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padic

  

evalp

  

p-adic evaluation

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

evalp(ex, p, s)

evalp(ex, p)

evalp(ex)

Parameters

ex

-

expression of rational numbers and/or p-adic numbers

p

-

(optional) prime number or positive integer

s

-

(optional) positive integer

Description

• 

This function computes the p-adic value of the expression ex.

• 

The parameter s sets the size of the resulting expression, where "size" means the number of terms of the p-adic number which will be printed.  If omitted, it defaults to the value of the global variable Digitsp, which is initially assigned the value 10.

• 

The expression ex can contain any of the operations +, -, *, /, ^, and any of the functions defined in the padic package.  See padic/functions.

• 

If the second and third arguments are omitted, then the expression ex must be a p-adic number.

• 

If the result of the computation is not convergent in the p-adic field, then the routine returns FAIL.

• 

A p-adic number x is represented in Maple using the unevaluated function call PADIC() whose argument is another unevaluated function call of the form p_adic(pp, s, l) where pp is the prime p, s is the p-adic order of x, and l is the list of coefficients. For example,

PADICp_adic3,2,2,1,2,1,1,2,1

  

represents the p-adic number

232+31+2+3+32+233+O34

  

The print routine print/PADIC is used by the prettyprinter to format the p-adic number on screen.

• 

The command with(padic,evalp) allows the use of the abbreviated form of this command.

Examples

withpadic:

aevalpⅇ34634725,3

a:=1+232+33+34+35+236+O39

(1)

bevalpRootOf2x3+2x1,3

b:=1+3+233+34+35+37+O39

(2)

evalpab,3

1+232+36+237+O39

(3)

evalplog

232+34+35+38+39+O311

(4)

Digitsp15

Digitsp:=15

(5)

evalpk=1∞kk!,7

6+67+672+673+674+675+676+677+678+679+6710+6711+6712+6713+O714

(6)

See Also

padic

padic/functions

padic[ordp]

padic[ratvaluep]

padic[rootp]

 


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