On 8/9/06, Miller, Raul D <[EMAIL PROTECTED]> wrote:
The text of the dictionary provides a definition for
minors which does not require square matrices:
minors=: }."1 @ (1&([\.))
Even if you don't know enough J to read that expression,
(perhaps you are not familiar with \.) you could examine
what it does on arrays of indices.
For example, consider the results of
(;$)minors i. 2 2
(;$)minors i. 3 3
(;$)minors i. 4 3
etc.
The definition of minors is only part of the definition of u . v.
And the fact that it does not require square matrices does
not explain whether that is intentional, and if yes, what is
u . v meant to do on non-square matrices. And to observe
that u . v is intentionally generalized in this way, I would first
have to have *guessed* that somehow -- but how do you
guess very unusual things?
Then I would have to delve into experimenting, reading lots
of definitions, making new guesses, trying to comprehend
how the whole thing works, reading again some definitions,
proving or refuting guesses, formulating new guesses ... all
that for a single entry in the dictionary, because its definition
does not say *explicitly* what it defines (and why not what is
being aimed at with it).
Call me extremely lazy, of marginal intellectual abilities,
having very low capacity of comprehending formal texts etc.
or all that together. Or, as Roger seems to prefer, a
``perverse interpreter'' of the dictionary text. But I am still
of the opinion that a couple of words added here and there
to clarify the meaning of some definitions won't kill anyone.
Boyko
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