pau'au

valsi

pau'au

type

experimental cmavo

creator

krtisfranks

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 + x₃p_x2)^k divides x₁)), where p_n 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 p_x2-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

krtisfranks

vote information

1

time

Thu Oct 27 05:51:43 2022

Examples

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