Possible sortings of a list depending on parameters
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solvelib::conditionalSort(l) sorts the list
ascending order. Unlike for
only the usual order on the real numbers and not the internal order
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
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 non-real 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 two-element list
amounts to solving the inequality
all occurring parameters.
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
x must be nonnegative.
Sometimes cases are not recognized as impossible.
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
The complexity of sorting a list of n elements is up to .