the order of a p-adic expansion of a rational function - Maple Help

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padic[orderp] - the order of a p-adic expansion of a rational function

padic[lcoeffp] - the leading coefficient of a p-adic expansion of a rational function

Calling Sequence

orderp(ex, p, x)

lcoeffp(ex, p, x)

Parameters

ex

-

rational function

p

-

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

x

-

independent variable

Description

• 

The orderp command computes the order at p of the p-adic expansion of a rational function ex in x.

• 

The lcoeffp command computes the leading coefficient  at p of the p-adic expansion of a rational function ex in x.

Examples

withpadic:

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

(1)

orderpx3+1x2+3x+5,x2+2,x

0

(2)

lcoeffpx3+1x2+3x+5,x2+2,x

13x13

(3)

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

p_adic1x,1,1,3,4,4,32,76311x+p_adic1x,1,1,3,4,4,32,76321x2+p_adic1x,1,1,3,4,4,32,76331x3+p_adic1x,1,1,3,4,4,32,76341x4+p_adic1x,1,1,3,4,4,32,76351x5+p_adic1x,1,1,3,4,4,32,76361x6+O1x5

(4)

orderpx3+1x2+3x+5,1x,x

1

(5)

lcoeffpx3+1x2+3x+5,1x,x

1

(6)

See Also

padic, padic[expansion]


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