padic[expansion] - p-adic expansion
|
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,
|
|
represents the p-adic expansion
|
|
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
|
|
>
|
|
>
|
|
![p_adic(x, 0, [1/5, -3/25, 4/125, 128/625, -404/3125, 572/15625])[3][1]+p_adic(x, 0, [1/5, -3/25, 4/125, 128/625, -404/3125, 572/15625])[3][2]/x+p_adic(x, 0, [1/5, -3/25, 4/125, 128/625, -404/3125, 572/15625])[3][3]/x^2+p_adic(x, 0, [1/5, -3/25, 4/125, 128/625, -404/3125, 572/15625])[3][4]/x^3+p_adic(x, 0, [1/5, -3/25, 4/125, 128/625, -404/3125, 572/15625])[3][5]/x^4+p_adic(x, 0, [1/5, -3/25, 4/125, 128/625, -404/3125, 572/15625])[3][6]/x^5+O(x^6)](/support/helpjp/helpview.aspx?si=9067/file04403/math140.png)
| (1) |
>
|
|

| (2) |
>
|
|
![p_adic(1/x, -1, [1, -3, 4, 4, -32])[3][1]/``(1/x)+p_adic(1/x, -1, [1, -3, 4, 4, -32])[3][2]/``(1/x)^2+p_adic(1/x, -1, [1, -3, 4, 4, -32])[3][3]/``(1/x)^3+p_adic(1/x, -1, [1, -3, 4, 4, -32])[3][4]/``(1/x)^4+p_adic(1/x, -1, [1, -3, 4, 4, -32])[3][5]/``(1/x)^5+O(``(1/x)^4)](/support/helpjp/helpview.aspx?si=9067/file04403/math154.png)
| (3) |
|
|