normalize

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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] waruna [Example] |
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* 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: |

normalize.txt · Last modified: 2017/11/14 07:50 by waruna