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.
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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.

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



Examples


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


Suppose that the unknowns a and b are realvalued. 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 complexvalued with complex conjugate b_bar. The conjugate of a+I*b is aI*b_bar:
>


 (2) 
Now suppose that both a and b are complexvalued. Compute the complex conjugate of a+I*b:
>


 (3) 


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