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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 name PARI is a pun about the project's early stages when the authors started to implement a library for "Pascal ARIthmetic" in the Pascal programming language (although they quickly switched to C), and after "pari de Pascal" (Pascal's Wager). [3] The first version of the gp calculator was originally called GPC, for Great Programmable ...
Graph showing the symmetry of the addition function Some forms of symmetry can be directly linked to commutativity. When a commutative operation is written as a binary function z = f ( x , y ) , {\displaystyle z=f(x,y),} then this function is called a symmetric function , and its graph in three-dimensional space is symmetric across the plane y ...
Aside from polynomial functions, tensors that act as functions of several vectors can be symmetric, and in fact the space of symmetric -tensors on a vector space is isomorphic to the space of homogeneous polynomials of degree on . Symmetric functions should not be confused with even and odd functions, which have a different sort of symmetry.
Windows Calculator, since Windows 98, uses arbitrary precision for basic operations (addition, subtraction, multiplication, division) and 32 digits of precision for advanced operations (square root, transcendental functions). SmartXML, a free programming language with integrated development environment (IDE) for mathematical calculations ...
The following polynomials in two variables X 1 and X 2 are symmetric: + + + + (+) as is the following polynomial in three variables X 1, X 2, X 3: . There are many ways to make specific symmetric polynomials in any number of variables (see the various types below).
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The cost of the solution produced by the algorithm is within 3/2 of the optimum. To prove this, let C be the optimal traveling salesman tour. Removing an edge from C produces a spanning tree, which must have weight at least that of the minimum spanning tree, implying that w(T) ≤ w(C) - lower bound to the cost of the optimal solution.