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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

Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.

• 

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,ai_bar, i=1..n, 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

Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.

withtensor:

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

conja+Ib

aIb

(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:

conja+Ib,b,b_bar

aIb_bar

(2)

Now suppose that both a and b are complex-valued. Compute the complex conjugate of a+I*b:

conja+Ib,a,a_bar,b,b_bar

a_barIb_bar

(3)

See Also

conjugate, evalc, tensor(deprecated)


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