Public Function calcequation() Dim first As String = "" Dim sec As Double Dim firstop As String = "" Dim secop As String = "" Dim third As String = "" Dim fourth As Double If a = 1 Then first = "x" third = "x" ElseIf a <> 1 Then a = a / 2 End If If a = 1 Then first = "x" third = "x" ElseIf a <> 1 Then first = a.ToString() + "x" third = a.ToString() + "x" End If If b > 0 And c > 0 Then firstop = "+" secop = "+" If c <= 100 And c > 0 Then Do Until sec * fourth = c And sec + fourth = b If fourth / 10 = 1 Or fourth / 10 = 2 Or fourth / 10 = 3 Or fourth / 10 = 4 Or fourth / 10 = 5 Or fourth / 10 = 6 Or fourth / 10 = 7 Or fourth / 10 = 8 Or fourth / 10 = 9 Or fourth / 10 = 10 Then sec = sec + 1 fourth = 0 End If fourth = fourth + 1 Loop End If If c <= 200 And c > 100 Then Do Until sec * fourth = c And sec + fourth = b If fourth / 10 = 11 Or fourth / 10 = 12 Or fourth / 10 = 13 Or fourth / 10 = 14 Or fourth / 10 = 15 Or fourth / 10 = 16 Or fourth / 10 = 17 Or fourth / 10 = 18 Or fourth / 10 = 19 Or fourth / 10 = 20 Then sec = sec + 1 fourth = 0 End If fourth = fourth + 1 Loop End If End If If b > 0 And c < 0 Then End If If b < 0 And c > 0 Then If b >= -100 And b < 0 Then Do Until sec * fourth = c And sec + fourth = b If fourth / 10 = -1 Or fourth / 10 = -2 Or fourth / 10 = -3 Or fourth / 10 = -4 Or fourth / 10 = -5 Or fourth / 10 = -6 Or fourth / 10 = -7 Or fourth / 10 = -8 Or fourth / 10 = -9 Or fourth / 10 = -10 Then sec = sec - 1 fourth = 0 End If fourth = fourth - 1 Loop End If If b >= -200 And b < -100 Then Do Until sec * fourth = c And sec + fourth = b If fourth / 10 = -11 Or fourth / 10 = -12 Or fourth / 10 = -13 Or fourth / 10 = -14 Or fourth / 10 = -15 Or fourth / 10 = -16 Or fourth / 10 = -17 Or fourth / 10 = -18 Or fourth / 10 = -19 Or fourth / 10 = -20 Then sec = sec - 1 fourth = 0 End If fourth = fourth - 1 Loop End If End If If sec < 0 Then secabsolute = Math.Abs(sec) If fourth < 0 Then fourthabsolute = Math.Abs(fourth) If sec > 0 Then Dim num As Integer num = sec * 2 secabsolute = sec - num End If If fourth > 0 Then Dim num As Integer num = fourth * 2 fourthabsolute = fourth - num End If x = secabsolute.ToString() + " or x= " + fourthabsolute.ToString() '"(" + first + firstop + sec.ToString() + ")(" + third + secop + fourth.ToString() + ")" Return x End Function

cat SciProg/Checkpoint4_1.java // Calculates square roots import java.io.Console; // For console IO public class Checkpoint4_1 { /*private static double read_double() { double ret; boolean done; do { done = true; try { ret = new Double(c.readLine()); } catch ( NumberFormatException e ) { done = false; } } while ( !done ) ; return ret; }*/ public static void main(String[] args) { double a,b,c,x_one,x_two,disc; // Declaring variables for later use - the coefficients, x co-ordinates and discriminant. String temp; // For input from console. Console myConsole = System.console(); // Initialise console as currently used console. // Explanatory text follows. myConsole.printf("This program will take three arguments from the command line: the coefficients\na,b and c in the equation ax^2 + bx + c = 0.\ It will then print out the roots of the quadratic (or linear) equation.\n"); temp = myConsole.readLine(); // These six lines take a string from the terminal then attempt to read a Double from it. a = new Double(temp); // Will die if not able to read one properly but input sanitisation hardly seems necessary. temp = myConsole.readLine(); b = new Double(temp); temp = myConsole.readLine(); c = new Double(temp); if(a!=0) // Checks if we have a quadratic. { disc = b*b - 4*a*c; // Sets discriminant. if(disc > 0) // Two roots. { x_one = (-1*b - Math.sqrt(disc))/2*a; x_two = (-1*b + Math.sqrt(disc))/2*a; myConsole.printf("The quadratic has two roots at %.2f and %.2f.\n",x_one,x_two); } else if(disc == 0) // Single root. { x_one = (-1*b)/(2*a); myConsole.printf("The quadratic has a double root at %.2f.\n",x_one); } else // Complex roots. { x_one = (-1*b)/(2*a); x_two = Math.sqrt(-1*disc)/(2*a); myConsole.printf("The quadratic has two complex roots at %.2f - %.2fi and %.2f + %.2fi.\n",x_one,x_two,x_one,x_two); } } else if(b!=0) // If it's not a quadratic, is it linear? { x_one = -1*c/b; myConsole.printf("This linear equation has a root at %.2f.\n",x_one); } else // If not that then it must be constant. { myConsole.printf("This is a constant equation and has no roots.\n"); } System.exit(0); // Time to go. } }

for(int j = 0; j < length; ++j) { if(denom % factors[j] == 0) denom /= factors[j]; }

for(int j = 0; j < length; ++j) { while(denom % factors[j] == 0) { denom /= factors[j]; } }

Imports Microsoft.Win32 Imports System.IO Imports System.Math Public Class Form1 Dim num1 As Double = 24 Dim Prime() As Integer = {2, 3, 5, 7, 11, 13} Dim reducenum1Array() As Integer = {num1} Dim divisorArray() As Integer = {} Dim Toreducenum1Array As Integer Dim TodivisorArray As Integer Dim remainder As Double Dim complete As Boolean = False Dim newsize As Integer = 2 Dim newsize1 As Integer = 1 Dim out As Integer Public Sub reducenum1() for1: For Each temp As Integer In reducenum1Array Toreducenum1Array = temp setvalue_reducenum1Array() for2: For Each number As Integer In Prime remainder = IEEERemainder(temp, number) If remainder = 0 Then TodivisorArray = number setvalue_divisorArray() If number = 13 Then complete = True Exit Sub End If Next number GoTo for2 Next temp GoTo for1 End Sub Public Sub setvalue_reducenum1Array() Array.Resize(reducenum1Array, newsize) reducenum1Array.SetValue(Toreducenum1Array, newsize1) End Sub Public Sub setvalue_divisorArray() End Sub Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click Application.Exit() End Sub Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click reducenum1() ' setvalue_reducenum1Array() setvalue_divisorArray() For i As Integer = 0 To newsize Dim value As Integer value += 1 Label2.Text = Label2.Text + reducenum1Array.GetValue(value).ToString() Next End Sub End Class

Public Sub reducenum1() for1: For Each number As Integer In Prime remainder = IEEERemainder(temp, number) If remainder = 0 Then value = temp / number Label2.Text = Label2.Text + value.ToString() temp = value GoTo for1 End If If number = 13 Then complete = True Exit Sub End If Next number End Sub

Public Sub reducenum1() 'enters the sub routine reduce num1 temp = num1 'sets the value of temp [currently Nothing] to the value of num1 [currently x1] for1: For Each number As Integer In Prime 'for numbers 2,3,5,7,11,13 do whats next remainder = IEEERemainder(temp, number) 'set remainder to the value of the left over [ie remainder] of temp divided by number If remainder = 0 Then 'if there is no remiander [it divides evenly into temp thus giving you the gcf of temp] remainder = IEEERemainder(temp2, number) 'set remainder to the value of temp2 [the denominator of x1 and x2] divded by number If remainder = 0 Then 'if there is no left over value2 = temp2 / number 'divid temp2 [denominator of x1 and x2] set value to value2 value = temp / number 'do the same as above except for the nominator of x1 valuestore = valuestore + "-" + value.ToString() 'set the new value of the nominator of x1 to a string seperating numbers by a - temp = value 'sets temp to the value of temp/number [ie emulating an array in the For Each loop temp2 = value2 christ = number GoTo for1 'repeat the process over and over [it does this because there is still a possibility of reducing the nominator AND denominator of x1] End If End If If number = 13 Then 'if number=13 [ie you cannot divide by the first 6 prime numbers exit loop complete = True Exit Sub End If Next number End Sub Public Function findnumber1() Dim length As Integer value = temp / christ valuestore = valuestore + "-" + value.ToString() length = valuestore.LastIndexOf("-") bob = valuestore.Remove(length) length = bob.LastIndexOf("-") length += 1 jesus = bob.Remove(0, length) Return jesus End Function '''<summary> ''' the above function does some fancy stuff ''' first of all it fixes the error that the For Each loop does not account for that ''' that is the fact that the For Each loop divides by the number of indexes of denominator ''' so 8=2x2x2 [3 indexs] it is important to note that 8 is the sample denominator ''' (64/2) does that 3 times which results in 16 ''' however 16/1 is NOT a reduction of 64/8 ''' 8/1 is the fully reduced 64/8 ''' we get this by dividing outside the for statement ''' one last time ''' then it finds the last index the - ''' and deletes anything after the last - ''' then it finds the last index of - again ''' the difference is that at the begining there is a - after the actual number you want ''' the second index of - gets the index of the - before the number you want ''' and the first last index of - deletes from the - to the end ''' the second last index of deletes from the begining to the- ''' which is a problem because -8 is not the answer we want ''' so we add 1 to the last index of - so we delete upto the number ''' you want not the - ''' and all of this is repeated for num2 '''</summary>