Scratch Paper.sagews

#implement Euclidean Algorithm and count number of steps
def EALength(a,b):
    #count number of steps in Euclidean Algorithm
    #if a<b then switch em
    if a < b:
        temp = a
        a = b
        b = temp
    r=b
    steps =0
    while r>0:
        temp = b
        r = a% b
        a = temp
        b = r
        steps += 1
    return steps

def MaxSteps(N):
    Max = 0
    maxx =0
    maxy =0
    for x in[1..N]:
        for y in [1..N]:
            EA = EALength(x,y)
            if(EA > Max):
                maxx =x
                maxy =y
                Max =EA
    print("x = ", maxx)
    print("y = ", maxy)
    print("Max steps: ", Max)
    
    
def AverageSteps(N):
    total = 0
    count = 0
    for x in[1..N]:
        for y in [1..N]:
            EA = EALength(x,y)
            total += EA
            count += 1
            
            
    AverageSteps = float(total/count)
    print("AverageSteps is ", AverageSteps)

    

MaxSteps(50);
AverageSteps(12);

('x = ', 21) ('y = ', 34) ('Max steps: ', 7) ('AverageSteps is ', 1.8888888888888888)

euler_phi(16)

8

 p = matrix_plot(matrix(2,[1,1,3,3]))
p