intervalOptionList -- convert a list type object to list of options for intervals

Description

This function converts a List type object to a IntervalOptionList type object.

First, assume that we have the following ring, polynomial system, and interval.

i1 : R = QQ[x1,x2,y1,y2];

i2 : f = polySystem {3*y1 + 2*y2 -1, 3*x1 + 2*x2 -7/2, x1^2 + y1^2 -1, x2^2 + y2^2 -1};

i3 : (I1, I2, I3, I4) = (interval(.94,.96), interval(.31,.33), interval(-.31,-.29), interval(.94,.96));

We want to plug in "I1" into "x1", "I2" into "x2", "I3" into "y1" and "I4" into "y2".

Then, write a List object as the way we want.

i4 : l = {("x1" => "I1"), ("x2" => "I2"), ("y1" => "I3"), ("y2" => "I4")}

o4 = {x1 => I1, x2 => I2, y1 => I3, y2 => I4}

o4 : List

Then, use intervalOptionList function to convert the type of "l" to IntervalOptionList.

i5 : intervalOptionList l

o5 = {x1 => I1, x2 => I2, y1 => I3, y2 => I4}

o5 : IntervalOptionList