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injectivitylemma6.py: fix bugs in comments. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2020-04-26 11:58:21 +01:00
parent e859145e33
commit d93cabbaf8
1 changed files with 3 additions and 3 deletions
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injectivitylemma6.py
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@ -13,11 +13,11 @@
# { (0, 2r_i - 1, 0), if s_i = 1
# { (2r_i - 1, 0, 0), if s_i = 2
# (a, b, c) := (2a + d_i, 2b + e_i, 2c + f_i)
# Output [a.ζ^2 + b.ζ + c] P.
# Output [a.ζ^2 + b.ζ + c] P.
#
# For each i ∈ [0, λ), the mapping (r_i, s_i) ↦ (d_i, e_i, f_i) is injective,
# and exactly one of d_i, e_i, f_i ∈ {-1, 0, +1} is 0.
# Let M_k = {(d, e, f : {-1, 0, +1}^k) for all i, exactly one of d_i, e_i, f_i is 0}.
# and exactly one of d_i, e_i, f_i ∈ {-1, 0, +1} is nonzero.
# Let M_k = {(d, e, f : {-1, 0, +1}^k) for all i, exactly one of d_i, e_i, f_i is nonzero}.
# So (r, s) ↦ (d, e, f) : M_λ is also injective.
#
# Lemma: For k ≥ 0, (d, e, f) ∈ M_k ↦ (∑_{j ∈ [0, k-1)} d_j 2^j,