In SATN-42 (Sharp APL Technical Notes), 1982-04-01,
Ken Iverson described several uses monads derived
from the dot operator. Translated from APL into
J, these are:
+./ . *.
+ / . *.
<./ . +
>./ . +
<./ . *
>./ . *
<./ . >.
>./ . <.
Computation of f/ .g can be sped up for f and g
in domains which permit Gaussian elimination.
This has not been done in the current
implementation.
----- Original Message -----
From: Ewart Shaw <[EMAIL PROTECTED]>
Date: Friday, December 1, 2006 8:09 am
Subject: [Jprogramming] monadic ~:/ . *.
> The only common monadic uses of . seem to be
>
> determinant=: -/ . *
> permanent=: +/ . *
>
> (see e.g. . from the J help vocabulary page). However, I recently
> wanted to check that a set of n boolean vectors of length n are
> linearly independent over the finite field GF(2) (i.e. 0 & 1 multiply
> as normal, and addition is mod 2). This can be verified by
>
> det2=: ~:/ . *.
>
> which is 1 when the (n x n) argument y has linearly independent rows.
> At least I think it is! Possible applications include binary codes
> and Zobrist hashing (using e.g. the first several columns as hash key
> and the remaining columns to disambiguate collisions).
>
> Note that det2 is very slow on a 10x10 matrix or larger
> (like permanent, time is roughly proportional to !#y).
>
>
> NB.============================== J script
> ==============================
> hashmat=: 3 : 0 NB. hack to give "random-looking"
> m=. m0=. ?. (2#y)$2 NB. invertible yxy matrix over GF(2)
> for_i. i. y do.
> if. -. (ii=. <i,i){m do.
> m=. 1 ii}m
> m0=. (-. ii{m0) ii} m0
> end.
> m=. m ~: (i{"1 m) *./ i{m
> end.
> m0
> )
>
> det2=: ~:/ . *. NB. Determinant for GF(2)
>
> hammdist=: ([: +/ ~:)"1/~ NB. Hamming distance
>
> NB.============================== example
> ===============================
> ] H8=: hashmat 8
> 1 1 0 1 1 1 0 0
> 0 1 0 1 0 0 1 0
> 0 0 1 0 1 1 1 0
> 0 0 0 1 1 1 0 1
> 1 0 0 1 1 0 1 0
> 1 0 0 0 0 0 0 1
> 0 0 1 0 0 1 0 0
> 1 0 0 1 0 1 0 0
> det2 H8
> 1
> hammdist H8
> 0 4 5 3 3 5 5 2
> 4 0 5 5 3 5 5 4
> 5 5 0 4 4 6 2 5
> 3 5 4 0 4 4 4 3
> 3 3 4 4 0 4 6 3
> 5 5 6 4 4 0 4 3
> 5 5 2 4 6 4 0 3
> 2 4 5 3 3 3 3 0
>
> NB.============================== end
> ===================================
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