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Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
An unpublished computational program written in Pascal called Abra inspired this open-source software. Abra was originally designed for physicists to compute problems present in quantum mechanics. Kespers Peeters then decided to write a similar program in C computing language rather than Pascal, which he renamed Cadabra. However, Cadabra has ...
Concretely, in the case where the vector space has an inner product, in matrix notation these can be thought of as row vectors, which give a number when applied to column vectors. We denote this by V ∗ := Hom ( V , K ) {\displaystyle V^{*}:={\text{Hom}}(V,K)} , so that α ∈ V ∗ {\displaystyle \alpha \in V^{*}} is a linear map α : V → K ...
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]
Scientific notation; Set-builder notation; Shriek map; Smooth maximum; Software calculator; Steinhaus–Moser notation; Summation; Symbolic language (mathematics) Symbolic language (programming) Symbols of grouping
Nim: bigints and multiple GMP bindings. OCaml: The Num library supports arbitrary-precision integers and rationals. OpenLisp: supports arbitrary precision integer numbers. Perl: The bignum and bigrat pragmas provide BigNum and BigRational support for Perl. PHP: The BC Math module provides arbitrary precision mathematics.
Ricci calculus, and index notation more generally, distinguishes between lower indices (subscripts) and upper indices (superscripts); the latter are not exponents, even though they may look as such to the reader only familiar with other parts of mathematics.
For example, consider the multi-view model [32] which is a probabilistic latent variable model. In this model, the generation of samples are posited as follows: there exists a hidden random variable that is not observed directly, given which, there are several conditionally independent random variables known as the different "views" of the ...