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SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3] SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies.
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces .
OGRePy [34] is Python port of the Mathematica package OGRe (see § Software for use with Mathematica), released in 2024 for Python 3.12 and later. It utilizes SymPy for symbolic computations and Jupyter as a notebook interface. OGRePy allows calculating arbitrary tensor formulas using any combination of addition, multiplication by scalar, trace ...
An inner product space is a normed vector space whose norm is the square root of the inner product of a vector and itself. The Euclidean norm of a Euclidean vector space is a special case that allows defining Euclidean distance by the formula d ( A , B ) = ‖ A B → ‖ . {\displaystyle d(A,B)=\|{\overrightarrow {AB}}\|.}
In computer science, symbolic execution (also symbolic evaluation or symbex) is a means of analyzing a program to determine what inputs cause each part of a program to execute. An interpreter follows the program, assuming symbolic values for inputs rather than obtaining actual inputs as normal execution of the program would.
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,
It is the prototypical example of an F-space that, for most reasonable measure spaces, is not locally convex: in or ([,]), every open convex set containing the function is unbounded for the -quasi-norm; therefore, the vector does not possess a fundamental system of convex neighborhoods.