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Algebraic structure decomposed into a direct sum
mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a
Graded_vector_space
Graded vector space with applications to theoretical physics
In mathematics, a super vector space is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded vector space, that is, a vector space over a field K {\displaystyle
Super_vector_space
Type of algebraic structure
gradation or grading. A graded module is defined similarly (see below for the precise definition). It generalizes graded vector spaces. A graded module that
Graded_ring
Algebraic structure in linear algebra
of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces are
Vector_space
Broad concept generalizing scalars in mathematics and physics
on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is called
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Algebraic structure in homological algebra
differential graded Lie algebra (or DGLA) is a differential graded analogue of a Lie algebra. That is, it is a differential graded vector space, ( L ∙ , d
Differential_graded_algebra
Index of articles associated with the same name
V=\bigoplus _{i\in I}V_{i}} of spaces. A graded linear map is a map between graded vector spaces respecting their gradations. A graded ring is a ring that is
Graded_structure
Algebraic study of differential equations
this graded vector space: V ∙ = ⨁ m ∈ Z V m {\displaystyle V_{\bullet }=\bigoplus _{m\in \mathbb {Z} }V_{m}} A differential graded vector space or chain
Differential_algebra
Topics referred to by the same term
meanings Graded poset, a partially ordered set equipped with a rank function, sometimes called a ranked poset Graded vector space, a vector space with an
Grade
Number of vectors in any basis of the vector space
In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes
Dimension_(vector_space)
Mathematical operation on vector spaces
{\displaystyle V\otimes W} of two vector spaces V {\displaystyle V} and W {\displaystyle W} (over the same field) is a vector space to which is associated a bilinear
Tensor_product
Algebra associated to any vector space
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle
Exterior_algebra
Tool in mathematical dimension theory
or a module is a special case of the Hilbert–Poincaré series of a graded vector space. The Hilbert polynomial and Hilbert series are important in computational
Hilbert series and Hilbert polynomial
Hilbert_series_and_Hilbert_polynomial
"Smallest" commutative algebra that contains a vector space
\bigoplus _{n=0}^{\infty }\operatorname {Sym} ^{n}(V),} which is a graded vector space (or a graded module). It is not an algebra, as the tensor product of two
Symmetric_algebra
Category whose objects are R-modules and whose morphisms are module homomorphisms
) Category of rings Derived category Module spectrum Category of graded vector spaces Category of representations Change of rings Morita equivalence Stable
Category_of_modules
Formal power series in algebra
inductive hypothesis. An example of graded vector space is associated to a chain complex, or cochain complex C of vector spaces; the latter takes the form 0
Hilbert–Poincaré_series
Algebraic structure designed for geometry
{Z} } -graded vector space to Z 2 {\displaystyle \mathrm {Z} _{2}} -graded vector space. The geometric product respects this coarser grading. Thus in
Geometric_algebra
The suspension S V {\displaystyle SV} of a graded vector space V {\displaystyle V} is the graded vector space defined by ( S V ) i = V i + 1 {\displaystyle
Homotopy_associative_algebra
mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra
Graded_Lie_algebra
abstract algebra and topology, a differential graded Lie algebra (or dg Lie algebra, or dgla) is a graded vector space with added Lie algebra and chain complex
Differential graded Lie algebra
Differential_graded_Lie_algebra
Tensor invariant under permutations of vectors it acts on
polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric
Symmetric_tensor
Vector space with a partial order
ordered vector space or partially ordered vector space is a real vector space equipped with a partial order that is compatible with the vector space operations
Ordered_vector_space
field is of characteristic zero is made. A homotopy Lie algebra on a graded vector space V = ⨁ V i {\displaystyle V=\bigoplus V_{i}} is a continuous derivation
Homotopy_Lie_algebra
Invariant of mathematical knots
bracket [ D ] {\displaystyle \left[D\right]} , a cochain complex of graded vector spaces. This is the analogue of the Kauffman bracket in the construction
Khovanov_homology
over that coalgebra. A graded vector space V can be made into a comodule. Let I be the index set for the graded vector space, and let C I {\displaystyle
Comodule
Non-tensorial representation of the spin group
complex vector space that can be associated with Euclidean space. Spinors can be thought of as companion geometric objects to Euclidean space that, like
Spinor
Supersymmetric generalization of the Poincaré algebra
Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing
Super-Poincaré_algebra
Overview of and topical guide to algebraic structures
Lie algebras. Graded algebra: a graded vector space with an algebra structure compatible with the grading. The idea is that if the grades of two elements
Outline of algebraic structures
Outline_of_algebraic_structures
Monster and modular connection
Thompson suggested that because the graded dimension is just the graded trace of the identity element, the graded traces of nontrivial elements g of M
Monstrous_moonshine
Canonical commutation or anticommutation relations
{\displaystyle V} be a real Z 2 {\displaystyle \mathbb {Z} _{2}} -graded vector space equipped with a nonsingular antisymmetric bilinear superform ( ⋅
CCR_and_CAR_algebras
Mathematical operation on vectors in 3D space
Euclidean vector space (named here E {\displaystyle E} ), and is denoted by the symbol × {\displaystyle \times } . Given two linearly independent vectors a and
Cross_product
Manifold with supersymmetry structure
geometry, graded manifolds are extensions of the concept of manifolds based on ideas coming from supersymmetry and supercommutative algebra. Both graded manifolds
Graded_manifold
Topics referred to by the same term
theory of modular forms Hilbert–Poincaré series, associated to a graded vector space, in algebra This disambiguation page lists mathematics articles associated
Poincaré_series
Semigroup action
of a Lie superalgebra is an action of Lie superalgebra L on a Z2-graded vector space V, such that if A and B are any two pure elements of L and X and
Representation of a Lie superalgebra
Representation_of_a_Lie_superalgebra
Manifold upon which it is possible to perform calculus
manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection
Differentiable_manifold
Type of two-dimensional quasiparticle
dictionary. Anyonic Lie algebra – Graded vector space equipped with a bilinear operator Flux tube – Tube-like region of space with constant magnet flux along
Anyon
Generalization of vector spaces from fields to rings
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)
Module_(mathematics)
the property d 2 = 0 {\displaystyle d^{2}=0} . In other words, the graded vector space Ω X ∗ ( E ) {\displaystyle \Omega _{X}^{*}(E)} is a cochain complex
Flat_vector_bundle
_{i=0}^{\infty }(-1)^{i}\operatorname {tr} (\phi ^{-1}|V_{i})} for a graded vector space V ∗ {\displaystyle V_{*}} , provided the series on the right absolutely
Moduli stack of principal bundles
Moduli_stack_of_principal_bundles
In mathematics, a prehomogeneous vector space (PVS) is a finite-dimensional vector space V together with a subgroup G of the general linear group GL(V)
Prehomogeneous_vector_space
Mathematical theory of topological spaces
differential graded cocommutative coalgebras. (The associated coalgebra is the rational homology of X as a coalgebra; the dual vector space is the rational
Rational_homotopy_theory
Base space for supersymmetric theories
super vector space. This is denoted as R m | n {\displaystyle \mathbb {R} ^{m|n}} , the Z 2 {\displaystyle \mathbb {Z} _{2}} -graded vector space with
Superspace
algebra on a set X is naturally graded. The 1-graded component of the free Lie algebra is just the free vector space on that set. One can alternatively
Free_Lie_algebra
Construction in homological algebra
\operatorname {Tor} _{*}^{R}(k,k)} is the free graded-commutative divided power algebra on a graded vector space π*(R). When k has characteristic zero, π*(R)
Tor_functor
Framework for studying stochastic partial differential equations
bounded from below and has no accumulation points; the model space: a graded vector space T = ⊕ α ∈ A T α {\displaystyle T=\oplus _{\alpha \in A}T_{\alpha
Regularity_structure
Locally convex topological vector space that is also a complete metric space
Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that
Fréchet_space
Algebra used in 2D conformal field theories and string theory
a bcβγ system. By allowing the underlying vector space to be a superspace (i.e., a Z/2Z-graded vector space V = V + ⊕ V − {\displaystyle V=V_{+}\oplus
Vertex_operator_algebra
Algebra based on a vector space with a quadratic form
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional
Clifford_algebra
Graded vector space equipped with a bilinear operator
In mathematics, an anyonic Lie algebra is a U(1) graded vector space L {\displaystyle L} over C {\displaystyle \mathbb {C} } equipped with a bilinear
Anyonic_Lie_algebra
Algebraic object with geometric applications
of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There
Tensor
{\mathfrak {X}}^{\bullet }(M)=\bigoplus _{k}{\mathfrak {X}}^{k}(M)} is a graded vector space. Furthermore, there is a wedge product ∧ : X k ( M ) × X l ( M )
Polyvector_field
Mathematical theory
{e}}t} }^{\ast }(X\times _{K}{\overline {K}},\mathbf {Q} _{p})} of graded vector spaces with GK-action (the de Rham cohomology is equipped with the Hodge
P-adic_Hodge_theory
polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric
Symmetry_in_mathematics
Gauge theory with supersymmetry
translation in the (parameter) space. This superspace is a Z 2 {\displaystyle {\mathbb {Z} _{2}}} -graded vector space W = W 0 ⊕ W 1 {\displaystyle {\mathcal
Supersymmetric_gauge_theory
Writing Lie algebra sets as matrices
is a (not necessarily associative) Z2 graded algebra A which is a representation of L as a Z2 graded vector space and in addition, the elements of L acts
Lie_algebra_representation
projective spaces. Let k be an algebraically closed field, and V be a finite-dimensional vector space over k. The symmetric algebra of the dual vector space V*
Algebraic geometry of projective spaces
Algebraic_geometry_of_projective_spaces
Mathematics procedure
projectivization is a procedure which associates with a non-zero vector space V a projective space P(V), whose elements are one-dimensional subspaces of V. More
Projectivization
with a vector defines a graded derivation of degree ℓ = −1, whereas the exterior derivative is a graded derivation of degree ℓ = 1. The vector space of all
Frölicher–Nijenhuis_bracket
Graded lie algebra structure
Nijenhuis–Richardson bracket is a graded Lie algebra structure on the space of alternating multilinear forms of a vector space to itself, introduced by A. Nijenhuis
Nijenhuis–Richardson_bracket
Generalization of the inverse function theorem
surjective with a smooth tame right inverse. A graded Fréchet space consists of the following data: a vector space F {\displaystyle F} a countable collection
Nash–Moser_theorem
topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order ≤ making it into an ordered vector space whose
Ordered topological vector space
Ordered_topological_vector_space
Type of algebra over a commutative ring
In algebra, given a commutative ring R, the graded-symmetric algebra of a graded R-module M is the quotient of the tensor algebra of M by the ideal I generated
Graded-symmetric_algebra
geometry, a weighted projective space P(a0,...,an) is the projective variety Proj(k[x0,...,xn]) associated to the graded ring k[x0,...,xn] where the variable
Weighted_projective_space
Algebraic structure in mathematics
(x)=\lambda ^{2}-\lambda \mu a-\mu ^{2}b\in R.} A graded quadratic algebra A is determined by a vector space of generators V = A1 and a subspace of homogeneous
Quadratic_algebra
Vector space equipped with a bilinear product
mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure
Algebra_over_a_field
Local ring in commutative algebra
For example, if R is a commutative graded algebra over a field k such that R has finite dimension as a k-vector space, R = k ⊕ R1 ⊕ ... ⊕ Rm, then R is
Gorenstein_ring
Topics referred to by the same term
of a differential k-form An element of a k-dimensional vector space, especially a four-vector used in relativity to mean a quantity related to four-dimensional
K-vector
_{i=0}^{n}G_{i}} is isomorphic to F n {\displaystyle F_{n}} as vector spaces). Any graded algebra graded by N {\displaystyle \mathbb {N} } , for example A = ⨁
Filtered_algebra
Topics referred to by the same term
equipped with an associative bilinear vector product Superalgebra, a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded algebra Lie algebras, Poisson algebras
Algebra_(disambiguation)
Various mathematical dualites
duality arises as follows: for a 1-dimensional vector space V over a field k, with dual vector space V ∗ {\displaystyle V^{*}} , the exterior algebra
Koszul_duality
Order for the terms of a polynomial
the graded reverse lexicographic order, which follows, is easier to compute and provides the same information on the input set of polynomials. Graded reverse
Monomial_order
Object in geometric algebra
object in the geometric algebra (also called Clifford algebra) of a vector space that represents a rotation about the origin. More precisely, for each
Rotor_(mathematics)
Element of an exterior algebra
algebra Λ(V) of a vector space V. This algebra is graded, associative and alternating, and consists of linear combinations of simple k-vectors (also known as
Multivector
stable vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle
Stable_vector_bundle
Multivariate derivative (mathematics)
rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of f {\displaystyle f} . If the gradient
Gradient
Set with operations obeying given axioms
elements of the field (called scalars), and elements of the vector space (called vectors). Abstract algebra is the name that is commonly given to the
Algebraic_structure
Physical quantity that changes sign with improper rotation
physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under continuous rigid transformations such as rotations
Pseudovector
Four-dimensional number system
Quaternions can be used to represent vectors in three-dimensional space, which provides a definition of the quotient of two vectors. Quaternions were first described
Quaternion
Overview of and topical guide to category theory
categories Category of vector spaces Category of graded vector spaces Category of chain complexes Category of finite dimensional Hilbert spaces Category of sets
Outline_of_category_theory
Generalization of vector bundles
{N} } -graded ring, be a projective scheme over a Noetherian ring R 0 {\displaystyle R_{0}} . Then each Z {\displaystyle \mathbb {Z} } -graded R {\displaystyle
Coherent_sheaf
Algebraic structure used in analysis
In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket
Lie_algebra
Physical quantities taking values at each point in space and time
physical quantity – represented by a scalar, vector, spinor, or tensor – that has a value for each point in space and time. An example of a scalar field is
Field_(physics)
Partially ordered set equipped with a rank function
Sometimes a graded poset is called a ranked poset but that phrase has other meanings; see Ranked poset. A rank or rank level of a graded poset is the
Graded_poset
Ring that is also a vector space or a module
multiplication operations together give A the structure of a module or vector space over K. In this article we will also use the term K-algebra to mean an
Associative_algebra
Position of something in relation to its surroundings
strike and dip in geology and grade on maps and signs. A unit vector may also be used to represent an object's normal vector direction or the relative direction
Orientation_(geometry)
Branch of mathematics
{\displaystyle A} is a graded algebra, the quotient category qgr A {\displaystyle \operatorname {qgr} A} , obtained from graded modules by factoring out
Noncommutative_geometry
a graded-commutative associative algebra. If the fibers of E are not commutative then Ω(M,E) will not be graded-commutative. For any vector space V there
Vector-valued differential form
Vector-valued_differential_form
Type of surface topology
combinatorial objects. This explains the Lie algebra structure of the graded vector space of Jacobi diagrams in terms of the Hopf algebra structure of Cob
Clasper_(mathematics)
Algebraic structure
which guarantee commutativity of a ring are also known. A graded ring R = ⨁i∊Z Ri is called graded-commutative if, for all homogeneous elements a and b, ab
Commutative_ring
Type of monoidal category
the Drinfeld center of the category of G {\displaystyle G} -graded (complex) vector spaces. That is, D ( G ) = Z ( Vec G ) {\displaystyle {\mathcal {D}}(G)={\mathcal
Modular_tensor_category
Setting of relativistic physics in geometric algebra
_{k}\gamma _{0}\end{aligned}}} Space–time split is a method for representing an even-graded vector of spacetime as a vector in the Pauli algebra, an algebra
Spacetime_algebra
coalgebra of a vector space or module is a coalgebra analog of the free algebra of a vector space. The cofree coalgebra of any vector space over a field
Cofree_coalgebra
Exterior algebraic map taking tensors from p forms to n-p forms
map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator
Hodge_star_operator
bracket, is a type of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields. There are two
Schouten–Nijenhuis_bracket
Projective analogue of the spectrum of a ring
arise from graded modules by this construction. The corresponding graded module is not unique. A special case of the sheaf associated to a graded module is
Proj_construction
Specification of a derivative along a tangent vector of a manifold
case of Euclidean space, one usually defines the directional derivative of a vector field in terms of the difference between two vectors at two nearby points
Covariant_derivative
associated graded vector space ⨁ i = 0 n W i / W i + 1 {\displaystyle \bigoplus _{i=0}^{n}W_{i}/W_{i+1}} is canonically isomorphic to the space of smooth
Valuation_(geometry)
Partially ordered vector space, ordered as a lattice
Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are
Riesz_space
Exterior product of vectors
product of three vectors a, b, and c: a ∧ b ∧ c . {\displaystyle a\wedge b\wedge c.} In vector spaces of dimension ≤ 3, every k-vector is a blade. In dimension
Blade_(geometry)
Expression that may be integrated over a region
-dimensional manifold, and in general space of k {\displaystyle k} -covectors on an n {\displaystyle n} -dimensional vector space, is n {\displaystyle n} choose
Differential_form
GRADED VECTOR-SPACE
GRADED VECTOR-SPACE
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Boy/Male
American, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hindu, Indian, Irish, Jamaican, Latin, Romanian, Slovenia, Spanish, Swedish, Swiss, Tamil, Ukrainian
Victorious; Conqueror; Winner; Champion; One who Conquers; Victory
Male
English
Roman Latin name VICTOR means "conqueror."Â
Girl/Female
German, Teutonic
Guarded
Male
Russian
(Cyrillic Виктор): Slavic form of Roman Latin Victor, VIKTOR means "conqueror." In use by the Bulgarians, Russians and Serbians. Compare with another form of Viktor.
Boy/Male
Spanish
Victor.
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Surname or Lastname
English
English : variant of Grace.
Surname or Lastname
Scottish
Scottish : Anglicized form of the Gaelic personal name Eachann (earlier Eachdonn, already confused with Norse Haakon), composed of the elements each ‘horse’ + donn ‘brown’.English : found in Yorkshire and Scotland, where it may derive directly from the medieval personal name. According to medieval legend, Britain derived its name from being founded by Brutus, a Trojan exile, and Hector was occasionally chosen as a personal name, as it was the name of the Trojan king’s eldest son. The classical Greek name, HektÅr, is probably an agent derivative of Greek ekhein ‘to hold back’, ‘hold in check’, hence ‘protector of the city’.German, French, and Dutch : from the personal name (see 2 above). In medieval Germany, this was a fairly popular personal name among the nobility, derived from classical literature. It is a comparatively rare surname in France.
Boy/Male
American, British, English
Gray-haired; Son of the Gray Family; Son of Gregory
Boy/Male
Gaelic
noble.
Male
Arthurian
, sir Hector de Maris; (defender).
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
Boy/Male
English American
Doctor; teacher.
Girl/Female
American, Arabic, Australian, British, Chinese, Christian, Danish, English, French, German, Gujarati, Indian, Irish, Jamaican, Latin, Muslim, Portuguese, Swedish
Mercy; God's Favor; Grace; Grace of God; Kindness; Thanks; Love; Favour; Blessing; Charm; Good will
Male
English
 Anglicized form of Scottish Gaelic Eachann, HECTOR means "brown horse." Compare with another form of Hector.
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
Girl/Female
Latin American English Irish
Grace.
GRADED VECTOR-SPACE
GRADED VECTOR-SPACE
Boy/Male
Indian, Telugu
Brother of Lord Ram
Boy/Male
Hindu
Lord Shiva
Girl/Female
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Mythological, Oriya, Sanskrit, Sindhi, Telugu, Traditional
Believe; Veneration
Boy/Male
Danish, Finnish, French, German, Latin, Shakespearean, Swedish
Born Fifth
Boy/Male
Australian, German, Polish
Famous Ruler; To Rule with Greatness or Peace
Boy/Male
Hindu
Biblical
Malchom, their king; their counselor
Boy/Male
American, Australian, British, Dutch, English
Quaking Fen
Biblical
first fruits
Girl/Female
Assamese, Gujarati, Hindu, Indian, Tamil, Telugu
Young; Not Becoming Old
GRADED VECTOR-SPACE
GRADED VECTOR-SPACE
GRADED VECTOR-SPACE
GRADED VECTOR-SPACE
GRADED VECTOR-SPACE
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
a.
Furnished with a grate or grating; as, grated windows.
n.
Same as Radius vector.
n.
A woman who wins a victory; a female victor.
n.
A step or degree in any series, rank, quality, order; relative position or standing; as, grades of military rank; crimes of every grade; grades of flour.
v. i.
To lay out or cultivate a garden; to labor in a garden; to practice horticulture.
v. t.
To cultivate as a garden.
n.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
An African weaver bird (Textor alector).
a.
Endowed with grace; beautiful; full of graces; honorable.
a.
Divested of blades; as, bladed corn.
n.
A graded ascending, descending, or level portion of a road; a gradient.
n.
The turning factor of a quaternion.
v. t.
To tamper with and arrange for one's own purposes; to falsify; to adulterate; as, to doctor election returns; to doctor whisky.
a.
Braided
n.
One who grades, or that by means of which grading is done or facilitated.
a.
Pertaining to a rector or a rectory; rectoral.
n.
The rate of regular or graded ascent or descent in a road; grade.
imp. & p. p.
of Grade