Search results
Results from the WOW.Com Content Network
This was considered a minor step compared to the others for smaller discrete log computations. However, larger discrete logarithm records [1] [2] were made possible only by shifting the work away from the linear algebra and onto the sieve (i.e., increasing the number of equations while reducing the number of variables).
is a non-degenerate bilinear form, that is, : is a map which is linear in both arguments, making it a bilinear form. By ϕ {\displaystyle \phi } being non-degenerate we mean that for each v ∈ V {\displaystyle v\in V} such that v ≠ 0 {\displaystyle v\neq 0} , there is a u ∈ V {\displaystyle u\in V} such that
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Numerical methods for ordinary differential equations approximate solutions to initial value problems of the form ′ = (,), =.. The result is approximations for the value of () at discrete times : = +, where is the time step (sometimes referred to as ) and is an integer.
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [ 1 ] [ 2 ] [ 3 ] On an expression or formula calculator , one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
Note that, since x + y is a vector and α is a multi-index, the expression on the left is short for (x 1 + y 1) α 1 ⋯(x n + y n) α n. Leibniz formula For smooth functions f {\textstyle f} and g {\textstyle g} , ∂ α ( f g ) = ∑ ν ≤ α ( α ν ) ∂ ν f ∂ α − ν g . {\displaystyle \partial ^{\alpha }(fg)=\sum _{\nu \leq \alpha ...
For example, in 3-D Euclidean space and using Cartesian coordinates; the coordinate vector A = (A 1, A 2, A 3) = (A x, A y, A z) shows a direct correspondence between the subscripts 1, 2, 3 and the labels x, y, z. In the expression A i, i is interpreted as an index ranging over the values 1, 2, 3, while the x, y, z subscripts are only labels ...