tensor/conj

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tensor[conj] - complex conjugation of expressions involving complex unknowns

	Calling Sequence
	conj(expression, [ [a1, a1_bar], [a2, a2_bar], ... ])

Parameters

expression	-	algebraic expression to conjugate
[[a1, a1_bar], [a2, a2_bar], ...]	-	(optional) list of pairs of conjugates (names of unknowns and their conjugates)

Description

•	The function conj(expr, [[a1,a1_bar], [a2,a2_bar], ... ]) computes the complex conjugate of the algebraic expression expr by making the following substitutions:

-I is substituted for I (this is the default if only one argument is specified).

For each pair of names, , , ai is substituted for ai_bar and ai_bar is substituted for ai.

•

The effect of these substitutions is to produce the complex conjugate of an expression which is assumed to contain only real-valued unknowns except for those which are listed in the second argument. The unknowns listed in the second argument are complex-valued and are replaced by their complex conjugate (unknown).

Examples

Suppose that the unknowns a and b are real-valued. Compute the conjugate of a+I*b:

(1)

Notice that since all of the unknowns in the expression `a+I*b' are real, you did not need to specify a second argument in the call to conj (alternatively, you could have passed the empty list: []).

Now suppose that b is complex-valued with complex conjugate b_bar. The conjugate of a+I*b is a-I*b_bar: