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Discussion of "ju'u"
[parent] [root]
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 suchthat a_i is a single-digit number in that base for all i.
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 recent changes jbovlaste main This is jbovlaste, the lojban dictionary system. The main code was last changed on Wed 07 Oct 2020 05:54:55 PM PDT. All content is public domain. By submitting content, you agree to place it in the public domain to the fullest extent allowed by local law. jbovlaste is an official project of the logical language group, and is now headed by Robin Lee Powell. E-mail him if you have any questions. care to log in?