compute the inverse of an object with respect to noncommutative products - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Physics : Physics/Inverse

Physics[Inverse] - compute the inverse of an object with respect to noncommutative products

Calling Sequence

Inverse(f)

Parameters

f

-

any mathematical expression

Description

• 

The Inverse command, when applied to an object, represents the object's (noncommutative) multiplicative inverse; that is, Inverse(Z) * Z = Z * Inverse(Z) = 1, where * herein represents the Physics[*] product, whose commutativity depends on the operands (see also type, commutative).

• 

The %Inverse command is the inert form of Inverse; that is, it represents the same mathematical operation while displaying the operation unevaluated. To evaluate the operation, use the value command.

• 

The results returned by Inverse are constructed as follows:

  

- If f is of commutative type, then return 1f.

  

- If f is a matrix, then return its inverse.

  

- If f is equal to Inverse(g) for some g, then return g.

  

- If f is a noncommutative product, then distribute:InverseA*BInverseB*InverseA.

  

- If f is a * (commutative) product, then distribute:InverseA*BInverseA*InverseB.

  

- Otherwise, return the unevaluated expression Inversef.

• 

All noncommutative products introduced by Inverse have their operands sorted and normalized automatically by the Physics[*] operator. This ensures that the basic simplifications and identities for these products are taken into account in the returned results.

• 

A `print/Inverse` procedure makes the display of this function appear as a power, as in

Inverse(Q);

InverseQ

(1)

Examples

with(Physics):

Setup(mathematicalnotation = true);

mathematicalnotation=true

(2)

First, set prefixes for identifying anticommutative and noncommutative variables.

Setup(anticommutativeprefix = Q, noncommutativeprefix = Z);

anticommutativeprefix=Q,noncommutativeprefix=Z

(3)

Inverse(Z1) * Z1;

1

(4)

Consider now the list of objects of commutative, anticommutative, and noncommutative types.

[a, Inverse(Q), Q1 * Z2, A * B, a * (Q1 * Q2)];

a,InverseQ,Q1Z2,AB,aQ1Q2

(5)

The multiplicative inverses of these objects are:

map(Inverse, (5));

1a,Q,InverseZ2InverseQ1,1AB,InverseQ1InverseQ2a

(6)

In turn out that the multiplicative inverses of these inverses are the original objects themselves.

map(Inverse, (6));

a,InverseQ,Q1Z2,AB,aQ1Q2

(7)

 

See Also

Physics, Physics conventions, Physics examples, Physics Updates, Tensors - a complete guide, Mini-Course Computer Algebra for Physicists, Physics[*], Setup, type/anticommutative, type/noncommutative