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p-adic Functions

Calling Sequence

sinp(ex, p, s)  or  evalp(sin(ex, p, s))

sinp(ex, p)  or  evalp(sin(ex, p))

sinp(ex)

...

Parameters

ex

-

expression of rational numbers and p-adic numbers

p

-

prime number or positive integer

s

-

positive integer

Description

• 

The following functions evaluate the p-adic version of the corresponding real-valued function (obtained by dropping the final p from the name).

sinp

cosp

tanp

cscp

secp

cotp

sinhp

coshp

tanhp

cschp

sechp

cothp

arcsinp

arccosp

arctanp

arccscp

arcsecp

arccotp

arcsinhp

arccoshp

arctanhp

arccschp

arcsechp

arccothp

expp

logp

sqrtp

 

 

 

• 

sinp is a short form for evalp@sin, and similarly for each of the other functions above.

• 

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.

• 

The expression ex can contain any of the operations +, -, *, /, ^, and any of the functions defined in the padic package.

• 

If the second and third arguments are omitted, then the expression ex must be a p-adic number.

• 

If the result of the computation is not convergent in the p-adic field, then the routine returns FAIL.

• 

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

• 

These functions are part of the padic package, and so can only be used after performing the command with(padic) or with(padic,<function-name>).

Examples

withpadic&colon;

cosp3&comma;3

1&plus;32&plus;234&plus;36&plus;237&plus;38&plus;O39

(1)

cosp3&plus;&comma;3

FAIL

(2)

cos3

cos3

(3)

evalf

0.9899924966

(4)

evalp&comma;3

1&plus;32&plus;234&plus;36&plus;237&plus;38&plus;O39

(5)

Digitsp:=8

Digitsp:=8

(6)

evalp&ExponentialE;3&comma;3

1&plus;3&plus;32&plus;233&plus;234&plus;36

(7)

logp

3&plus;O38

(8)

arctanhpx&comma;p&comma;10

padic:-arctanhpx&comma;p&comma;10

(9)

evalsubsx&equals;6&comma;p&equals;3&comma;

23&plus;232&plus;233&plus;35&plus;37&plus;38&plus;O310

(10)

op

p_adic3&comma;1&comma;2&comma;2&comma;2&comma;0&comma;1&comma;0&comma;1&comma;1&comma;0&comma;1

(11)

evalp

23&plus;232&plus;233&plus;35&plus;37&plus;38&plus;O310

(12)

See Also

padic, padic[evalp], padic[valuep]


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