As with integers, operations related to division are key to many computations with polynomials. Mathematica includes not only highly optimized univariate polynomial-division ...

MultiplicativeOrder[k, n] gives the multiplicative order of k modulo n, defined as the smallest integer m such that k^m \[Congruent] 1 mod n. MultiplicativeOrder[k, n, {r_1, ...

Reduce[expr, vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers. Reduce[expr, vars, dom] does the reduction over the ...

Some integer functions. The remainder on dividing 17 by 3. The integer part of 17/3.

 

In two decades of intense algorithmic development, Mathematica has established a new level of numerical computation. Particularly notable are its many original highly ...

Mathematica's symbolic architecture allows it to represent any equation as a symbolic expression that can be manipulated using any of Mathematica's powerful collection of ...

DifferentialRootReduce[expr, x] attempts to reduce expr to a single DifferentialRoot object as a function of x.DifferentialRootReduce[expr, {x, x_0}] takes the initial ...

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

NSolve[expr, vars] attempts to find numerical approximations to the solutions of the system expr of equations or inequalities for the variables vars. NSolve[expr, vars, ...