Possible sortings of a list depending on parameters
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solvelib::conditionalSort(l
)
solvelib::conditionalSort(l)
sorts the list l
in
ascending order. Unlike for sort
,
only the usual order on the real numbers and not the internal order
(see sysorder
)
is used. solvelib::conditionalSort
does a case
analysis if list elements contain indeterminates.
solvelib::conditionalSort
invokes the inequality
solver to get simple conditions in the case analysis. The ability
of solvelib::conditionalSort
to recognize sortings
as impossible is thus limited by the ability of the inequality solver
to recognize an inequality as unsolvable. See Example 3.
Only expressions representing real numbers can be sorted. It is an error if nonreal numbers occur in the list; it is implicitly assumed that all parameters take on only such values that cause all list elements to be real.
Sorting is unstable, i.e. equal elements may be placed in any order in the resulting list; these cases may be listed separately in the case analysis.
The usual simplifications for piecewise defined objects are applied, e.g., equalities that can be derived from a condition are applied (by substitution) to the list.
solvelib::conditionalSort
takes into account
the assumptions on all occurring identifiers.
In the simplest case, sorting a twoelement list [a,b]
just
amounts to solving the inequality a<=b
w.r.t.
all occurring parameters.
solvelib::conditionalSort([x,x^2])
If, by implicit or explicit assumptions on the parameters, no different sortings can occur, the result is just a list.
According to the implicit assumption that all list elements
are real, x
must be nonnegative.
solvelib::conditionalSort([sqrt(x), 3])
Sometimes cases are not recognized as impossible.
assume(x>5): solvelib::conditionalSort([x,gamma(x)])

List of arithmetical expressions 
List if the sorting is the same for all possible parameter values;
or an object of type piecewise
if some case analysis
is necessary.
The complexity of sorting a list of n elements is up to .