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mathematics, in the representation theory of algebraic groups, a linear representation of an algebraic group is said to be rational if, viewed as a map
Rational_representation
Quotient of two integers
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p q {\displaystyle {\tfrac {p}{q}}} of two integers
Rational_number
Plane curve
\,0).} Rational representations of conic sections are commonly used in computer-aided design (see Bézier curve). A parametric representation, which uses
Ellipse
Quality of being agreeable to reason
Rationality is the quality of being guided by or based on reason. In this regard, a person acts rationally if they have a good reason for what they do
Rationality
Mathematics concept
given by a rational representation of an algebraic torus, the definition of G is as the Zariski closure of the image in the representation of the circle
Mumford–Tate_group
order 3, the representation ring RQ(C3) is isomorphic to Z[X]/(X2 − X − 2), where X corresponds to the irreducible rational representation of dimension
Representation_ring
Ratio of polynomial functions
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator
Rational_function
Fraction with denominator a power of two
terminating binary representation. Addition, subtraction, and multiplication of any two dyadic rationals produces another dyadic rational, according to the
Dyadic_rational
Number representing a continuous quantity
cause exponential explosion in the size of representation of a single number (for instance, squaring a rational number roughly doubles the number of digits
Real_number
Number in {..., –2, –1, 0, 1, 2, ...}
integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers
Integer
Wiki criticizing religion and pseudoscience
RationalWiki is an online wiki which is written from a scientific skeptic, secular, and progressive perspective. Its stated goals are to "analyze and refute
RationalWiki
Number represented as a0+1/(a1+1/...)
fraction representation for a real number is finite if and only if it is a rational number. In contrast, the decimal representation of a rational number
Simple_continued_fraction
Expression of numbers as sequences of digits
71828182845904523536... π = 3.14159265358979323846... Every decimal representation of a rational number can be converted to a fraction by converting it into a
Decimal_representation
Group theory concept
Then F is the real numbers or the complex numbers, and there is a rational representation of G giving rise to ρ by restriction. Mostow rigidity theorem Local
Superrigidity
finite-dimensional rational representation arises as the restriction to the subgroup of a finite-dimensional rational representation of the whole group
Observable_subgroup
Theorem in ring theory
on regular rings are Cohen–Macaulay. In other words, if V is a rational representation of a linearly reductive group G over a field k, then there exist
Hochster–Roberts_theorem
Sporadic simple group
that if a finite group has an absolutely irreducible faithful rational representation of dimension 23 and has no subgroups of index 23 or 24 then it
Conway_group_Co3
Plane curve: conic section
a\cosh t,\\y=b\sinh t,\end{cases}}\qquad t\in \mathbb {R} .} As a rational representation { x = ± a t 2 + 1 2 t , y = b t 2 − 1 2 t , t > 0 {\displaystyle
Hyperbola
Decimal representation of a number whose digits are periodic
that a number is rational if and only if its decimal representation is repeating or terminating. For example, the decimal representation of 1/3 becomes
Repeating_decimal
Notation for expressing numbers
official representation of the number zero. Ideally, a numeral system will: Represent a useful set of numbers (e.g. all integers, or rational numbers)
Numeral_system
Theorem in economics
famous example of a utility representation theorem is the Von Neumann–Morgenstern utility theorem, which shows that any rational agent has a utility function
Utility representation theorem
Utility_representation_theorem
ratio of an integer to a non-zero integer. All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real numbers (
List_of_types_of_numbers
Representation of a curve by a function of a parameter
involving only rational functions (that is fractions of two polynomials) are preferred, if they exist. In the case of the circle, such a rational parameterization
Parametric_equation
Ecological rationality is a particular account of practical rationality, which in turn specifies the norms of rational action – what one ought to do in
Ecological_rationality
tensor products of the fundamental representation and its dual. The irreducible factors of such a representation are also called tensor representations
Tensor_representation
Representation of an algebra as a free module
G} is a linearly reductive group and V {\displaystyle V} is a rational representation of G {\displaystyle G} , then K [ V ] {\displaystyle K[V]} is finitely-generated
Hironaka_decomposition
inequalities with rational coefficients, such that the encoding length of each inequality (i.e., the binary encoding length of all rational numbers appearing
N-dimensional_polyhedron
Base-16 numeric representation
decimal for representing rational numbers since a larger proportion lies outside its range of finite representation. All rational numbers finitely representable
Hexadecimal
Roots of multiple multivariate polynomials
basis. The rational univariate representation or RUR is a representation of the solutions of a zero-dimensional polynomial system over the rational numbers
System of polynomial equations
System_of_polynomial_equations
French architect and author (1814–1879)
the rational construction of the building. In Entretiens sur l'architecture, Viollet-le-Duc praised the Greek temple for its rational representation of
Eugène_Viollet-le-Duc
Used to count, measure, and label
decimal representation. For example, 0.999..., 1.0, 1.00, 1.000, ..., all represent the natural number 1. For real numbers that are not rational numbers
Number
Algebraic structure with addition, multiplication, and division
and division are defined and behave as the corresponding operations on rational numbers do. A field is thus a fundamental algebraic structure that is widely
Field_(mathematics)
focused on non-commutative algebras, and unified much earlier work on the representation theory of groups. These Index numbers are used for cross-referencing
Emmy_Noether_bibliography
American philosopher academic and author
Towards a Liberatory Epistemology, Rationality, Representation, and Race, The Virtue of Feminist Rationality, Rationality and Feminist Philosophy, and Epistemic
Deborah_Heikes
Number with a real and an imaginary part
field of rational numbers Q {\displaystyle \mathbb {Q} } (the polynomial x2 − 2 does not have a rational root, because √2 is not a rational number) nor
Complex_number
1818 book by Arthur Schopenhauer
The World as Will and Representation (WWR; German: Die Welt als Wille und Vorstellung), sometimes translated as The World as Will and Idea, is the central
The World as Will and Representation
The_World_as_Will_and_Representation
Soviet and Russian mathematician
Correcting Codes". Problemy Peredachi Informatsii. VD Goppa (1971). "Rational Representation of Codes and (L,g)-Codes". Problemy Peredachi Informatsii. VD Goppa
Valery_Goppa
Number system extending the rational numbers
theory, given a prime number p, the p-adic numbers form an extension of the rational numbers that is distinct from the real numbers, though with some similar
P-adic_number
Method of representing curves and surfaces in computer graphics
Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing
Non-uniform_rational_B-spline
Number that is not a ratio of integers
mathematics, the irrational numbers are all the real numbers that are not rational numbers; that is, irrational numbers are those that cannot be expressed
Irrational_number
theorem remains true if "rational" and "cyclic subgroup" are replaced with "integer" and "elementary subgroup". In Linear Representation of Finite Groups Serre
Artin's theorem on induced characters
Artin's_theorem_on_induced_characters
Sporadic simple group
that if a finite group has an absolutely irreducible faithful rational representation of dimension 23 and has no subgroups of index 23 or 24 then it
Conway_group_Co2
Certain functors from the category of modules over a fixed commutative ring to itself
cells, then Sλ(V) is an irreducible GL(V)-representation of highest weight λ. In fact, any rational representation of GL(V) is isomorphic to a direct sum
Schur_functor
Ratio of two numbers
rational number (for example 2 2 {\displaystyle \textstyle {\frac {\sqrt {2}}{2}}} ), or even do not represent any number (for example the rational fraction
Fraction
Function with unusual fractal properties
+a_{n}}}}.} A rational number x {\displaystyle x} has a terminating continued-fraction representation [ a 0 ; a 1 , a 2 , … , a m ] {\displaystyle
Minkowski's question-mark function
Minkowski's_question-mark_function
Concept in mathematics
} is the left regular representation of G. The representation π {\displaystyle \pi } defined above is a rational representation: for each vector v in
Equivariant_sheaf
Figure-eight-shaped curve on a sphere
can be represented exactly by a 3D rational Bézier segment of degree 4, and there is an infinite family of rational Bézier control points generating that
Viviani's_curve
rationals or over the local field Q p {\displaystyle \mathbb {Q} _{p}} , suggesting that there is no easy way to construct the Artin representation explicitly
Artin_conductor
Number expressed in the base-2 numeral system
(zero) and 1 (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient
Binary_number
Term denoting the human agent of economic decisions
Trade-off talking rational economic person (TOTREP) is one term, among others, used to denote, in the field of choice analysis, the rational, human agent of
Trade-off talking rational economic person
Trade-off_talking_rational_economic_person
Major type of automorphic form in mathematics
:{\textrm {GL}}_{g}(\mathbb {C} )\rightarrow {\textrm {GL}}(V)} be a rational representation, where V {\displaystyle V} is a finite-dimensional complex vector
Siegel_modular_form
Function that is discontinuous at rationals and continuous at irrationals
textbook on Riemann's notion of integration. Since every rational number has a unique representation with coprime (also termed relatively prime) p ∈ Z {\displaystyle
Thomae's_function
Development of linear transformations forming the Lorentz group
ω2=-c2. He concluded that this is the principal ingredient for a rational representation of the group of Lorentz transformations: V = Q 1 v Q 2 T 1 T 2
History of Lorentz transformations
History_of_Lorentz_transformations
Capacity for consciously making sense of things
sometimes used to refer to rationality, although the latter is more about its application. Reasoning involves using more-or-less rational processes of thinking
Reason
Paradox about the perception of probability
If that much is known about the execution of the lottery, it is then rational to accept that some ticket will win. Suppose that an event is considered
Lottery_paradox
Four-dimensional number system
For comparison, the natural numbers, N , {\displaystyle \mathbb {N} ,} rational numbers, Q , {\displaystyle \mathbb {Q} ,} and real numbers, R , {\displaystyle
Quaternion
Study of rational collective decision-making
theory is a branch of welfare economics that seeks to extend the theory of rational choice to collective decision-making. Social choice studies the behavior
Social_choice_theory
Binary tree of rational numbers
vertices correspond one-to-one to the positive rational numbers. The tree is rooted at the number 1, and any rational number q expressed in simplest terms as
Calkin–Wilf_tree
Rational Polynomial Coefficients (RPCs) provide a compact representation of a ground-to-image geometry, allowing photogrammetric processing without requiring
Rational polynomial coefficient
Rational_polynomial_coefficient
Ordered binary tree of rational numbers
one by a shorter continued fraction shows that every rational number has a unique representation in which the last coefficient is greater than one. Then
Stern–Brocot_tree
Formal language that can be expressed using a regular expression
science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression
Regular_language
Rational-number approximation of a real number
by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers
Diophantine_approximation
Set of data types that represent numbers in a given programming language
tower conceptually "sits on" a more fundamental type, so an integer is a rational number and a number, but the converse is not necessarily true, i.e. not
Numerical_tower
character on a finite group is a rational linear combination of characters induced from cyclic subgroups. 3. Artin representation is used in the definition
Glossary of representation theory
Glossary_of_representation_theory
Mathematical arithmetic dynamics function
Galois representation attached to f {\displaystyle f} with basepoint α {\displaystyle \alpha } . Arboreal representations attached to rational functions
Arboreal Galois representation
Arboreal_Galois_representation
Positional numeral system
dyadic rationals play in binary numbers, providing a possibility to multiply. Other numbers have standard representations in base-φ, with rational numbers
Golden_ratio_base
In mathematics, the rational normal curve is a smooth, rational curve C of degree n in projective n-space Pn. It is a simple example of a projective variety;
Rational_normal_curve
established that rational Bézier and rational B-spline based curve representation schemes can be combined with dual quaternion representation of spatial displacements
Rational_motion
Type of monoidal category
of rational conformal field theory. In the context of quantum field theory, modular tensor categories are used to store algebraic data for rational conformal
Modular_tensor_category
Each semi-simple algebraic group is geometrically reductive
unipotent radical is trivial). For any non-zero invariant vector in a rational representation of G, there is an invariant homogeneous polynomial that does not
Haboush's_theorem
Government system where political power lies with the people
distinguished:[need quotation to verify] a cognitive effect (competence to make rational choices, better information-processing) an ethical effect (support of democratic
Democracy
In logic, a rational consequence relation is a non-monotonic consequence relation satisfying certain properties listed below. A rational consequence relation
Rational_consequence_relation
G. In the setting of Sato, G is an algebraic group and V is a rational representation of G which has a (nonempty) open orbit in the Zariski topology
Prehomogeneous_vector_space
Number in base-10 numeral system
point in the decimal representation of a number, the same string of digits starts repeating indefinitely, the number is rational. or, dividing both numerator
Decimal
trivially a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers
List_of_numbers
the deep skies, a perspective representation of the Carpathian Mountains, hope for a better future, the color of rational reasoning, freshness of the spirit
Rusyn_flag
Mathematical terminology
term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring in representation theory, but
Galois_representation
Problem in number theory
sums of non-negative cubes and sums of rational cubes. All integers have a representation as a sum of rational cubes, but it is unknown whether the sums
Sums_of_three_cubes
a face (mirror) of the Goursat tetrahedron. Each edge is labeled by a rational value corresponding to the reflection order, being π/dihedral angle. A
Goursat_tetrahedron
Special function in mathematics
between the Hurwitz zeta function and the Lommel functions. When a is a rational number, Hurwitz's formula leads to the following functional equation: For
Hurwitz_zeta_function
Branch of elementary mathematics
decimal fractions. Not all rational numbers have a finite representation in the decimal notation. For example, the rational number 1 3 {\displaystyle {\tfrac
Arithmetic
Fully simplified fraction
to ensure the fraction is actually irreducible. Every rational number has a unique representation as an irreducible fraction with a positive denominator
Irreducible_fraction
Curve defined as zeros of polynomials
Wikipedia's list of curves are rational and hence have similar rational parameterizations. Rational plane curves are rational curves embedded into P 2 {\displaystyle
Algebraic_curve
British mathematician
the London Mathematical Society for his article Baby Verma modules for rational Cherednik algebras. In 2008 he was awarded a 5-year EPSRC Leadership Fellowship
Iain_Gordon
Array in complex analysis
analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants Rm, n to a given complex formal power series. Certain
Padé_table
Scheduling algorithm, the first piece of data inserted into a queue is processed first
Representation of a FIFO queue
FIFO (computing and electronics)
FIFO_(computing_and_electronics)
irrationals as a periodic sequence of rational or integer numbers has been solved. However, the periodic representation does not derive from an algorithm
Hermite's_problem
Open problem on 3x+1 and x/2 functions
as when the domain is the integers: an 'even' such rational is divided by 2; an 'odd' such rational is multiplied by 3 and then 1 is added. A closely related
Collatz_conjecture
Multivariate functions can be written using univariate functions and summing
In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous
Kolmogorov–Arnold representation theorem
Kolmogorov–Arnold_representation_theorem
relational language to represent degrees of belief that should be held by a rational agent. Conditional probability values represent degrees of belief based
Pure_inductive_logic
2004 work by Daniel C. Hallin and Paolo Mancini
majoritarian), type of pluralism (individual vs. organized), degree of rational-legal authority, and degree of pluralism (moderate vs. polarized) with
Comparing_Media_Systems
Mathematical framework
functional, known as the constrained functional, provides a complete representation of all possible interpolants. By varying g ( x ) {\displaystyle g(\mathbf
Theory of functional connections
Theory_of_functional_connections
Result concerning properties of Galois representations associated with modular forms
elliptic curve). In particular for p ≫ NN1+ε, the mod p Galois representation of a rational newform cannot be isomorphic to an irrational newform of level
Ribet's_theorem
Anscombe-Aumann framework, Anscombe-Aumann approach, or Anscombe-Aumann representation theorem) is a framework to formalizing subjective expected utility (SEU)
Anscombe-Aumann subjective expected utility model
Anscombe-Aumann_subjective_expected_utility_model
Software design modeling notation
Booch's company Rational Software purchasing Ivar Jacobson's Objectory company and merging their model into the UML. At the time Rational and Objectory
Unified_Modeling_Language
Type of representation in representation theory
the representation is quaternionic. All representation of the symmetric groups are real (and in fact rational), since we can build a complete set of irreducible
Real_representation
Economics theorem
model (also known as Savage's framework, Savage's axioms, or Savage's representation theorem) is a formalization of subjective expected utility (SEU) developed
Savage's subjective expected utility model
Savage's_subjective_expected_utility_model
Economic model of personal preferences
variable. A basic assumption in classic economics is that the choices of a rational person choices are guided by a preference relation, which can usually be
Random_utility_model
integers and rationals. OpenLisp: supports arbitrary precision integer numbers. Perl: The bignum and bigrat pragmas provide BigNum and BigRational support
List of arbitrary-precision arithmetic software
List_of_arbitrary-precision_arithmetic_software
maps, the decomposition theorem also applies to Chow motives. Consider a rational morphism f : X → P 1 {\displaystyle f:X\rightarrow \mathbb {P} ^{1}} from
Decomposition theorem of Beilinson, Bernstein and Deligne
Decomposition_theorem_of_Beilinson,_Bernstein_and_Deligne
RATIONAL REPRESENTATION
RATIONAL REPRESENTATION
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Animated; Rational
Girl/Female
Indian
Optional
Girl/Female
Hindu, Indian
Rational
Boy/Male
Tamil
Rational
Boy/Male
Arabic, Muslim
National Leader
Boy/Male
Indian
Talker, Speaker, Rational
Boy/Male
English
National protector.
Girl/Female
Hindu, Indian
Rational
Boy/Male
Hindu, Indian, Tamil
Revolving; Pearl
Girl/Female
Christian, German, Greek, Hebrew
Noble; Kind; Rational; Great Happiness
Boy/Male
Hindu
Rational
Boy/Male
Tamil
Rational
Boy/Male
Muslim/Islamic
Categorical (decision) talker, speaker, rational
Boy/Male
Indian, Tamil
National Boy; Lord Krishna
Boy/Male
Muslim
Talker, Speaker, Rational
Boy/Male
American, Anglo, British, English, Teutonic
National Protector; Wealthy Defender
Boy/Male
Gujarati, Hindu, Indian
Lord of Pleasure
Boy/Male
Hindu, Indian
National Player
Boy/Male
Hindu
Rational
Girl/Female
German, Greek
Noble; Kind; Rational
RATIONAL REPRESENTATION
RATIONAL REPRESENTATION
Surname or Lastname
English
English : variant of Warwick.English : metonymic occupational name for a maker of warrocks, wedges of timber that were used to tighten the joints in a scaffold.
Girl/Female
Bengali, Indian
Machine
Girl/Female
Indian, Punjabi, Sikh
Fortunate
Boy/Male
Hindu, Indian
Day
Boy/Male
Muslim/Islamic
One who is worthy of thanks deserving, commendable
Boy/Male
Muslim/Islamic
Slave of the Manifest
Boy/Male
British, Celtic, English, German, Hebrew, Swedish
Attached; Combined
Boy/Male
Bengali, Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Sanskrit, Sindhi, Tamil, Telugu, Traditional
Lord of Man; The King; The King of the Country
Boy/Male
Indian, Modern, Tamil
Truthful
Girl/Female
Muslim/Islamic
Laaibah is the prettiest women in all the jannats (heavens). She will be in
RATIONAL REPRESENTATION
RATIONAL REPRESENTATION
RATIONAL REPRESENTATION
RATIONAL REPRESENTATION
RATIONAL REPRESENTATION
a.
Given to foolish or visionary expectations; whimsical; fanciful; as, a notional man.
a.
Relatively small; inconsiderable; insignificant; as, a fractional part of the population.
adv.
In a rational manner.
v. t.
To supply with rations, as a regiment.
a.
Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man.
a.
Notional.
a.
Not rational; void of reason or understanding; as, brutes are irrational animals.
a.
Attached to one's own country or nation.
a.
Involving an option; depending on the exercise of an option; left to one's discretion or choice; not compulsory; as, optional studies; it is optional with you to go or stay.
a.
Having reason, or the faculty of reasoning; endowed with reason or understanding; reasoning.
a.
Relating to the reason; not physical; mental.
a.
Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula.
n.
The state of being national; national attachment; nationality.
a.
Involving surds; not capable of being expressed in rational numbers; radical; irrational; as, a surd expression or quantity; a surd number.
n.
A rational being.
a.
Of or pertaining to a nation; common to a whole people or race; public; general; as, a national government, language, dress, custom, calamity, etc.
a.
An explanation or exposition of the principles of some opinion, action, hypothesis, phenomenon, or the like; also, the principles themselves.
v. t.
To form a rational conception of.
a.
Fractional.
a.
Of or pertaining to fractions or a fraction; constituting a fraction; as, fractional numbers.