The symbolic character of Mathematica makes possible a uniquely coherent approach to integer sequences, integrating functional forms, equations, generating functions, and ...

 

The equations of motion for a free rigid body whose center of mass is at the origin are given by the following Euler equations (see [MR99]). Two quadratic first integrals of ...

FactorSquareFreeList[poly] gives a list of square-free factors of a polynomial, together with their exponents.

MatrixExp[m] gives the matrix exponential of m. MatrixExp[m, v] gives the matrix exponential of m applied to the vector v.

Abs[z] gives the absolute value of the real or complex number z.

Supporting a large number of numerical integration methods for differential equations is a lot of work. In order to cut down on maintenance and duplication of code, common ...

PolynomialMod[poly, m] gives the polynomial poly reduced modulo m. PolynomialMod[poly, {m_1, m_2, ...}] reduces modulo all of the m_i.

PolynomialQuotient[p, q, x] gives the quotient of p and q, treated as polynomials in x, with any remainder dropped.

Finding the structure of polynomials written in expanded form. Here is a polynomial in two variables. This is the polynomial in expanded form.