Phrases d21 and d22 and their constituents are:
ip=: +/ .*
cst=: C.!.2@(#:i.)@:#~ NB. Complete skew tensor
d21=: cross1=: [ ip [EMAIL PROTECTED]@[ ip ] NB. Generalized cross-product
d22=: cross2=: ((_1: |.[)*(1:|.]))-((1: |.[)*(_1: |. ]))
NB. Conventional cross product (not valid for dimension greater than 3)
cross2 can be shortened using the nvv fork which
was not available at the time of the original writing
of J Phrases:
cross2a=: ((_1 |.[)*(1|.])) - ((1 |.[)*(_1 |. ]))
Moreover, depending on your tastes, the following may
be preferred:
cross2b=: (_1&|[EMAIL PROTECTED] * 1&|[EMAIL PROTECTED]) - (1&|[EMAIL
PROTECTED] * _1&|[EMAIL PROTECTED])
As is commonly the case, a derivation from the general
case may be more insightful:
cross1a=: [ ip (cst 3) ip ]
cross1b=: ip (cst 3)&ip
] x=: _40 + 3 [EMAIL PROTECTED] 100
15 _35 15
] y=: _40 + 3 [EMAIL PROTECTED] 100
33 18 10
x cross1 y
620 _345 _1425
x cross1a y
620 _345 _1425
x cross1b y
620 _345 _1425
x cross2 y
620 _345 _1425
x cross2a y
620 _345 _1425
x cross2b y
620 _345 _1425
cst 3
0 0 0
0 0 1
0 _1 0
0 0 _1
0 0 0
1 0 0
0 1 0
_1 0 0
0 0 0
----- Original Message -----
From: Roger Hui <[EMAIL PROTECTED]>
Date: Wednesday, August 15, 2007 15:56
Subject: Re: [Jprogramming] a vector product
To: Programming forum <[email protected]>
> Please see phrases d21 and d22 in
> http://www.jsoftware.com/jwiki/JPhrases/ParitySymmetry
>
>
>
> ----- Original Message -----
> From: Tracy Harms <[EMAIL PROTECTED]>
> Date: Wednesday, August 15, 2007 15:33
> Subject: [Jprogramming] a vector product
> To: [email protected]
>
> > In "Elementary Matrix Theory", Howard Eves defines a vector
> > product, for
> > three-dimensional (real) Cartesian coordinate use, so:
> >
> > c = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1)
> >
> > (Above, all numerals are subscripts denoting vector elements.)
> >
> > I implemented that calculation of c with the following definitions:
> >
> > atomsb =: 1 0 { atomsa =: 3 4 A. i.3
> > vp =: -/@:((atomsa { [) * atomsb { ])
> >
> > My question is, does this seem as good a way as any to handle
> > this? In
> > particular, is this a case where it is not worth trying to
> shoe-
> > horn the
> > functions into a dot phrasing?
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