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from sage.all import *
def batch_inversion(L):
r"""Does n inversions in 3(n-1)M+1I.
Input:
- L: list of elements to invert.
Output:
- [1/x for x in L]
"""
# Given L=[a0,...,an]
# Computes multiples=[a0, a0.a1, ..., a0...an]
multiples=[L[0]]
for ai in L[1:]:
multiples.append(multiples[-1]*ai)
# Computes inverses=[1/(a0...an),...,1/a0]
inverses=[1/multiples[-1]]
for i in range(1,len(L)):
inverses.append(inverses[-1]*L[-i])
# Finally computes [1/a0,...,1/an]
result=[inverses[-1]]
for i in range(2,len(L)+1):
result.append(inverses[-i]*multiples[i-2])
return result
def product_theta_point(theta1,theta2):
a,b=theta1
c,d=theta2
return [a*c,b*c,a*d,b*d]
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