Concepts inNote on the end game in homotopy zero curve tracking
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign (=), for example asserts that x+3 is equal to 5. The = symbol was invented by Robert Recorde (1510�), who considered that nothing could be more equal than parallel straight lines with the same length.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (Greek ὁμός = same, similar, and τόπος = place) if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions. An outstanding use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology. In practice, there are technical difficulties in using homotopies with certain spaces.
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Function (mathematics)
In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is –3, then the output is 9, and we may write f(–3) = 9.
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Hyperplane
A hyperplane is a concept in geometry. It is a generalization of the plane into a different number of dimensions. A hyperplane of an n-dimensional space is a flat subset with dimension n − 1. By its nature, it separates the space into two half spaces.
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Nonlinear system
This article describes the use of the term nonlinearity in mathematics. For other meanings, see nonlinearity (disambiguation). 50x40px This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations.
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Italic type
In typography, italic type is a cursive typeface based on a stylized form of calligraphic handwriting. Owing to the influence from calligraphy, such typefaces often slant slightly to the right. Different glyph shapes from roman type are also usually used—another influence from calligraphy. True italics are therefore distinct from oblique type, in which the font is merely distorted into a slanted orientation.
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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