normalize

# Differences

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 normalize [2017/11/14 07:46]waruna [Normalization Rules] Fixed rule 4 and 5. latex plugin does not work anymore, therefore used the mathjax plugin normalize [2017/11/14 07:50] (current)waruna [Example] Both sides previous revision Previous revision 2017/11/14 07:50 waruna [Example] 2017/11/14 07:46 waruna [Normalization Rules] Fixed rule 4 and 5. latex plugin does not work anymore, therefore used the mathjax plugin 2017/11/14 07:22 waruna [Normalization Rules] 2017/11/14 07:20 waruna [Normalization Rules] 2017/04/19 14:14 external edit 2017/11/14 07:50 waruna [Example] 2017/11/14 07:46 waruna [Normalization Rules] Fixed rule 4 and 5. latex plugin does not work anymore, therefore used the mathjax plugin 2017/11/14 07:22 waruna [Normalization Rules] 2017/11/14 07:20 waruna [Normalization Rules] 2017/04/19 14:14 external edit Line 41: Line 41: * In the computation for C, expression A[i] is equivalent to A.(i %%->%% i), f is an identity function, rule number one is satisfied. So A.(i %%->%% i) %%=>%% A. * In the computation for C, expression A[i] is equivalent to A.(i %%->%% i), f is an identity function, rule number one is satisfied. So A.(i %%->%% i) %%=>%% A. * In the computation for C, expression {i| 0 %%<=%% i < N}: ({i|0 %%<=%% i < 2N}:A[i]) matches rule number 6, where D1 = {i| 0 %%<=%% i < N}, D2={i|0 %%<=%% i < 2N}. D=D1 ∩ D1 ={i|0 %%<=%% i < N}, the expression is changed to {i|0 %%<=%% i < N}:A. * In the computation for C, expression {i| 0 %%<=%% i < N}: ({i|0 %%<=%% i < 2N}:A[i]) matches rule number 6, where D1 = {i| 0 %%<=%% i < N}, D2={i|0 %%<=%% i < 2N}. D=D1 ∩ D1 ={i|0 %%<=%% i < N}, the expression is changed to {i|0 %%<=%% i < N}:A. - * In the computation for D, expression (i, j %%->%% j, i)@({|0 %%<=%% i < N\}:A[i]) matches rule number 7, where D = {i,j |0 %%<=%% i < N }, f=(i, j %%->%% j, i). D'​=f^(-1)(D)={i,​j|0 %%<=%% j < N}, the expression is changed to {i,j|0 %%<=%% j < N}:A[i,j]; + * In the computation for D, expression (i, j %%->%% j, i)@({|0 %%<=%% i < N}:A[i]) matches rule number 7, where D = {i,j |0 %%<=%% i < N }, f=(i, j %%->%% j, i). D'​=f^(-1)(D)={i,​j|0 %%<=%% j < N}, the expression is changed to {i,j|0 %%<=%% j < N}:A[i,j]; The result for the above program after normalization is: The result for the above program after normalization is: