solutions1.sagews

f(x)

plot(x^2-3*x+1,-2,2,figsize=[4,3])

var('t')

t

find_root(cos(t)-t,0,3)

0.7390851332151607

#Minimal element
def minimal_el(L):
    m=L[0]
    for j in range(1,len(L)):
        if L[j]<m:
            m=L[j]
    return m        

M=[1,-3,2,5,173]

S=[sin(0.5*k) for k in range(10)];S

[0.000000000000000, 0.479425538604203, 0.841470984807897, 0.997494986604054, 0.909297426825682, 0.598472144103957, 0.141120008059867, -0.350783227689620, -0.756802495307928, -0.977530117665097]

minimal_el(S)

-0.977530117665097

[2*c for c in S ]

[0.000000000000000, 0.958851077208406, 1.68294196961579, 1.99498997320811, 1.81859485365136, 1.19694428820791, 0.282240016119734, -0.701566455379240, -1.51360499061586, -1.95506023533019]

f(x)

plot(x^2-3*x+1,-2,2,figsize=[4,3])

var('t')

t

find_root(cos(t)-t,0,3)

0.7390851332151607

#Minimal element
def minimal_el(L):
    m=L[0]
    for j in range(1,len(L)):
        if L[j]<m:
            m=L[j]
    return m        

M=[1,-3,2,5,173]

S=[sin(0.5*k) for k in range(10)];S

[0.000000000000000, 0.479425538604203, 0.841470984807897, 0.997494986604054, 0.909297426825682, 0.598472144103957, 0.141120008059867, -0.350783227689620, -0.756802495307928, -0.977530117665097]

minimal_el(S)

-0.977530117665097

[2*c for c in S ]

[0.000000000000000, 0.958851077208406, 1.68294196961579, 1.99498997320811, 1.81859485365136, 1.19694428820791, 0.282240016119734, -0.701566455379240, -1.51360499061586, -1.95506023533019]