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circledast

Represents a binary operation symbol showing a circled asterisk, commonly used in abstract algebra and mathematical notation.

Overview

Serves as a specialized mathematical operator indicating specific binary operations, particularly in advanced algebra, group theory, and theoretical mathematics.

  • Often employed to denote convolution operations or special product structures
  • Useful in distinguishing between multiple binary operations in the same context
  • Frequently appears in academic papers and advanced mathematical texts where standard multiplication or addition symbols are insufficient
  • Provides a visually distinct alternative to similar circular operators like \odot or \otimes

Examples

Using circledast as a binary operation in abstract algebra.

G⊛H={gh:g∈G,h∈H}G \circledast H = \{gh : g \in G, h \in H\} 
G \circledast H = \{gh : g \in G, h \in H\}

Representing a special tensor product operation between vectors.

u⃗⊛v⃗=(u1v1u2v2u3v3)\vec{u} \circledast \vec{v} = \begin{pmatrix} u_1v_1 \\ u_2v_2 \\ u_3v_3 \end{pmatrix} 
\vec{u} \circledast \vec{v} = \begin{pmatrix} u_1v_1 \\ u_2v_2 \\ u_3v_3 \end{pmatrix}

Defining a custom binary operation in group theory.

(a⊛b)⊛c=a⊛(b⊛c)(a \circledast b) \circledast c = a \circledast (b \circledast c) 
(a \circledast b) \circledast c = a \circledast (b \circledast c)