compute the Grassmannian parity, as 0, 1 or undefined, according to whether an expression is commutative, anticommutative or noncommutative

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Physics[GrassmannParity] - compute the Grassmannian parity, as 0, 1 or undefined, according to whether an expression is commutative, anticommutative or noncommutative

	Calling Sequence
	GrassmannParity(expression)

Parameters

expression

algebraic expression, or relation between them, or a set or list of them

Description

•	The GrassmannParity command computes the Grassmannian parity of expression, that is, 0, 1 or undefined, according to whether expression is commutative, anticommutative or noncommutative. In this sense, the parity here is equivalent to the type.

Compatibility

•	The Physics[GrassmannParity] command was introduced in Maple 16.

•	For more information on Maple 16 changes, see Updates in Maple 16.

Examples

(1)

Set theta as an anticommutative prefix (see Setup)

$[anticommutativeprefix = {_lambda, theta}]$

(2)

(3)

The parity of (3) is 0 despite the presence of anticommutative variables: a product of two of them is overall commutative

(4)

A commutative function of commutative and anticommutative variables: its parity is zero

(5)

(6)

A taylor expansion as well as an exact expansion for it respectively performed with Gtaylor and ToFieldComponents

(7)

(8)

Note that the expansion performed with Gtaylor does not preserve the parity of (5) while the one performed with ToFieldComponents does:

(9)

(10)

The coefficient of order zero of both expansions preserves the parity; the difference appears with respect to the the coefficient of order 1

(11)

(12)

(13)

(14)

To understand this difference between the Taylor and the exact expansions performed with Gtaylor and ToFieldComponents see the expansion's definitions in the respective help pages