I'm still in favor of words starting at 0. As for matrix rows and columns,
it would be more...wait for it... natural to start at 0, but since the
literature overwhelmingly prefers to start at 1, maybe it's better to
conform with it (there are a few "historical accidents" like that, for
instance defining \pi as half what it should be, and since the consequences
are very mild, it stays like that).
And to state the obvious: since most results using the fact that rows and
columns are natural numbers have them intervene in the form (-1)^{i+j},
shifting both row and column indices by 1 does not change the parity of the
sum, so these statements are unaffected.
Benoit
On Friday, August 28, 2020 at 6:14:57 PM UTC+2 Alexander van der Vekens
wrote:
>
> There was a discussion in
> https://groups.google.com/g/metamath/c/UwTUuNPgaB0/m/NdWefzG4AgAJ about
> the indices for words. Currently, the indices for words start with 0, and
> the proposal to change this was not accepted.
>
> For matrices, however, the things are different: The indices for rows and
> colums usually start with 1, as Thierry explained, so I agree with Thierry.
> And having the planned conversion function should dispel any doubt.
>
> Alexander
>
> On Friday, August 28, 2020 at 9:45:33 AM UTC+2 Thierry Arnoux wrote:
>
>> Hi all,
>>
>> I recently formalized a proof of the Laplace expansion of determinants (~
>> mdetlap), which I think would be useful to pull to the main part of
>> set.mm. Because the formula makes calculation based on the row and
>> column indices of the element of the matrix, I'm using matrix with integer
>> indices (in contrast with the rest of the development on matrices which is
>> based on arbitrary sets).
>>
>> I chose indices in ` ( 1 ... N ) ` , so that the top-left matrix element
>> is a11 (in set.mm written ` ( 1 A 1 ) ` ). It seems using indices
>> starting from one is the convention used for mathematics, I have not found
>> yet a reference with indices starting at zero (and neither did Norm),
>> however we would like to run this through the community. Most programming
>> languages start indices with zero, with the exception of R and several
>> others.
>>
>> In set.mm words indices start with zero.
>>
>> What's your opinion? Should matrix indices start with one or zero?
>>
>> Thanks for your input!
>>
>> BR,
>> _
>> Thierry
>>
>>
>> PS. I would later like to define a "literal" matrix function which would
>> be used like this to transform words (for any matrix size up to 8x8) into
>> matrices :
>>
>> ( litMat ` <" <" A B C "> <" D E F "> <" G H I "> "> )
>>
>> This would allow a bridge/conversion.
>>
>
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