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To compute the p-adic ordinal of a rational number, one determines the highest power of the prime p that divides its numerator after clearing denominators.
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To compute the p-adic ordinal of a rational number, one determines the highest power of the prime p that divides its numerator after clearing denominators.
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Related words
p-adic ordinal
Noun
(number
theory)
A
function
of
rational
numbers,
with
prime
number
p
as
parameter,
which
is
defined
for
some
non-zero
integer
x
as
the
largest
integer
r
such
that
pʳ
divides
x;
is
defined
for
some
non-zero
rational
number
a/b
as
the
p-adic
ordinal
of
a
minus
the
p-adic
ordinal
of
b;
and
is
defined
for
0
as
infinity.
Japanese Meaning
（数論）素数 p をパラメーターとする有理数の関数。具体的には、非ゼロ整数 x に対して、p の累乗の中で x を割る中で最大となる指数 r を返す関数。非ゼロ有理数 a/b に対しては、分子 a の p 進序数から分母 b の p 進序数を引いた値を返し、0 に対しては無限大と定義される。
Related Words
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