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Discussion of "ju'u"

Comment #1: A more nailed-down definition
Curtis W Franks (Sun Jun 21 22:07:36 2015)

I propose that it be specified somewhere that the following interpretation
is to be made for ".a'y ju'u by" ("a base b"):

Let n, m be integers such that n, m > 0; let 'a' be represented by a string
of digits, from left to right, (a_n, a_(n-1), ..., a_2, a_1, a_0, a_(-1),
a_(-2), ..., a_(-m+1), a_(-m)), with a_n being leftmost and a_(-m) being
rightmost; let b be any number such that exponentiation of b by any integer
in [-m, n] is defined (and preferably: strictly monotonic increasing fast
enough with respect to increasing values in the exponent). Then: .a'y ju'u
by = (a_n, a_(n-1), ..., a_2, a_1, a_0, a_(-1), a_(-2), ..., a_(-m)) ju'y
by = ((a_n)*(b^n)) + ((a_(n-1))*(b^(n-1))) + ... + ((a_2)*(b^2)) +
((a_1)*(b^1)) + ((a_0)*(b^0)) + ((a_(-1))*(b^(-1))) + ((a_(-2))*(b^(-2))) +
... + ((a_(-m+1))*(b^(-m+1))) + ((a_(-m))*(b^(-m))).

Comment #2: Re: A more nailed-down definition
Curtis W Franks (Sun Jun 21 22:08:44 2015)

krtisfranks wrote:
> I propose that it be specified somewhere that the following
interpretation
> is to be made for ".a'y ju'u by" ("a base b"):
>
> Let n, m be integers such that n, m > 0; let 'a' be represented by a
string
> of digits, from left to right, (a_n, a_(n-1), ..., a_2, a_1, a_0, a_(-1),

> a_(-2), ..., a_(-m+1), a_(-m)), with a_n being leftmost and a_(-m) being
> rightmost; let b be any number such that exponentiation of b by any
integer
> in [-m, n] is defined (and preferably: strictly monotonic increasing fast

> enough with respect to increasing values in the exponent). Then: .a'y
ju'u
> by = (a_n, a_(n-1), ..., a_2, a_1, a_0, a_(-1), a_(-2), ..., a_(-m)) ju'y

> by = ((a_n)*(b^n)) + ((a_(n-1))*(b^(n-1))) + ... + ((a_2)*(b^2)) +
> ((a_1)*(b^1)) + ((a_0)*(b^0)) + ((a_(-1))*(b^(-1))) + ((a_(-2))*(b^(-2)))
+
> ... + ((a_(-m+1))*(b^(-m+1))) + ((a_(-m))*(b^(-m))).


Oops: "[-m, n]" is supposed to be an interval from -m to n which includes
both of those endpoints.

Comment #3: Re: A more nailed-down definition
Curtis W Franks (Sun Jun 21 22:26:54 2015)

krtisfranks wrote:
> I propose that it be specified somewhere that the following
interpretation
> is to be made for ".a'y ju'u by" ("a base b"):
>
> Let n, m be integers such that n, m > 0; let 'a' be represented by a
string
> of digits, from left to right, (a_n, a_(n-1), ..., a_2, a_1, a_0, a_(-1),

> a_(-2), ..., a_(-m+1), a_(-m)), with a_n being leftmost and a_(-m) being
> rightmost; let b be any number such that exponentiation of b by any
integer
> in [-m, n] is defined (and preferably: strictly monotonic increasing fast

> enough with respect to increasing values in the exponent). Then: .a'y
ju'u
> by = (a_n, a_(n-1), ..., a_2, a_1, a_0, a_(-1), a_(-2), ..., a_(-m)) ju'y

> by = ((a_n)*(b^n)) + ((a_(n-1))*(b^(n-1))) + ... + ((a_2)*(b^2)) +
> ((a_1)*(b^1)) + ((a_0)*(b^0)) + ((a_(-1))*(b^(-1))) + ((a_(-2))*(b^(-2)))
+
> ... + ((a_(-m+1))*(b^(-m+1))) + ((a_(-m))*(b^(-m))).


In order to be clear, 'a' would normally be expressed with "pi" between
digit 'a_0' and 'a_(-1)'. All other commas are technically "pi'e"'s, but
I assumed for simplicity that the base for each digit was constant and such
that a_i is a single-digit number in that base for all i.

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