HermiteDecomposition[m] gives the Hermite normal form decomposition of an integer matrix m.

x + y + z represents a sum of terms.

At the core of Mathematica is the foundational idea that everything —data, programs, formulas, graphics, documents—can be represented as symbolic expressions. And it is this ...

It may happen that a given ODE is not linear in y(x) but can be viewed as a linear ODE in x(y). In this case, it is said to be an inverse linear ODE. This is an inverse ...

Assumptions is an option for functions such as Simplify, Refine, and Integrate that specifies default assumptions to be made about symbolic quantities.

PrimePi[x] gives the number of primes \[Pi] (x) less than or equal to x.

SquareFreeQ, PrimePowerQ, KroneckerSymbol, ChineseRemainder and PrimitiveRoot have been added to the built-in Mathematica kernel functions. NextPrime and PreviousPrime are ...

NextPrime[n] gives the next prime above n.NextPrime[n, k] gives the k\[Null]^th prime above n.

Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...