For example,
Given a list of symbolic expressions:
ClearAll[a,o,t];
myexpr =
{
1 - t + 2 a[1] + (2 - t + 2 a[1]) (-1 + t + a[1] + o[1]) + (1 + a[1]) (-1 + t + a[1] + o[1])^2,
-1 + t + a[1] + o[1]
}
Given conditions on those symbols:
mycond = (1 <= t <= 3 && a[1] == t && o[1] > 3 - 2 t + a[1]) || (t > 3 && a[1] == t && o[1] >= 0)
And given "transformation" function foo,
How can I "apply" those conditions to the expression and generate examples?
By "apply", I mean:
Every case of conditions separated by || is handled on its own.
In every case, for subcondition of form X == Y, all X get replaced by Y (or the other way around) so only one of the two remains in the expressions.
In case of a >=,> or <=,< subconditions, those set up the relative bounds for symbols, lets call them boundLow,boundHigh. If no bound is set, the extreme bounds are used.
The final bounds depend on given extreme bounds boundMin,boundMax which restrict bounds boundLow,boundHigh by having final bounds for every symbol: Max[boundLow,boundMin],Min[boundHigh,boundMax].
That is, the desired output is in this example: (After == substitutions in myexpr and myconds)
{Table[foo[myexpr],{t,Max[1,boundMin],Min[3,boundMax]},{o[1],Max[4-t,boundMin],boundMax}],
Table[foo[myexpr],{t,Max[4,boundMin],boundMax},{o[1],Max[0,boundMin],boundMax}]}
Where we have tables of examples generated by applying the myconds (which consist of two cases separated by || and thus we have two tables) to myexpr.
In the above example, I manually did the == replacements with /. -> and manually set the bounds - how can I automate this process of "applying" conditions to expressions to generate examples?
Motivation
The above example is an actual output from an algorithm I'm trying to make that solves a problem I'm trying to solve - in this question, I'm wondering how can I generate examples from such outputs, to analyze them.
