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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.
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 ...
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 .
The Stanford Research Institute Problem Solver, known by its acronym STRIPS, is an automated planner developed by Richard Fikes and Nils Nilsson in 1971 at SRI International. [1] The same name was later used to refer to the formal language of the inputs to this planner.
Lis (Library of Iterative Solvers for linear systems; pronounced lis]) is a scalable parallel software library to solve discretized linear equations and eigenvalue problems that mainly arise from the numerical solution of partial differential equations using iterative methods.
It contains the modular group PSL(2, Z). Also closely related is the 2-fold covering group, Mp(2, R), a metaplectic group (thinking of SL(2, R) as a symplectic group). Another related group is SL ± (2, R), the group of real 2 × 2 matrices with determinant ±1; this is more commonly used in the context of the modular group, however.
In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function on the m -fold product of upper half-planes H {\displaystyle {\mathcal {H}}} satisfying a certain kind of functional equation .