exp(PadicNumber) -- p-adic exponential function

Function: exp
Usage:

exp x
Inputs:
- x, a p-adic number,
Outputs:
- a p-adic number, the p-adic exponential of x;

Description

Returns the $p$-adic exponential of $x$, defined by the power series $\exp_p x = \sum_{n=0}^\infty x^n / n!$. The series converges when $|x|_p < p^{-1/(p-1)}$.

i1 : exp QQ_7 7

o1 = 1 + 1*7^1 + 4*7^2 + 2*7^3 + 3*7^5 + 2*7^6 + 4*7^7 + 3*7^8 + 4*7^9 +
     2*7^10 + 4*7^11 + 1*7^13 + 1*7^14 + 3*7^15 + 3*7^16 + 4*7^17 + 5*7^18 +
     1*7^19

o1 : QQ  (of precision 20)
       7

i2 : log oo

o2 = 1*7^1

o2 : QQ  (of precision 20)
       7

Caveat

An error is raised if the series does not converge.

Ways to use this method:

exp(PadicNumber) -- p-adic exponential function

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Padic.m2:863:0.

exp(PadicNumber) -- p-adic exponential function

Description

Caveat

Menu

Ways to use this method: