Dom::ImageSet
-- the domain of
images of sets under mappingsDom::ImageSet
is the domain of all sets of complex
numbers that can be written as the set of all values taken on by some
mapping, i.e., sets of the form {f(x1, ..., xn);
xi ∈Si } for some function
f and some sets S1, ..., Sn
.
Dom::ImageSet()
solve
to express sets like {k*PI
; k in Z } .Dom::ImageSet
belongs to the category Cat::Set
--arithmetical and set-theoretic
operations are inherited from there.Dom::ImageSet
(f, x, S)
represents the set
of all values that can be obtained by substituting some element of
S
for x
in the expression f
.
Dom::ImageSet
(f, [x1...], [S1...])
represents the set of all values that can be obtained by substituting,
for each i, the identifier xi by some
element of Si in the expression
f
.
Dom::ImageSet
(f, x, S)
Dom::ImageSet
(f, [x1...], [S1...])
f |
- | arithmetical expression |
x |
- | identifier or indexed identifier |
S |
- | set of any type |
Cat::Set
solve
for an
overview of the different kinds of sets in MuPAD.changevar(dom A, identifier oldvar, identifier
newvar)
oldvar
by newvar
both in the
expression and in the list of variables. This gives (mathematically)
the same set, since {f(x) ; x ∈S }= {f(y) ; y ∈S
}.newvar
must not equal any element of
the list of variables; this is not checked!setvar(dom A, identifier newvar)
A
is replaced by
newvar
both in the expression and in the (one-element)
list of variables. This method may only be applied for image sets in
one variable.setvar(any A, identifier newvar)
A
that is not an image set, the method
"setvar"
is applied to all image sets contained in the
expression A
. A
might be, for example, a
union, intersection, etc. of image sets and other sets.homogpointwise(any Op)
Op
. Op
must be a function that
maps each finite sequence of (arbitrarily many) complex numbers to a
single complex number (e.g. their sum or product). Op
is
set forth to the class of image sets by defining
Op(A1,...,An)
to be the set of all
Op(a1,..,an)
, where ai
∈Ai for each i.Op
must accept arithmetical expressions as
arguments.isEmpty(dom A)
A
is empty if and only if one of its parameters ranges
over the empty set. This method tries to decide whether this is the
case and returns TRUE
, FALSE
, or
UNKNOWN
.substituteBySet(arithmetical expression
a, identifier x, dom
A)
A
for x
in the
expression a
. That is, viewing a=a(x) as a
function C C, this method returns {a(x); x ∈A
}, the image of the restriction of that function to
A
.indets(dom A)
A
depends on."variables"
to obtain the bound
parameters.indets
.expr(dom A)
f
; similarly if several variables range over
several sets.expr
.variables(dom A)
[x1,...,xn]
.indets
.nvars(dom A)
sets(dom A)
[S1,...,Sn]
.print(dom A)
A
on
the screen.We define S to be the set of all integer multiples of π.
>> S:=Dom::ImageSet(k*PI, k, Z_)
{ X1*PI | X1 in Z_ }
We may now apply the usual set-theoretic operations.
>> S intersect Dom::Interval(3..7)
{PI, 2 PI}