A Diophantine polynomial system is an expression constructed with polynomial equations and inequalities combined using logical connectives and quantifiers where the variables ...

When a differential system has a certain structure, it is advantageous if a numerical integration method preserves the structure. In certain situations it is useful to solve ...

In a statement like x^4+x^2>0, Mathematica treats the variable x as having a definite, though unspecified, value. Sometimes, however, it is useful to be able to make ...

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

Mathematica provides powerful functions to compute state-feedback and estimator gains using pole-placement or optimal techniques. In addition, it has functions that directly ...

Resolve[expr] attempts to resolve expr into a form that eliminates ForAll and Exists quantifiers. Resolve[expr, dom] works over the domain dom. Common choices of dom are ...

General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...

Interpolation[{f_1, f_2, ...}] constructs an interpolation of the function values f_i, assumed to correspond to x values 1, 2, ... . Interpolation[{{x_1, f_1}, {x_2, f_2}, ...

JacobiSymbol[n, m] gives the Jacobi symbol (n/m).

MathieuCPrime[a, q, z] gives the derivative with respect to z of the even Mathieu function with characteristic value a and parameter q.