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padic

  

expansion

  

p-adic expansion

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

expansion(ex, p, x, s)

expansion(ex, p, x)

Parameters

ex

-

rational function

p

-

irreducible (or square-free) polynomial or 1/x (or infinity)

x

-

independent variable

s

-

(optional) a positive integer

Description

• 

This function computes the p-adic expansion of a rational function ex.

• 

The parameter s sets the size of the resulting expression, where "size" means the number of terms of the p-adic expansion which will be printed.  If omitted, it defaults to number 6.

• 

A p-adic expansion is represented in Maple using the unevaluated function call PADIC() whose argument is another unevaluated function of the form p_adic() which has three arguments. The first argument is the polynomial p or 1/x. The second argument is the p-adic order at p. The third argument is the list of coefficients. For example,

PADICp_adicx,0,1,1,1,1,1,1

  

represents the p-adic expansion

1x+x2x3+x4x5+Ox6

  

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

• 

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

Examples

withpadic:

expansionx3+1x2+3x+5,x,x

p_adicx,0,15,325,4125,128625,4043125,5721562531+p_adicx,0,15,325,4125,128625,4043125,5721562532x+p_adicx,0,15,325,4125,128625,4043125,5721562533x2+p_adicx,0,15,325,4125,128625,4043125,5721562534x3+p_adicx,0,15,325,4125,128625,4043125,5721562535x4+p_adicx,0,15,325,4125,128625,4043125,5721562536x5+Ox6

(1)

expansionx3+1x2+3x+5,x2+2,x

p_adicx2+2,0,13x13,49,481+481x,4729x16729,4656186561x,2059049x+445904931+p_adicx2+2,0,13x13,49,481+481x,4729x16729,4656186561x,2059049x+445904932x2+2+p_adicx2+2,0,13x13,49,481+481x,4729x16729,4656186561x,2059049x+445904933x2+22+p_adicx2+2,0,13x13,49,481+481x,4729x16729,4656186561x,2059049x+445904934x2+23+p_adicx2+2,0,13x13,49,481+481x,4729x16729,4656186561x,2059049x+445904935x2+24+p_adicx2+2,0,13x13,49,481+481x,4729x16729,4656186561x,2059049x+445904936x2+25+Ox2+26

(2)

expansionx3+1x2+3x+5,1x,x,5

p_adic1x,1,1,3,4,4,32311x+p_adic1x,1,1,3,4,4,32321x2+p_adic1x,1,1,3,4,4,32331x3+p_adic1x,1,1,3,4,4,32341x4+p_adic1x,1,1,3,4,4,32351x5+O1x4

(3)

See Also

padic

padic/functions

padic[lcoeffp]

padic[orderp]

 


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