It is perhaps most easily thought of as an algebraic extension of multivariable polynomials—an extension that permits exponents to be arbitrary real numbers (rather than just non-negative integers) while requiring the independent variables to be strictly positive (so that division by zero and other inappropriate algebraic operations are not encountered).
Signomials are closed under addition, subtraction, multiplication, and scaling.
are non-negative integers, then the signomial becomes a polynomial whose domain is the positive orthant.
The term "signomial" was introduced by Richard J. Duffin and Elmor L. Peterson in their seminal joint work on general algebraic optimization—published in the late 1960s and early 1970s.
A recent introductory exposition involves optimization problems.
[1] Nonlinear optimization problems with constraints and/or objectives defined by signomials are harder to solve than those defined by only posynomials, because (unlike posynomials) signomials cannot necessarily be made convex by applying a logarithmic change of variables.