User blog:Wythagoras/HAN

On some comments on blog posts members of the community said that the w/ operator of HAN is difficult to understand, and I'm going to change that in this blog post. After that, I shall explain some similarities of HAN with BEAF.

2 array chain
a![1]w/[1] expands to a![1,1...1,1,2] with a a's

If the first array isn't [1], you must solve it using the normal way.

3![2]w/[1] expands to ((3![1]w/[1])![1]w/[1])![1]w/[1]

3![1,2]w/[1] expands to 3!1,1]w/[1],1]w/[1] which expands to 3![[1]w/[1w/[1]

3![1,1,2]w/[1] expands to 3![1,[1,1,1]w/[1],1]w/[1] which expands to 3![1,[1]w/[1]]w/[1]

3![1,2,2]w/[1] expands to 3![[1,1,2]w/[1],1,2]w/[1]

If the first array is [1], and the second is not [1]:

a![1]w/[2] expands to a![1,2]w/[1]

a![1]w/[3] expands to a![1,1,2]w/[1]

a![1]w/[1,2] expands to a![1]w/1, which expands to a![1,1...1,1,2]w/[1]

If the first entry of the second array is bigger than 1, put it in the first array. Otherwise, solve the array.

Larger chain
a![1]w/[1]w/[1] expands to a![1]w/[1,1...1,1,2] with a a's

If the first array isn't [1], solve that linear array.

a![1,2]w/[1]w/[1] expands to a!1]w/[1]w/[1w/[1]w/[1]

If the first array is [1], but the second isn't, solve that array.

a![1]w/[2]w/[1] expands to a![1,1...1,1,2]w/[1]w/[1]

a![1]w/[1,2]w/[1] expands to a![1]w/1]w/[1]w/[1w/[1]

If the first and the second array are [1], but the third isn't, solve that array.

a![1]w/[1]w/[1,2] expands to a![1]w/[1,1...1,1,2]w/[1]

If the first, the second array and the third array are [1], but the fourth isn't, solve that array.

a![1]w/[1]w/[1]w/[1] expands to a![1]w/[1]w/[1,1...1,1,2]

etc.

Dimensional arrays
a![1(1)2] expands to a![1]w/[1]w/[1]...[1]w/[1]w/[1]

a![1,2(1)2] expands to a![[1(1)2](1)2]

a![1(1)2]w/[1] (the w/ operator works in the first row) expands to a![1,1...1,1,2(1)2]

a![1(1)2]w/[1(1)2] (the w/ operator works in the first row) expands to a![1(1)2]w/[1]w/[1]...[1]w/[1]w/[1]

a![1(1)2]w/[2(1)2] (the w/ operator works in the first row) expands to a![1,2(1)2]w/[1(1)2]

a![1(1)2]w/[1(1)2]w/[1] (the w/ operator works in the first row) expands to a![1(1)2]w/[1,1...1,1,2(1)2]

a![1(1)3] expands to a![1(1)2]w/[1(1)2]w/[1(1)2]...[1(1)2]w/[1(1)2]w/[1(1)2]

a![1(1)k+1] expands to a![1(1)k]w/[1(1)k]w/[1(1)k]...[1(1)k]w/[1(1)k]w/[1(1)k]