It is also found in compound names such as Faraman-ullah ‘order of Allah’.

    Farman

  • Chancellor
  • Surname or Lastname

    English and Scottish

    Chancellor

    English and Scottish : status name for a secretary or administrative official, from Old French chancelier, Late Latin cancellarius ‘usher (in a law court)’. The King’s Chancellor was one of the highest officials in the land, but the term was also used to denote the holder of a variety of offices in the medieval world, such as the secretary or record keeper in a minor manorial household. In some cases the name undoubtedly originated as a nickname or as an occupational name for someone in the service of such an official.

    Chancellor

  • Eustace
  • Surname or Lastname

    English

    Eustace

    English : from the personal name Eustace (Latin Eustacius, from Greek Eustakhyos, meaning ‘fruitful’, blended with the originally distinct name Eustathios ‘orderly’). The name was borne by various minor saints, but little is known of the most famous St. Eustace, patron saint of hunters, said to have been converted by the vision of a crucifix between the antlers of a hunted stag. In some cases this may be an Americanized form of a Greek family name based on Eusthathios, such as Eustathiadis or Eustathidis.

    Eustace

  • Dwight
  • Surname or Lastname

    English

    Dwight

    English : from Diot, a pet form of the female personal name Dye. Reaney also suggests that this may also be an altered form of Thwaite (see Thwaites).Timothy Dwight (1752–1817), Congregational divine, author, and president of Yale College (1795–1817), was the dominant figure in the established order of CT. He was born in Northampton, MA, a descendant of John Dwight who came from Dedham, England, in 1635 and settled in Dedham, MA, and the grandson of Jonathan Edwards, the great theologian of American Puritanism.

    Dwight

  • Monomita
  • Girl/Female

    Bengali, Indian

    Monomita

    A Secret Friend

    Monomita

  • Freer
  • Surname or Lastname

    English

    Freer

    English : from Old French and Middle English frere ‘friar’ (Latin frater, literally ‘brother’). This was a status name for a member a religious order, especially a mendicant order, and may also have been a nickname for a pious person or for someone employed at a monastery.Americanized spelling of French Frère (see Frere).North German and Dutch : cognate of Friedrich.

    Freer

  • Niyati | நியதீ
  • Girl/Female

    Tamil

    Niyati | நியதீ

    Necessity, Restriction, The fixed order of things, Destiny, Fate

    Niyati | நியதீ

  • Council
  • Surname or Lastname

    English

    Council

    English : nickname for a wise or thoughtful man, from Anglo-Norman French counseil ‘consultation’, ‘deliberation’, also ‘counsel’, ‘advice’ (Latin consilium, from consulere ‘to consult’). This form was probably influenced by the similar meaning of Anglo-Norman French councile ‘council’, ‘assembly’ (Latin concilium ‘assembly’, from the archaic verb concalere ‘to call together’, ‘to summon’), and it may also have been an occupational name for a member of a royal council or, more probably, a manorial council.Americanized spelling of German Künzel (see Kuenzel).

    Council

  • Ing
  • Surname or Lastname

    English

    Ing

    English : from the Old Norse and Middle English personal name Ing(a), a short form of various names with the first element Ing- (see Ingle).English : habitational name from an Essex place name, Ing, which survives with various manorial affixes in the names Fryerning, Ingatestone, Ingrave, and Margaretting, and which is probably from an Old English tribal name Gēingas ‘people of the district’.Jewish (eastern Ashkenazic) : nickname from Yiddish ing ‘young’.Chinese : possibly a variant of Wu 1.Chinese : possibly a variant of Wu 4.

    Ing

  • Niyathi | நீயதீ
  • Girl/Female

    Tamil

    Niyathi | நீயதீ

    Necessity, Restriction, The fixed order of things, Destiny, Fate

    Niyathi | நீயதீ

  • Court
  • Surname or Lastname

    English and French

    Court

    English and French : topographic name from Middle English, Old French court(e), curt ‘court’ (Latin cohors, genitive cohortis, ‘yard’, ‘enclosure’). This word was used primarily with reference to the residence of the lord of a manor, and the surname is usually an occupational name for someone employed at a manorial court.English : nickname from Old French, Middle English curt ‘short’, ‘small’ (Latin curtus ‘curtailed’, ‘truncated’, ‘cut short’, ‘broken off’).Irish : reduced form of McCourt.

    Court

  • Corte
  • Surname or Lastname

    Italian, Spanish, and Portuguese

    Corte

    Italian, Spanish, and Portuguese : from corte ‘court’ (Latin cohors ‘yard’, ‘enclosure’, genitive cohortis), applied as an occupational name for someone who worked at a manorial court or a topographic name for someone who lived in or by one.English : variant spelling of Court.Americanized spelling of Korte.

    Corte

  • Gilbert
  • Surname or Lastname

    English (of Norman origin), French, and North German

    Gilbert

    English (of Norman origin), French, and North German : from Giselbert, a Norman personal name composed of the Germanic elements gīsil ‘pledge’, ‘hostage’, ‘noble youth’ (see Giesel) + berht ‘bright’, ‘famous’. This personal name enjoyed considerable popularity in England during the Middle Ages, partly as a result of the fame of St. Gilbert of Sempringham (1085–1189), the founder of the only native English monastic order.Jewish (Ashkenazic) : Americanized form of one or more like-sounding Jewish surnames.The Devon family of Gilbert can be traced to Geoffrey Gilbert (died 1349), who represented Totnes in Parliament in 1326. His descendants included Sir Humphrey Gilbert (died 1583), who discovered Newfoundland.

    Gilbert

  • Moomal
  • Girl/Female

    Arabic, Muslim

    Moomal

    Beautiful

    Moomal

  • Pradarsh | ப்ரதர்ஷ
  • Boy/Male

    Tamil

    Pradarsh | ப்ரதர்ஷ

    Appearance, Order

    Pradarsh | ப்ரதர்ஷ

  • Winford
  • Surname or Lastname

    English

    Winford

    English : habitational name from either of two places named Winford, in Somerset or in Newchurch on the Isle of Wight, or from Wynford Eagle in Dorset. The first and last are named from a Celtic river name meaning ‘white or bright stream’, the last having acquired a manorial prefix from the del Egle family, who were there in the 13th century. Winford, Isle of Wight, is named from an unattested Old English winn ‘meadow’ + Old English ford ‘ford’.

    Winford

  • Niralya | நீரல்ய
  • Boy/Male

    Tamil

    Niralya | நீரல்ய

    Orderly

    Niralya | நீரல்ய

  • Dominick
  • Surname or Lastname

    English

    Dominick

    English : from a vernacular form of the Late Latin personal name Dominicus ‘of the Lord’. This was borne by a Spanish saint (1170–1221) who founded the Dominican order of friars. In medieval England it may have been used as a personal name for a child born on a Sunday. As an English surname it is comparatively rare, and in the U.S. it has undoubtedly absorbed cognates in other European languages; for the forms, see Hanks and Hodges 1988.

    Dominick

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MONOMIAL ORDER

Online names & meanings

  • Satyavath
  • Boy/Male

    Hindu

    Satyavath

    A metronymic of the sage Vyasa

  • Gelston
  • Surname or Lastname

    English

    Gelston

    English : habitational name from a place so named in Lincolnshire. The place name, recorded in the Domesday book as Cheuelestune, is probably from an Old Norse personal name Gjǫfull + Old English tūn ‘farmstead’, ‘village’.

  • TEODÓRA
  • Female

    Hungarian

    TEODÓRA

    Feminine form of Hungarian Tódor, TEODÓRA means "gift of God."

  • Surbhii
  • Girl/Female

    Indian

    Surbhii

    Fragrance

  • Path
  • Boy/Male

    Arabic, Modern

    Path

    Road; The Way

  • Gursees
  • Girl/Female

    Indian, Sikh

    Gursees

    Head of Guru

  • Gaylen
  • Boy/Male

    Gaelic

    Gaylen

    Tranquil.

  • Field
  • Boy/Male

    Australian, British, English

    Field

    A Field

  • BAN
  • Male

    Arthurian

    BAN

    , (white); the father of Lancelot.

  • Ronell
  • Boy/Male

    Gaelic Scandinavian English

    Ronell

    Rules with counsel. Form of Ronald from Reynold.

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MONOMIAL ORDER

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MONOMIAL ORDER

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MONOMIAL ORDER

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Other words and meanings similar to

MONOMIAL ORDER

AI search in online dictionary sources & meanings containing MONOMIAL ORDER

MONOMIAL ORDER

  • Binomial
  • n.

    An expression consisting of two terms connected by the sign plus (+) or minus (-); as, a + b, or 7 - 3.

  • Monodic
  • a.

    Alt. of Monodical

  • Monomial
  • a.

    Consisting of but a single term or expression.

  • Manorial
  • a.

    Of or pertaining to a manor.

  • Monodical
  • a.

    For one voice; monophonic.

  • Motory
  • n.

    Alt. of Motorial

  • Binominal
  • a.

    Of or pertaining to two names; binomial.

  • Monome
  • n.

    A monomial.

  • Monodical
  • a.

    Homophonic; -- applied to music in which the melody is confined to one part, instead of being shared by all the parts as in the style called polyphonic.

  • Monodical
  • a.

    Belonging to a monody.

  • Monaxial
  • a.

    Having only one axis; developing along a single line or plane; as, monaxial development.

  • Manerial
  • a.

    See Manorial.

  • Binomial
  • a.

    Consisting of two terms; pertaining to binomials; as, a binomial root.

  • Monomial
  • n.

    A single algebraic expression; that is, an expression unconnected with any other by the sign of addition, substraction, equality, or inequality.

  • Monomyary
  • n.

    One of the Monomya.

  • Monomyary
  • a.

    Of or pertaining to the Monomya.

  • Motor
  • n.

    Alt. of Motorial

  • Mononomial
  • n. & a.

    Monomyal.

  • Binomial
  • a.

    Having two names; -- used of the system by which every animal and plant receives two names, the one indicating the genus, the other the species, to which it belongs.

  • Motorial
  • n.

    Causing or setting up motion; pertaining to organs of motion; -- applied especially in physiology to those nerves or nerve fibers which only convey impressions from a nerve center to muscles, thereby causing motion.