find all roots of a polynomial with rational coefficients in a p-adic number field - Maple Help

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padic[rootp] - find all roots of a polynomial with rational coefficients in a p-adic number field

Calling Sequence

rootp (pol, p, s)  or  evalp (RootOf(pol),p, s)

rootp (pol, p)  or  evalp(RootOf(pol), p)

Parameters

pol

-

polynomial with rational coefficients

p

-

prime number or positive integer

s

-

(optional) positive integer

Description

• 

This function computes all roots in the given p-adic number field of the polynomial pol.

• 

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.

• 

See padic[evalp] for an explanation of the representation of p-adic numbers in Maple.

• 

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

Examples

withpadic:

rootpx251,5

1

(1)

rootpx2+1,5

3+35+252+353+54+256+57+458+O59,2+5+252+53+354+455+256+357+O59

(2)

rootpx2+1,3

f:=75x3+3x2+8x+3

f:=75x3+3x2+8x+3

(3)

evalpRootOff,5,15

452+451+25+352+354+355+56+357+458+259+2510+4511

(4)

See Also

padic, padic/functions, padic[evalp]


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