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A causal network is an acyclic digraph arising from an evolution of a substitution system, and representing its history. The illustration above shows a causal network ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

The process of computing or obtaining an integral. A more archaic term for integration is quadrature.

A procedure for decomposing an N×N matrix A into a product of a lower triangular matrix L and an upper triangular matrix U, LU=A. (1) LU decomposition is implemented in the ...

A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...

A substitution system in which rules are used to operate on a string consisting of letters of a certain alphabet. String rewriting systems are also variously known as ...

Consider expressions built up from variables and constants using function symbols. If v_1, ..., v_n are variables and t_1, ..., t_n are expressions, then a set of mappings ...

The number 24 is equal to 4! (four factorial). A number puzzle asks to construct 24 in as many ways possible using elementary mathematical operations on three copies of the ...

The substitution of re^(itheta) for z in a polynomial p(z). p(z) is then plotted as a function of theta for a given r in the complex plane. By varying r so that the curve ...

If a sequence has the property that the block growth function B(n)=n+1 for all n, then it is said to have minimal block growth, and the sequence is called a Sturmian ...