From 6eb0d953ec283c6dcf93be0edff7a456e2019686 Mon Sep 17 00:00:00 2001 From: Sagi Kedmi Date: Wed, 23 Dec 2015 15:13:04 +0200 Subject: [PATCH 1/3] Add + between two parts of the equation --- explanation/explanation.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/explanation/explanation.tex b/explanation/explanation.tex index b21e8de..0da2f31 100644 --- a/explanation/explanation.tex +++ b/explanation/explanation.tex @@ -34,7 +34,7 @@ \section{Proof} &= (d\oplus z)^{-1}(z+rd)\\ &= (d + z - 2(d\wedge z))^{-1}(z+rd)\\ \iff ds + zs - 2s(d\wedge z)&= z + rd\\ - \iff (s-1)z &= 2s(d\wedge z) (s-r)d\\ + \iff (s-1)z &= 2s(d\wedge z)+(s-r)d\\ &= \sum_i 2^i d_i z_i 2s + \sum_i 2^i d_i (r-s) \\ &= \sum_i d_i 2^i (r + (2z_i - 1)s) \\ \end{align*} From 8e8636f02db06539fd3070992b014a506f899a83 Mon Sep 17 00:00:00 2001 From: Sagi Kedmi Date: Wed, 23 Dec 2015 15:13:44 +0200 Subject: [PATCH 2/3] Swap between r and s in the equation --- explanation/explanation.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/explanation/explanation.tex b/explanation/explanation.tex index 0da2f31..959ce5c 100644 --- a/explanation/explanation.tex +++ b/explanation/explanation.tex @@ -34,7 +34,7 @@ \section{Proof} &= (d\oplus z)^{-1}(z+rd)\\ &= (d + z - 2(d\wedge z))^{-1}(z+rd)\\ \iff ds + zs - 2s(d\wedge z)&= z + rd\\ - \iff (s-1)z &= 2s(d\wedge z)+(s-r)d\\ + \iff (s-1)z &= 2s(d\wedge z)+(r-s)d\\ &= \sum_i 2^i d_i z_i 2s + \sum_i 2^i d_i (r-s) \\ &= \sum_i d_i 2^i (r + (2z_i - 1)s) \\ \end{align*} From 0b215d4614516049e63b31583b07ec30b5e3c89a Mon Sep 17 00:00:00 2001 From: Sagi Kedmi Date: Wed, 23 Dec 2015 15:14:26 +0200 Subject: [PATCH 3/3] Add fixed explanation.pdf --- explanation/explanation.pdf | Bin 98410 -> 98344 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/explanation/explanation.pdf b/explanation/explanation.pdf index 22994304726db58c9e36f53591a9a36ff38270ab..e8c1ede9a9b1327040a66a7d81e148af20cc78ea 100644 GIT binary patch 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