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revert -- revert lists or character strings, invert series expansions

Introduction

revert reverses the ordering of the elements in a list and the ordering of characters in a string. For a series expansion, it returns the functional inverse.

Call(s)

revert(object)

Parameters

object - a list, a character string, or a series expansion of type Series::Puiseux

Returns

an object of the same type as the input object, or a symbolic call of type "revert".

Overloadable:

object

Related Functions

series, substring

Details

Example 1

revert operates on lists and character strings:

>> revert([1, 2, 3, 4, 5])
                              [5, 4, 3, 2, 1]
>> revert("nuf si DAPuM ni gnimmargorP")
                       "Programming in MuPAD is fun"

revert operates on series:

>> revert(series(sin(x), x)) = series(arcsin(x), x)
                    3      5                3      5
                   x    3 x       6        x    3 x       6
               x + -- + ---- + O(x ) = x + -- + ---- + O(x )
                   6     40                6     40

The functional inverse of the expansion of exp around x = 0 is the expansion of the inverse function ln around x = exp(0) = 1:

>> revert(series(exp(x), x, 3)) = series(ln(x), x = 1, 3)
                       2
                (x - 1)             3
      (x - 1) - -------- + O((x - 1) ) =
                   2
      
                          2
                   (x - 1)             3
         (x - 1) - -------- + O((x - 1) )
                      2

Example 2

For all other types of objects, a symbolic function call is returned:

>> revert(x + y)
                               revert(x + y)

The following series expansion is not of type Series::Puiseux. Instead, a generalized expansion of type Series::gseries is produced. Consequently, revert does not compute an inverse:

>> revert(series(exp(-x)/(1 + x), x = infinity, 3))
                    /    1           1        /     1     \ \
              revert| -------- - --------- + O| --------- | |
                    | x exp(x)    2           |  3        | |
                    \            x  exp(x)    \ x  exp(x) / /

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