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Possible sortings of a list depending on parameters
This functionality does not run in MATLAB.
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 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 [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)])