NonCommutativeMultiply

The ordered product, for units that anticommute. cannot host one: `Multiply` is declared commutative, so canonicalisation sorts its operands before any handler runs and the sign is lost.

Wolfram LanguageNonCommutativeMultiply↗

NonCommutativeMultiply(a, b, …)the product of the operands, in the order written

GeometricProduct(a, b, …)alias, for the geometric-algebra reading

a \otimes binfix alias ()

Domain: Hypercomplex algebra

Details

• Wolfram spells this head the same way (infix `**`), keeping it apart from `Times`; matrix multiplication is likewise its own head, `Dot`
• On the COMMUTING families it simply agrees with , so it is safe to use everywhere
• A tensor product of two scalars is their product, so is
• Associative across mixed families: the commutation factor is a bicharacter
• Juxtaposition carries the sign on its own -- is caught before `Multiply`'s commutative sort can reach it
• An explicit or is not: it parses straight to a sorted `Multiply`, so it REFUSES two distinct anticommuting units rather than assert a sign it cannot justify

Examples

See also: Norm, Basis, Quaternions