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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
GeoGebra is an interactive mathematics software suite for learning and teaching science, technology, engineering, and mathematics from primary school up to the university level. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions, all of which can be edited ...
As modular forms also satisfy a certain kind of functional equation with respect to the group action of the modular group, this Fourier series may be expressed in terms of =. So if f {\displaystyle f} is a modular form, then there are coefficients c ( n ) {\displaystyle c(n)} such that f ( z ) = ∑ n ∈ N c ( n ) q n {\displaystyle f(z)=\sum ...
In that sense a modular equation becomes the equation of a modular curve. Such equations first arose in the theory of multiplication of elliptic functions (geometrically, the n 2 -fold covering map from a 2- torus to itself given by the mapping x → n · x on the underlying group) expressed in terms of complex analysis .
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae , published in 1801.
modular multiplications, where is the number of digits in the binary representation of and is the number of ones in the binary representation of . If the required quadratic nonresidue z {\displaystyle z} is to be found by checking if a randomly taken number y {\displaystyle y} is a quadratic nonresidue, it requires (on average) 2 {\displaystyle ...
Online computer algebra system with step-by step solutions. Xcas/Giac: Bernard Parisse 2000 2000 1.9.0-99: May 2024: Free GPL: General CAS, also adapted for the HP Prime. Compatible modes for Maple, MuPAD and TI89 syntax. Symbolic spreadsheets, Giac library for use with other programs. ARM ports for some PDAs with Linux or WinCE [26] Yacas
Magma includes the KANT computer algebra system for comprehensive computations in algebraic number fields. A special type also allows one to compute in the algebraic closure of a field. Module theory and linear algebra; Magma contains asymptotically fast algorithms for all fundamental dense matrix operations, such as Strassen multiplication ...
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