TeXipedia

dotplus

Represents addition with a centered dot, commonly used in mathematical notation to indicate specialized sum operations.

Overview

Appears in advanced mathematical contexts where a distinct addition operator is needed to differentiate from standard addition. Common applications include:

  • Abstract algebra and group theory to denote special binary operations
  • Mathematical logic and set theory for specialized operations
  • Computer science notation, particularly in formal specifications

The symbol combines the visual elements of both addition and multiplication, making it useful when describing hybrid or composite operations.

Examples

Expressing a combined addition and dot product operation in vector algebra.

a⃗∔b⃗=(a1+b1,a2+b2)⋅(1,1)\vec{a} \dotplus \vec{b} = (a_1 + b_1, a_2 + b_2) \cdot (1,1) 
\vec{a} \dotplus \vec{b} = (a_1 + b_1, a_2 + b_2) \cdot (1,1)

Defining a special binary operation in abstract algebra.

x∔y=(x+y)⋅zx \dotplus y = (x + y) \cdot z 
x \dotplus y = (x + y) \cdot z

Representing a combined element-wise addition and multiplication in matrix operations.

A∔B=(A+B)⋅CA \dotplus B = (A + B) \cdot C 
A \dotplus B = (A + B) \cdot C