[permalink] [id link]

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

from
Wikipedia

## Some Related Sentences

Every and root

__Every__system must have

**a**class designated as "

__root__", with one

**of**its creation procedures designated as "

__root__procedure ".

__Every__non-negative real number

**a**has

**a**unique non-negative square

__root__, called the principal square

__root__, which

**is**denoted by, where √

**is**called the radical sign or radix

**.**

*

__Every____root__**of****a**monic**polynomial****whose****coefficients****are****algebraic**integers**is**itself an**algebraic**integer**.**__Every__nth

__root__

**of**unity z

**is**

**a**primitive ath

__root__

**of**unity for some

**a**where 1 ≤

**a**≤ n: if z < sup > 1 </ sup >

__Every__name lookup must either start with

**a**query to

**a**

__root__server or use information that was once obtained from

**a**

__root__server

**.**

__Every__element

**of**the Quran

**is**mathematically composed — the suras, the verses, the words, the number

**of**certain letters, the number

**of**words from the same

__root__, the number and variety

**of**divine names, the unique spelling

**of**certain words, the absence or deliberate alteration

**of**certain letters within certain words, and many other elements

**of**the Quran besides its content

**.**

__Every__pipe

**is**placed in the

__root__directory

**of**the named pipe filesystem ( NPFS ), mounted under the special path ( that

**is**,

**a**pipe named " foo " would have

**a**full path name

**of**

; Sherrington's First Law:

__Every__posterior spinal nerve__root__supplies**a**particular area**of**the skin, with**a**certain overlap**of**adjacent dermatomes**.**__Every__prime power ( except powers

**of**2 ) has

**a**primitive

__root__; thus the multiplicative group

**of**integers modulo p < sup > n </ sup > ( or equivalently, the unit group

**of**the ring )

**is**cyclic

**.**

Every and polynomial

__Every__output

**of**an encoder can be described by its own transfer function, which

**is**closely related to the generator

__polynomial__

**.**

__Every__

__polynomial__in can be factorized into polynomials that

**are**irreducible over F

**.**This factorization

**is**unique up to permutation

**of**the factors and the multiplication

**of**the factors by nonzero constants from F ( because the ring

**of**polynomials over

**a**field

**is**

**a**unique factorization domain

**whose**units

**are**the nonzero constant polynomials ).

__Every__delta operator ' has

**a**unique sequence

**of**" basic polynomials ",

**a**

__polynomial__sequence defined by three conditions:

*

__Every__irreducible closed subset**of**P < sup > n </ sup >( k )**of**codimension one**is****a**hypersurface ; i**.**e., the zero set**of**some homogeneous__polynomial__**.**
*

__Every__Jacobi-like__polynomial__sequence can have its domain shifted and / or scaled so that its interval**of**orthogonality**is**, and has Q
*

__Every__Laguerre-like__polynomial__sequence can have its domain shifted, scaled, and / or reflected so that its interval**of**orthogonality**is**, and has Q =
*

__Every__Hermite-like__polynomial__sequence can have its domain shifted and / or scaled so that its interval**of**orthogonality**is**, and has Q__Every__field and every

__polynomial__ring over

**a**field ( in arbitrarily many variables )

**is**

**a**reduced ring

**.**

In mathematics, an integer-valued

__polynomial__( also known as**a**numerical__polynomial__) P ( t )**is****a**__polynomial__**whose**value P ( n )**is**an integer for every integer n**.**__Every____polynomial__with integer**coefficients****is**integer-valued, but the converse**is**not true**.**

Every and equation

__Every__holomorphic function can be separated into its real and imaginary parts, and each

**of**these

**is**

**a**solution

**of**Laplace's

__equation__on R < sup > 2 </ sup >.

Nordau saw in Jewish Emancipation the result

**of**'**a**regular__equation__:__Every__man**is**born with certain rights ; the Jews**are**human beings, consequently the Jews**are**born to own the rights**of**man**.**__Every__infinitesimal region

**of**space time may have its own proper time that corresponds to the gravitational time dilation there, where electromagnetic radiation and matter may be equally affected, since they

**are**made

**of**the same essence ( as shown in many tests involving the famous

__equation__E = mc < sup > 2 </ sup >).

__Every__solution

**of**the second half g

**of**the

__equation__defines

**a**unique direction for x via the first half f

**of**the equations, while the direction for y

**is**arbitrary

**.**

__Every__second-order linear ODE with three regular singular points can be transformed into this

__equation__

**.**

__Every__second-order linear ODE on the extended complex plane with at most four regular singular points, such as the Lamé

__equation__or the hypergeometric differential

__equation__, can be transformed into this

__equation__by

**a**change

**of**variable

**.**

Every and whose

__Every__library borrower, or at least those

__whose__taste goes beyond the five-cent fiction rentals, knows what it

**is**to hear the librarian say apologetically, `` I'm sorry, but we don't have that book

**.**

Group actions / representations:

__Every__group G can be considered as**a**category with**a**single object__whose__morphisms**are**the elements**of**G**.**A functor from G to Set**is**then nothing but**a**group action**of**G on**a**particular set, i**.**e**.****a**G-set**.**__Every__field theory

**of**particle physics

**is**based on certain symmetries

**of**nature

__whose__existence

**is**deduced from observations

**.**

__Every__cycle climaxes in the arrival

**of**The Leveler,

__whose__approach ( and fall )

**is**heralded by an ominous comet that appears in the sky

**.**

__Every__rational number / has two closely related expressions as

**a**finite continued fraction,

__whose__

**coefficients**can be determined by applying the Euclidean algorithm to

**.**

__Every__congruence relation has

**a**corresponding quotient structure,

__whose__elements

**are**the equivalence classes ( or congruence classes ) for the relation

**.**

*

__Every__connected graph G admits**a**spanning tree, which**is****a**tree that contains every vertex**of**G and__whose__edges**are**edges**of**G**.**__Every__morphism in

**a**concrete category

__whose__underlying function

**is**injective

**is**

**a**monomorphism ; in other words, if morphisms

**are**actually functions between sets, then any morphism which

**is**

**a**one-to-one function will necessarily be

**a**monomorphism in the categorical sense

**.**

__Every__family head in the Mafia selects

**a**man

__whose__characteristics already make him look approachable

**.**

She was raised there by her mother, Ellen Simmons,

__whose__Sioux name was Taté Iyòhiwin (__Every__Wind or Reaches for the Wind ).
*

__Every__Parliament constituted in conformity with the laws**of****a**sovereign State__whose__population it represents and on__whose__territory it functions may request affiliation to the Inter-Parliamentary Union**.**
" A man's home

**is**his castle "**is**translated in Gor as, "__Every__man**is**an Ubar within the circle**of**his sword " ( The Ubar**is****a**war-leader,**a**General who takes power at**a**time**of**crisis, and__whose__rule**is**tantamount to tyrant until the crisis**is**resolved**.**
During this period he lived with the French poet Pierre Martory,

__whose__books__Every__Question but One ( 1990 ), The Landscape Is behind the door ( 1994 ) and The Landscapist he has translated ( 2008 ), as he has Jean Perrault ( Camouflage ), Max Jacob ( The Dice Cup ), Pierre Reverdy and Raymond Roussel**.**__Every__governor since Ronald Reagan in 1968 has been subject to

**a**recall effort, but Gray Davis was the first governor

__whose__opponents gathered the necessary signatures to qualify for

**a**special election

**.**

__Every__artist she showed the script to had declined to take on the project, so it was offered to aspiring artist Arthur Adams,

__whose__samples had been given to editor Carl Potts and Nocenti, his assistant editor, by editor Al Milgrom

**.**

*

__Every__integrable subbundle**of**the tangent bundle — that**is**, one__whose__sections**are**closed under the Lie bracket — also defines**a**Lie algebroid**.**0.825 seconds.