def Deriv_D(k,N):
i = [1 for i in range(k)]
res=0.
for j in range(N^k):
valid = 1 #Test if index-tupel is valid i.e that there are no double indices
for p in range(k):
if i[p] in i[p+1:k]:
valid=0
if valid:
res+=1/2^sum(i)
i[0]+=1
for l in range(k-1):
if i[l]==N+1:
i[l]=1
i[l+1]+=1
return (-1)^k*res
N=10
der_d=[1]
k=1
der_d.append(Deriv_D(k,N))
print k
print der_d[k]
k=2
der_d.append(Deriv_D(k,N))
print k
print der_d[k]
k=3
der_d.append(Deriv_D(k,N))
print k
print der_d[k]
k=4
der_d.append(Deriv_D(k,N))
print k
print der_d[k]
k=5
der_d.append(Deriv_D(k,N))
print k
print der_d[k]
k=6
der_d.append(Deriv_D(k,N))
print k
print der_d[k]
k=7
der_d.append(Deriv_D(k,N))
print k
print der_d[k]
1 -0.999023437500000 2 0.664714813232422 3 -0.283764973282814 4 0.0750794825144112 5 -0.0119203815484070 6 0.00109979710714470 7 -0.0000568300670522603 1 -0.999023437500000 2 0.664714813232422 3 -0.283764973282814 4 0.0750794825144112 5 -0.0119203815484070 6 0.00109979710714470 7 -0.0000568300670522603 |
#################
#Plot parameters
#################
zmax=14
ymin=-2
ymax=2
var('z')
def D(z, N):
ret=1
for i in range(N-1):
ret*=(1-z/2^(i+1))
return ret
def Taylor_pol(z,k):
res=0
for i in range(k+1):
res+=1/factorial(i)*der_d[i]*z^i
return res
D_plot=plot(D(z,20), (z,0,zmax),rgbcolor='red', ymin=ymin, ymax=ymax)
TP1 = plot(Taylor_pol(z,1), (z,0,zmax))
TP2 = plot(Taylor_pol(z,2), (z,0,zmax))
TP3 = plot(Taylor_pol(z,3), (z,0,zmax))
TP4 = plot(Taylor_pol(z,4), (z,0,zmax))
TP5 = plot(Taylor_pol(z,5), (z,0,zmax))
TP6 = plot(Taylor_pol(z,6), (z,0,zmax))
TP7 = plot(Taylor_pol(z,7), (z,0,zmax))
show(D_plot+TP1+TP2+TP3+TP4+TP5+TP6+TP7)
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6 6 |
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