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In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Maps may be parameterized by a discrete-time or a continuous-time parameter.
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]
Hence, the fundamental group of the Cayley graph Γ(G) is isomorphic to the kernel of φ, the normal subgroup of relations among the generators of G. The extreme case is when G = {e}, the trivial group, considered with as many generators as F, all of them trivial; the Cayley graph Γ(G) is a bouquet of circles, and its fundamental group is F ...
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
The intersection graph of a circle packing is the graph having a vertex for each circle, and an edge for every pair of circles that are tangent. If the circle packing is on the plane, or, equivalently, on the sphere, then its intersection graph is called a coin graph ; more generally, intersection graphs of interior-disjoint geometric objects ...
SymPy includes features ranging from basic symbolic arithmetic to calculus, algebra, discrete mathematics, and quantum physics. It is capable of formatting the result of the computations as LaTeX code. [4] [5] SymPy is free software and is licensed under the 3-clause BSD. The lead developers are Ondřej Čertík and Aaron Meurer.
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points , lines , planes , circles , spheres , polygons , and so forth.
The book presents research-level mathematics, and is aimed at professional mathematicians interested in this and related topics. Reviewer Frédéric Mathéus describes the level of the material in the book as "both mathematically rigorous and accessible to the novice mathematician", presented in an approachable style that conveys the author's love of the material. [6]