pau'au
valsi
pau'au
type
experimental cmavo
creator
time entered
Thu Oct 27 04:13:15 2022
English
Definition #73015 - Preferred
selma'o
VUhU3
definition
ternary mekso operator: p-adic valuation; outputs (positive) infinity if x1 = 0 and, else, outputs sup(Set(k : k is a nonnegative integer, and MATH
$((1 - x_3)x_2 + x_3 p_{x_2})^k$
((1 - x3)x2 + x3px2)k divides x1)), where pn is the nth prime (such that p1 = 2).
notes
The terbri order here was defined in analogy to "de'o". Normally, x1 should be a rational number, and x2 should be a positive integer; some generalizations may be possible, though. x3 is either 0 xor 1, and indicates/toggles between modes: x3 = 0 yields the x2-adic valuation (even for nonprime x2); x3 = 1 yields the px2-adic valuation. MATH
$x_2 = 1, x_3 = 0$
x2 = 1, x3 = 0 yields positive infinity for any x1 which is within the domain. If x1 = n/m and is a rational noninteger number such that gcd(n, m) = 1, then pau'au MATH
$(x_1, x_2, x_3) =$
(x1, x2, x3) = pau'au MATH
$(n, x_2, x_3) -$
(n, x2, x3) - pau'au MATH
$(m, x_2, x_3)$
(m, x2, x3). See also: "fei'i", "pi'ei'oi". This word is often equivalent to or closely related to "pei'e'a" (which is, in some ways, more general but also is less flexible with respect to its input).
gloss words
- exponent of factors
- integer exponent
- maximum exponent of factor
- p-adic order
- p-adic valuation
- prime-logarithm
created by
vote information
1
time
Thu Oct 27 05:51:43 2022
Examples