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the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
It was originally known as "HECKE and Manin". After a short while it was renamed SAGE, which stands for ‘’Software of Algebra and Geometry Experimentation’’. Sage 0.1 was released in 2005 and almost a year later Sage 1.0 was released. It already consisted of Pari, GAP, Singular and Maxima with an interface that rivals that of Mathematica.
Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
Users submit queries and computation requests via a text field. WolframAlpha then computes answers and relevant visualizations from a knowledge base of curated, structured data that come from other sites and books.
It can be expressed by numerous definitions, for example "0 for negative inputs, output equals input for non-negative inputs". The term "ramp" can also be used for other functions obtained by scaling and shifting , and the function in this article is the unit ramp function (slope 1, starting at 0).
A drawing of the Petersen graph with slope number 3. In graph drawing and geometric graph theory, the slope number of a graph is the minimum possible number of distinct slopes of edges in a drawing of the graph in which vertices are represented as points in the Euclidean plane and edges are represented as line segments that do not pass through any non-incident vertex.
In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.
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