
How the operations work Addition Adding Intervals together is rather easy. To add Intervals together simply add the lowest X value together with the lowest Y value, then add the highest X value with the highest Y value. X Values: [a,b] Y Values: [c,d] When calculating Intervals the X values are placed "on top of" the Y values. Also the lowest value of either the X of the Y is placed first in the set. When adding you are adding a+c and b+d. X Values: [a,b] Y Values: + [c,d] Result: [e,f] [1,3] + [2,4] [3,7] Subtraction Subtracting Intervals is much like adding Intervals. To subtract Intervals simply subtract the lowest X value by the highest Y value, then subtract the highest X value by the lowest Y value. X Values: [a,b] Y Values: [c,d] When calculating Intervals the X values are placed "on top of" the Y values. Also the lowest value of either the X of the Y is placed first in the set. When subtracting you are subtracting ad and bc. X Values: [a,b] Y Values:  [c,d] Result: [e,f] [1,3]  [2,4] [3,1] Multiplication Multiplying Intervals is a lot more complicated then adding and subtracting Intervals. To multiply Intervals follow the steps below: low X=a high X=b low Y=c high Y=d low result=e high result=f A) If a >= 0 1. If c >= 0 a) a * c = e b) b * d = f 2. If d <= 0 a) b * c = e b) a * d = f 3. If neither 1 or 2 apply a) b * c = e b) b * d = e B) If b <= 0 1. If c >= 0 a) a * d = e b) b * c = f 2. If d <= 0 a) b * d = e b) a * c = f 3. If neither 1 of 2 apply a) a * d = e b) a * c = f C) If neither A of B apply 1. If c >= 0 a) a * d = e b) b * d = f 2. If d <= 0 a) b * c = e b) a * c = f 3. If neither 1 or 2 apply a) e = Minimum of (a * d, b * c) b) f = Maximum of (a * c, b * d) X Values: [a,b] Y Values: [c,d] When calculating Intervals the X values are placed "on top of" the Y values. Also the lowest value of either the X of the Y is placed first in the set. X Values: [a,b] Y Values: * [c,d] Result: [e,f] [1,3] * [2,4] [2,12] Division Dividing Intervals is a lot more complicated then adding and subtracting Intervals. To divide Intervals follow the steps below: low X=a high X=b low Y=c high Y=d low result=e high result=f A) If c >= 0 1. If a >= 0 a) a / d = e b) b / c = f 2. If b <= 0 a) a / c = e b) b / d = f 3. If neither 1 or 2 apply a) a / c = e b) b / c = e B) If d <= 0 1. If a >= 0 a) b / d = e b) a / c = f 2. If b <= 0 a) b / c = e b) a / d = f 3. If neither 1 of 2 apply a) b / d = e b) a / d = f C) If c <= 0 and d >= 0 1. If c >= 0 a) e = INFINITY b) f = +INFINITY X Values: [a,b] Y Values: [c,d] When calculating Intervals the X values are placed "on top of" the Y values. Also the lowest value of either the X of the Y is placed first in the set. X Values: [a,b] Y Values: / [c,d] Result: [e,f] [1,3] / [2,4] [.25,1.5] The calculator performs interval arithmetic operations and computers interval version of mathematical functions. It is an ongoing work. Definitions of Input Boxes: Input:  is the box where numbers are entered into the calculator Expressions:  is the box where expression like a+b are inputed Definitions of Buttons: Compute  computes the expression inputed in the Expressions box ClrX  clears the top set (x) of intervals ClrY  clears the bottom set (y) of intervals Enter  places the value in the Input Box into the next available spot AC  Clears all values Top  places the result into the X boxes +/  used to input negative numbers E  used to input scientific notation C  clears the Input Box ^  raise the X values by the power of Y NegX  switches the X values and turns them into the opposite value NegY  switches the Y values and turns them into the opposite value log  computes the common log of the X values sqrt  computes the square roots of the X values 1/x  reciprocal of the X values 1/y  reciprocal of the Y values e^X  raises e by the power of the X values ln  computes the natural log to the X values max  finds the maximum range min  finds the minimum range ABS  finds the absolute values IX  the intercept point IH  the convex hull View the source...  
