''of numbers $\alpha_1,\ldots,\alpha_n$''
L(\alpha_1,\ldots,\alpha_n|H) = L(H) = \min |a_1 \alpha_1 + \cdots + a_n \alpha_n|
724 bytes (124 words) - 19:48, 20 November 2014
...1,\ldots,a_m$, i.e. the number of solutions in non-negative integers $x_1,\ldots,x_m$ of the equation
D(z; a_1,\ldots,a_m) = \sum_n D(n;a_1,\ldots,a_m) z^n = \frac{1}{\left({1-z^{a_1}}\right)\cdots\left({1-z^{a_m}}\right)}
1 KB (185 words) - 16:46, 23 November 2023
...in \mathbb{N}$ ($j = 1,\ldots,k$). The element is also denoted by $x_{n_1 \ldots n_k}$.
475 bytes (99 words) - 18:52, 12 October 2014
...dots,z_k)$ with integer coefficients such that the $n$-tuple $\langle a_1,\ldots,a_n\rangle$ satisfies the predicate $\mathcal P$ if and only if the Diophan
$$P(a_1,\ldots,a_n,z_1,\ldots,z_k)=0\label{*}\tag{*}$$
1 KB (165 words) - 16:59, 14 February 2020
...associates with a tensor with components $ a^{i_{1} \ldots i_{p}}_{j_{1} \ldots j_{q}} $, $ p,q \geq 1 $, the tensor
b^{i_{2} \ldots i_{p}}_{j_{1} \ldots j_{q - 1}}
1 KB (237 words) - 02:26, 9 September 2015
$i,j = 1,2,\ldots$. When $1 \le i,j \le n$, the Kronecker symbol $\delta^i_j$ has $n^2$ compo
...dots j_p}$ (when $p \ge 2$ often denoted by $\epsilon^{i_1\ldots i_p}_{j_1\ldots j_p}$) are called the ''components'' of the Kronecker symbol. An [[affine t
2 KB (340 words) - 19:43, 13 January 2016
...$n$-th ''continuant'', $K(n)$, of a sequence $\mathbf{a} = a_1,\ldots,a_n,\ldots$ is defined recursively by
...also be obtained by taking the sum of all possible products of the $a_1,\ldots,a_n$ in which any pairs of consecutive terms are deleted.
2 KB (265 words) - 13:41, 12 December 2013
...ts,a_n$ exists if $a_1 \cdots a_n \neq 0$. It is usually denoted by $[a_1,\ldots,a_n]$.
1) the least common multiple of $a_1,\ldots,a_n$ is a divisor of any other common multiple;
2 KB (334 words) - 20:19, 2 November 2016
$$L=\{P_0,\ldots,P_n,\ldots,F_0,\ldots,F_m,\ldots\}$$
where $P_0,\ldots,P_n,\ldots,$ are [[predicate symbol]]s and $F_0,\ldots,F_m,\ldots,$ are function symbols for each of which a number of argument places is giv
1 KB (219 words) - 10:43, 18 October 2016
...$, $(x_i)_1^n$, $(x_i)_{i\in\{1,\ldots,n\}}$, $(x_1,\ldots,x_n)$, or $x_1,\ldots,x_n$. The number $n$ is called its length ($n\geq0$), $x_i$ is called the $
...\ldots,x_n)$ is the empty set for $n=0$, and $(x_1,\ldots,x_{n+1})=\{(x_1,\ldots,x_n),\{x_{n+1}\}\}$.
1 KB (251 words) - 21:18, 12 January 2016
...he number $0,\pm1,\ldots,\pm(m-1)/2$ if $m$ is odd or the numbers $0,\pm1,\ldots,\pm(m-2)/2,m/2$ if $m$ is even.
428 bytes (69 words) - 12:43, 23 November 2014
...\ldots,y_n)$ then the concatenation $xy$ is the word $(x_1,\ldots,x_m,y_1,\ldots,y_n)$: the notations $x|y$, $x \cdot y$ are also used. Denoting the empty
653 bytes (113 words) - 21:39, 12 January 2016
(-1)^{s+t} \det A_{i_1\ldots i_k}^{j_1\ldots j_k}
...j_k$, of some square matrix $A$ of order $n$; $\det A_{i_1\ldots i_k}^{j_1\ldots j_k}$ is the determinant of the matrix of order $n-k$ obtained from $A$ by
1 KB (182 words) - 11:43, 9 February 2021
a_1 & b_1 & 0 & 0 & \ldots & 0 & 0 \\
c_1 & a_2 & b_2 & 0 & \ldots & 0 & 0 \\
897 bytes (116 words) - 18:31, 14 April 2018
(\forall x_1,\ldots,x_n)\,(A_1 \wedge \cdots \wedge A_p \rightarrow A)
where $A_1,\ldots,A_p$ and $A$ denote atomic formulae of the form
1 KB (193 words) - 07:40, 21 October 2016
\phi : x \mapsto F(a_1,\ldots,a_{k-1},x,a_{k+1},\ldots,a_n)
where $F$ is the symbol of a basic operation in $\Omega$ and $a_1,\ldots,a_n$ are fixed elements of the set $A$.
557 bytes (88 words) - 16:59, 23 November 2023
...e propositions such that the truth value of $P_i$ is equal to $V_i$, $i=1,\ldots,n$.
806 bytes (143 words) - 16:55, 2 November 2014
...x_{2n-1} \omega = x_1 \ldots x_i (x_{i+1} \ldots x_{i+n})\omega x_{i+n+1} \ldots x_{i+2n-1} \omega
for all $i=1,\ldots,n$.
1 KB (190 words) - 20:52, 7 January 2016
f_2(x) = f[f_1(x)] \,,\ \ldots\ ,\,f_n(x) = f[f_{n-1}(x)]
are called the second, $\ldots$, $n$-th iterates of $f(x)$. E.g., putting $f(x) = x^\alpha$ one obtains
994 bytes (158 words) - 17:21, 8 September 2017
...s that are often used (next to the operators $\int \ldots dx$ and $\{ x : \ldots \}$), in which $x$ is an operator variable:
$\forall x (\ldots)$, $\exists x (\ldots)$, that is, the universal and existential quantifiers;
2 KB (315 words) - 19:45, 2 March 2018