A **Turing computable function**
is a function of an integral variable or a real or computable variable,
computable predicates that can be computed by a Turing
machine. Turing machines are discussed in the mathematical an logical
portion of article.

A **polynomial**
is a mathematical expression of one or more algebraic terms each of which
consists of a constant multiplied by one or more variables raised to a
nonnegative integral power. The general form of a polynomial is a
+ b** n** +c

The term **'difference'**
came about from the principle used to evaluate such expressions: a mathematical
technique called the Method of Differences, on which Babbage had carried
out important work. By this technique all polynomial evaluation could,
in principle, be reduced to addition.

**Subroutines** are
sets of instructions for computing commonly used functions that can be
called by the main program in the course of its execution.

**Loops** are repeated
applications of a series of instructions.

**Jumps **are conditional
branches of a program that allow it to move to another section of instructions
when the if clause (antecedent) is satisfied.

**Harmonic analysis **is
a mathematical procedure using integration to split up a complex waveform
into several simple waveforms of which it is composed.

The term **Isomorphic**
applies to mappings from one model to another model or set of objects as
well as one system to another such that all of the relevant relations are
preserved by the mapping. Isomorphic state changes are changes that
preserve a structure mapping from one thing to another across state changes.