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searching for Nth root 43 found (100 total)

alternate case: nth root

Root of unity (5,947 words) [view diff] exact match in snippet view article find links to article

when n is a multiple of the (positive) characteristic of the field. An nth root of unity, where n is a positive integer, is a number z satisfying the equation

Radical extension (775 words) [view diff] exact match in snippet view article find links to article

obtained by a tower of field extensions, each generated by adjoining an nth root of an element from the previous field. A simple radical extension is a

Discrete Fourier transform over a ring (3,992 words) [view diff] exact match in snippet view article find links to article

an integer, and let α ∈ R {\displaystyle \alpha \in R} be a principal nth root of unity, defined by: The discrete Fourier transform maps an n-tuple (

Cyclotomic unit (364 words) [view diff] exact match in snippet view article find links to article

field which is the product of numbers of the form (ζa n − 1) for ζ n an nth root of unity and 0 < a < n. The cyclotomic units form a subgroup of finite

Ernst Kummer (630 words) [view diff] exact match in snippet view article find links to article

that is, extensions generated by adjoining an nth root to a field already containing a primitive nth root of unity. This is a significant extension of

Kummer theory (1,970 words) [view diff] exact match in snippet view article find links to article

that the characteristic of K doesn't divide n, then adjoining to K the nth root of any element a of K creates a Kummer extension (of degree m, for some

Brauer group (2,937 words) [view diff] exact match in snippet view article find links to article

K be a field in which n is invertible such that K contains a primitive nth root of unity ζ. For nonzero elements a and b of K, the associated cyclic algebra

Projective linear group (5,613 words) [view diff] exact match in snippet view article find links to article

and PSL(n, F) are isomorphic if and only if every element of F has an nth root in F. As an example, note that PGL(2, C) = PSL(2, C), but that PGL(2, R)

Peirce's criterion (2,863 words) [view diff] exact match in snippet view article find links to article

m = float(m) # Check number of observations: if N > 1: # Calculate Q (Nth root of Gould's equation B): Q = (n ** (n / N) * (N - n) ** ((N - n) / N)) /

Birch–Tate conjecture (207 words) [view diff] exact match in snippet view article find links to article

let N be the largest natural number such that the extension of F by the Nth root of unity has an elementary abelian 2-group as its Galois group. Then the

Cyclotomic polynomial (5,525 words) [view diff] no match in snippet view article find links to article

minimal polynomial over the field of the rational numbers of any primitive nth-root of unity ( e 2 i π / n {\displaystyle e^{2i\pi /n}} is an example of such

Gauss's lemma (number theory) (3,199 words) [view diff] exact match in snippet view article

{\mathfrak {p}}=|{\mathcal {O}}_{k}/{\mathfrak {p}}|} . Assume that a primitive nth root of unity ζ n ∈ O k , {\displaystyle \zeta _{n}\in {\mathcal {O}}_{k},}

CM-field (718 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {Q} (\zeta _{n})} , which is generated by a primitive nth root of unity. It is a totally imaginary quadratic extension of the totally

Michel Rolle (937 words) [view diff] exact match in snippet view article find links to article

published in 1690. In that book Rolle firmly established the notation for the nth root of a real number, and proved a polynomial version of the theorem that today

Algebraic integer (1,496 words) [view diff] exact match in snippet view article find links to article

{\alpha ^{2}}{k}}&{\text{otherwise}}\end{cases}}} If ζn is a primitive nth root of unity, then the ring of integers of the cyclotomic field Q ( ζ n ) {\displaystyle

Representation ring (977 words) [view diff] exact match in snippet view article find links to article

complex representation sending a generator of the group to a primitive nth root of unity. More generally, the complex representation ring of a finite abelian

Weil pairing (805 words) [view diff] exact match in snippet view article find links to article

be coprime to char(K) if char(K) > 0) such that K contains a primitive nth root of unity. Then the n-torsion on E ( K ¯ ) {\displaystyle E({\overline {K}})}

DFT matrix (2,115 words) [view diff] exact match in snippet view article find links to article

ω = e − 2 π i / N {\displaystyle \omega =e^{-2\pi i/N}} is a primitive Nth root of unity in which i 2 = − 1 {\displaystyle i^{2}=-1} . We can avoid writing

Convergent series (1,966 words) [view diff] exact match in snippet view article find links to article

is inconclusive, and the series may converge or diverge. Root test or nth root test. Suppose that the terms of the sequence in question are non-negative

Conductor (class field theory) (1,227 words) [view diff] exact match in snippet view article

_{n}\right)} , where ζ n {\displaystyle \zeta _{n}} denotes a primitive nth root of unity. If n is the smallest integer for which this holds, the conductor

Convergence tests (2,228 words) [view diff] exact match in snippet view article find links to article

converge absolutely, conditionally or diverge. This is also known as the nth root test or Cauchy's criterion. Let r = lim sup n → ∞ | a n | n , {\displaystyle

CORDIC (7,232 words) [view diff] case mismatch in snippet view article find links to article

Hongbing (January 2020). "GH CORDIC-Based Architecture for Computing Nth Root of Single-Precision Floating-Point Number". IEEE Transactions on Very Large

P-compact group (1,263 words) [view diff] exact match in snippet view article find links to article

group of order n, acting on Z p {\displaystyle \mathbb {Z} _{p}} via an nth root of unity.) Generalizing the rank 1 case, any finite complex reflection

List of Laplace transforms (574 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\operatorname {\Gamma } (q+1) \over s^{q+1}}} Re(s) > 0 Re(q) > −1 nth root t n ⋅ u ( t ) {\displaystyle {\sqrt[{n}]{t}}\cdot u(t)} 1 s 1 n + 1 Γ ⁡

Cyclic group (4,113 words) [view diff] exact match in snippet view article find links to article

of rotations by rational angles is countable, but still not cyclic. An nth root of unity is a complex number whose nth power is 1, a root of the polynomial

Braille pattern dots-126 (2,678 words) [view diff] exact match in snippet view article find links to article

Two-Cell Chinese Braille hu- -í/-ú/-ǘ, 时 shí Nemeth Braille radical index (nth root) sign, directly over indicator Gardner Salinas Braille 2 Algerian Braille

Determinant (14,375 words) [view diff] exact match in snippet view article find links to article

\det(A+B)\geq \det(A)+\det(B){\text{.}}} Brunn–Minkowski theorem implies that the nth root of determinant is a concave function, when restricted to Hermitian positive-definite

Transcendental number theory (3,907 words) [view diff] exact match in snippet view article find links to article

={\tfrac {1}{3}}+\sum _{k=1}^{\infty }10^{-k!}.} It can be shown that the nth root of λ (a Liouville number) is a U-number of degree n. This construction

Trace (linear algebra) (5,564 words) [view diff] exact match in snippet view article

{sl}}_{n}\oplus K} , but the splitting of the determinant would be as the nth root times scalars, and this does not in general define a function, so the determinant

List of representations of e (2,425 words) [view diff] exact match in snippet view article find links to article

4^{4}}{1\cdot 3^{6}\cdot 5}}\right)^{1/4}\cdots ,} where the nth factor is the nth root of the product ∏ k = 0 n ( k + 1 ) ( − 1 ) k + 1 ( n k ) , {\displaystyle

EDSAC (3,667 words) [view diff] exact match in snippet view article find links to article

logarithms; miscellaneous; print and layout; quadrature; read (input); nth root; trigonometric functions; counting operations (simulating repeat until

Burke–Schumann flame (1,736 words) [view diff] exact match in snippet view article find links to article

function of the first kind and λ n {\displaystyle \lambda _{n}} is the nth root of J 1 ( λ ) = 0. {\displaystyle J_{1}(\lambda )=0.} Solution can also

Special unitary group (5,721 words) [view diff] exact match in snippet view article find links to article

/n\mathbb {Z} } , and is composed of the diagonal matrices ζ I for ζ an nth root of unity and I the n × n identity matrix. Its outer automorphism group

Midsphere (2,932 words) [view diff] no match in snippet view article find links to article

numbers that have no exact closed-form expression using arithmetic and nth-root operations. Alternatively, a simpler numerical method for constructing

Competitive Lotka–Volterra equations (3,114 words) [view diff] exact match in snippet view article find links to article

− 1 and where γ = e i 2 π / N {\displaystyle \gamma =e^{i2\pi /N}} the Nth root of unity. Here cj is the jth value in the first row of the circulant matrix

Field (mathematics) (10,305 words) [view diff] exact match in snippet view article

studied number fields. They are of the form Q(ζn), where ζn is a primitive nth root of unity, i.e., a complex number ζ that satisfies ζn = 1 and ζm ≠ 1 for

Schönhage–Strassen algorithm (4,580 words) [view diff] exact match in snippet view article find links to article

b_{j}'=\theta ^{j}b_{j},} where θ N = − 1 {\displaystyle \theta ^{N}=-1} is the nth root, one sees that: C k = ∑ ( i , j ) : i + j = k ≡ ( mod N ( n ) ) a i b j

Laplace transform (9,453 words) [view diff] exact match in snippet view article find links to article

{Re} (s)>0} Re ⁡ ( q ) > − 1 {\displaystyle \operatorname {Re} (q)>-1} nth root t n ⋅ u ( t ) {\displaystyle {\sqrt[{n}]{t}}\cdot u(t)} 1 s 1 n + 1 Γ ⁡

Simple continued fraction (9,622 words) [view diff] exact match in snippet view article find links to article

a_{n}\right)^{1/n}=K_{0}=2.6854520010\dots } Paul Lévy proved that the nth root of the denominator of the nth convergent converges to Lévy's constant lim

Discrete Fourier transform (12,333 words) [view diff] exact match in snippet view article find links to article

e − i 2 π / N {\displaystyle \omega _{N}=e^{-i2\pi /N}} is a primitive Nth root of unity. For example, in the case when N = 2 {\displaystyle N=2} , ω N

Euclidean algorithm (15,349 words) [view diff] exact match in snippet view article find links to article

numbers of the form x + ωy, where x and y are integers, and ω = e2iπ/n is an nth root of 1, that is, ωn = 1. Although this approach succeeds for some values

Feed-Drum (2,960 words) [view diff] exact match in snippet view article find links to article

{\displaystyle k_{m,n}=R_{m,n}/a} , where R m , n {\displaystyle R_{m,n}} is the nth root of the Bessel function of order m , J n ( m , x ) {\displaystyle m,Jn(m

Germán Sierra (5,133 words) [view diff] exact match in snippet view article find links to article

mathematics using quantum groups with the deformation parameter as an Nth root of unity. Moreover, alongside Miguel A. Martín-Delgado, he employed real