Search results
Results from the WOW.Com Content Network
That implies that any two rational functions F and G, in the function field of the modular curve, will satisfy a modular equation P(F,G) = 0 with P a non-zero polynomial of two variables over the complex numbers. For suitable non-degenerate choice of F and G, the equation P(X,Y) = 0 will actually define the modular curve.
Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process.
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.
In mathematics, the modular group is the projective special linear group (,) of matrices with integer coefficients and determinant, such that the matrices and are identified. The modular group acts on the upper-half of the complex plane by linear fractional transformations .
Modular form theory is a special case of the more general theory of automorphic forms, which are functions defined on Lie groups that transform nicely with respect to the action of certain discrete subgroups, generalizing the example of the modular group () ().
lp_solve is a free software command line utility and library for solving linear programming and mixed integer programming problems. It ships with support for two file formats, MPS and lp_solve's own LP format. [1] User-defined formats are supported via its "eXternal Language Interface" (XLI) [2] lp_solve also supports translating between model ...
Finding a representation of the cyclic group of two elements over F 2 is equivalent to the problem of finding matrices whose square is the identity matrix.Over every field of characteristic other than 2, there is always a basis such that the matrix can be written as a diagonal matrix with only 1 or −1 occurring on the diagonal, such as
The matrices [e 1, ..., e n] are divisible by all non-zero linear forms in the variables X i with coefficients in the finite field F q. In particular the Moore determinant [0, 1, ..., n − 1] is a product of such linear forms, taken over 1 + q + q 2 + ... + q n – 1 representatives of ( n – 1)-dimensional projective space over the field.