Constructors and pseudo-constructors

• BigRatInterval(lwb, upb) creates an interval with lower end point lwb and upper end point upb; gives error if lwb > upb

Queries and views

Let I be a BigRatInterval

• min(I) -- gives the lower end point of I
• max(I) -- gives the upper end point of I
• width(I) -- gives the width of I as a BigRat
• IsZeroInside(I) -- true iff min(I) < 0 and max(I) > 0

Operations

Basic interval arithmetic operations between two intervals I1 and I2:

• I1 + I2
• I1 - I2
• I1 * I2
• I1 / I2 gives error if I2 contains 0
• merge(I1, I2) union, but error if I1 and I2 are disjoint.
• square(I1) like I1*I1 but ensures lower bound is non-negative.
• soften(I1) widen I1 to make its end points nicer numbers (PROTOTYPE!)

Basic arithmetic operations between an interval I and a rational q:

• I + q and q + I
• I - q and q - I
• I * q and q * I

Division is not yet supported!