Domain of set of vectors that are images of sets under mappings
solvelib::VectorImageSet()
solvelib::VectorImageSet(v
,x
,S
)
Dom::ImageSet(v
,[x1, …]
,[S1, …]
)
solvelib::VectorImageSet
is the domain of
all sets of vectors of complex numbers that can be written as the
set of all values taken on by some mapping, i.e., sets of the form
for
some complexvalued functions f_{j} and
some sets S_{1},
…, S_{n} of
complex numbers.
Sets of this type are used by solve
to express solutions of systems
of equations like
.
solvelib::VectorImageSet(v, x, S)
represents
the set of all vectors that can be obtained by substituting some element
of S
for x
in the vector v
.
solvelib::VectorImageSet(v, [x1, ...], [S1, ...])
represents
the set of all values that can be obtained by substituting, for each i,
the identifier x_{i} by
some element of S_{i} in
the vector v
.
The user never needs to call solvelib::VectorImageSet
directly.
Instead, Dom::ImageSet
should
be used; it will automatically create a vector image set if its first
argument is a list or matrix. The entries and methods of the domain solvelib::VectorImageSet
are
the same as those of Dom::ImageSet
,
and may be found on that help page.
We create a set of twodimensional vectors:
S:= Dom::ImageSet([k*PI, k*I*PI], k, Z_)
Since this is a set of vectors, a solvelib::VectorImageSet
is
created automatically:
type(S)
Settheoretic operations (union, intersection, set difference)
may be applied to S
:
S intersect {[0, 0], [1, 1]}, S minus S
delete S:

List or 

Identifier or indexed identifier 

Set of any type 