- Home
- Get A Printable Dictionary
- Search Best Words
- Recent Changes
- How You Can Help
- valsi - All
- valsi - Preferred Only
- natlang - All
- natlang - Preferred Only
- Languages
- XML Export
- user Listing
- Report Bugs
- Utilities
- Status
- Help
- Admin Request
- Create Account
|
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.
|
-
|
|
|