the order of a p-adic number - Maple Help

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padic[ordp] - the order of a p-adic number

padic[valuep] - the p-adic valuation of a p-adic number

Calling Sequence

ordp(a, p)

ordp(a)

valuep(a, p)

valuep(a)

Parameters

a

-

rational number (2-argument case) or p-adic number (1-argument case)

p

-

prime number or positive integer greater than 1

Description

• 

The ordp command computes the p-adic order of the p-adic number a (evalp(a, p) in the 2-argument case), which is the degree of the leading term.

• 

The valuep command computes the p-adic valuation of the p-adic number a (evalp(a, p) in the 2-argument case), which is 1/p^ordp(a).

• 

For an explanation of the representation of p-adic numbers in Maple, see padic[evalp].

Examples

withpadic:

a:=234234234975

a:=234234234975

(1)

ordpa,5

2

(2)

evalpa,5,7

452+453+56+357+O58

(3)

a:=evalpa,5

a:=452+453+56+357+458+259+2511+4512+513+3514+2515+516

(4)

b:=evalp1a2,5

b:=454+453+252+451+4+25+453

(5)

ordpa

2

(6)

ordpb

4

(7)

ordpab,5

2

(8)

valuepab

52

(9)

valuepab,5

5-6

(10)

ordpxy2,5

padic:-ordpy2+x,5

(11)

valuepxy2,5

padic:-valuepxy2,5

(12)

See Also

padic, padic[evalp]


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