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





any mathematical expression



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






Setup(mathematicalnotation = true);



First, set prefixes for identifying anticommutative and noncommutative variables.

Setup(anticommutativeprefix = Q, noncommutativeprefix = Z);



Inverse(Z1) * Z1;



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

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



The multiplicative inverses of these objects are:

map(Inverse, (5));



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

map(Inverse, (6));




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