Sorry, there was a problem with the cut & paste
in my last msg. The group table should be
as follows. (When the identity is the first item,
the first row and the first column of the group
table should be t .)
<"2 t
+---+---+---+---+---+---+
|1 0|0 1|0 1|1 0|1 1|1 1|
|0 1|1 0|1 1|1 1|0 1|1 0|
+---+---+---+---+---+---+
<"_2 ~:/ .*"2/~ t
+---+---+---+---+---+---+
|1 0|0 1|0 1|1 0|1 1|1 1|
|0 1|1 0|1 1|1 1|0 1|1 0|
+---+---+---+---+---+---+
|0 1|1 0|1 1|1 1|0 1|1 0|
|1 0|0 1|0 1|1 0|1 1|1 1|
+---+---+---+---+---+---+
|0 1|1 0|1 1|1 1|0 1|1 0|
|1 1|1 1|1 0|0 1|1 0|0 1|
+---+---+---+---+---+---+
|1 0|0 1|0 1|1 0|1 1|1 1|
|1 1|1 1|1 0|0 1|1 0|0 1|
+---+---+---+---+---+---+
|1 1|1 1|1 0|0 1|1 0|0 1|
|0 1|1 0|1 1|1 1|0 1|1 0|
+---+---+---+---+---+---+
|1 1|1 1|1 0|0 1|1 0|0 1|
|1 0|0 1|0 1|1 0|1 1|1 1|
+---+---+---+---+---+---+
----- Original Message -----
From: Roger Hui <[EMAIL PROTECTED]>
Date: Friday, September 22, 2006 8:58 am
Subject: Re: [Jgeneral] I expect a table of ordered pairs for this
> a. The monad { computes a generalized Cartesian
> product. For example:
>
> {0 1 2;3 4 5 6
> +---+---+---+---+
> |0 3|0 4|0 5|0 6|
> +---+---+---+---+
> |1 3|1 4|1 5|1 6|
> +---+---+---+---+
> |2 3|2 4|2 5|2 6|
> +---+---+---+---+
>
> b. When using the dyad u/ to compute a function
> table, it can be helpful to apply <"_2 to the
> result. For example:
>
> t=: 2 2&$"1 #: i.16 NB. all 2-by-2 boolean matrices
> det=: -/ .* NB. determinant
> $t
> 16 2 2
> t=: (0~:det t)#t NB. non-singular 2-by-2 boolean matrices
> $t
> 6 2 2
> t=: t /: (,:=0 1) i. t NB. put identity matrix first
> <"2 t
> +---+---+---+---+---+---+
> |1 0|0 1|0 1|1 0|1 1|1 1|
> |0 1|1 0|1 1|1 1|0 1|1 0|
> +---+---+---+---+---+---+
> $ ~:/ .*"2/~ t
> 6 6 2 2
> <"_2 ~:/ .*"2/~ t NB. group table
> +---+---+---+---+---+---+
> |1 0|1 1|1 1|0 1|1 0|0 1|
> |0 1|0 1|1 0|1 1|1 1|1 0|
> +---+---+---+---+---+---+
> |1 0|1 1|1 1|0 1|1 0|0 1|
> |1 1|1 0|0 1|1 0|0 1|1 1|
> +---+---+---+---+---+---+
> |0 1|0 1|1 0|1 1|1 1|1 0|
> |1 1|1 0|0 1|1 0|0 1|1 1|
> +---+---+---+---+---+---+
> |1 1|1 0|0 1|1 0|0 1|1 1|
> |1 0|1 1|1 1|0 1|1 0|0 1|
> +---+---+---+---+---+---+
> |1 1|1 0|0 1|1 0|0 1|1 1|
> |0 1|0 1|1 0|1 1|1 1|1 0|
> +---+---+---+---+---+---+
> |0 1|0 1|1 0|1 1|1 1|1 0|
> |1 0|1 1|1 1|0 1|1 0|0 1|
> +---+---+---+---+---+---+
----------------------------------------------------------------------
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