meyers hw 1.ipynb

Kernel: SageMath (stable)

def nest(x, a):
    nested = 0
    for i in range(0, len(a)):
        nested = nested * x + a[i]
    return nested
a = [6,1,5,1,1]
b = [-3,4,5,-5,1]
c = [2,1,-1,0,1]

print(nest((1/3),a))
print(nest((1/3),b))
print(nest((1/3),c))

fa(x) = 6*x^4 + x^3 +5*x^2+x+1
fb(x) = -3*x^4+4*x^3+5*x^2-5*x+1
fc(x) = 2*x^4+x^3-x^2+1

print(fa(1/3))
print(fb(1/3))
print(fc(1/3))

2
0
77/81
2
0
77/81

Since method 1 == method 2, we must have done something right!