tensor(deprecated)/conj - Maple Help

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, $\left[\mathrm{ai},\mathrm{ai_bar}\right]$, $i=1..n$, 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.

 > $\mathrm{with}\left(\mathrm{tensor}\right):$

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

 > $\mathrm{conj}\left(a+Ib\right)$
 ${a}{-}{I}{}{b}$ (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:

 > $\mathrm{conj}\left(a+Ib,\left[\left[b,\mathrm{b_bar}\right]\right]\right)$
 ${a}{-}{I}{}{\mathrm{b_bar}}$ (2)

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

 > $\mathrm{conj}\left(a+Ib,\left[\left[a,\mathrm{a_bar}\right],\left[b,\mathrm{b_bar}\right]\right]\right)$
 ${\mathrm{a_bar}}{-}{I}{}{\mathrm{b_bar}}$ (3)