some simple numerical programs now that we have covered some basic python constructsit is time to start thinking about how we can combine those constructs to write some simple programs along the waywe'll sneak in few more language constructs and some algorithmic techniques exhaustive enumeration the code in figure prints the integer cube rootif it existsof an integer if the input is not perfect cubeit prints message to that effect #find the cube root of perfect cube int(raw_input('enter an integer')ans while ans** abs( )ans ans if ans** !abs( )print 'is not perfect cubeelseif ans -ans print 'cube root of' ,'is'ans figure using exhaustive enumeration to find the cube root for what values of will this program terminatethe answer is"all integers this can be argued quite simply the value of the expression ans** starts at and gets larger each time through the loop when it reaches or exceeds abs( )the loop terminates since abs(xis always positive there are only finite number of iterations before the loop must terminate whenever you write loopyou should think about an appropriate decrementing function this is function that has the following properties it maps set of program variables into an integer when the loop is enteredits value is nonnegative when its value is <= the loop terminates its value is decreased every time through the loop what is the decrementing function for the loop in figure it is abs(xans**