complex conjugation of expressions involving complex unknowns
conj(expression, [ [a1, a1_bar], [a2, a2_bar], ... ])
algebraic expression to conjugate
[[a1, a1_bar], [a2, a2_bar], ...]
(optional) list of pairs of conjugates (names of unknowns and their conjugates)
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).
Suppose that the unknowns a and b are real-valued. Compute the conjugate of a+I*b:
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:
Now suppose that both a and b are complex-valued. Compute the complex conjugate of a+I*b:
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