revert -- revert lists or
character strings, invert series expansions
Introductionrevert 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)
Parametersobject |
- | a list, a character string, or a series expansion of type
Series::Puiseux |
Returnsan object of the same type as the input object, or a symbolic call
of type "revert".
object
Related
Functions
Detailsrevert is a general function to compute inverses with
respect to functional composition, or to reverse the order of operands.
This type of functionality may be extended to further types of objects
via overloading.revert reverses the order of the
elements or characters, respectively. Further, for series expansions,
the functional inverse is returned.revert, the symbolic expression
revert(object) is returned.
Example
1revert 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
2For 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) / /