p-adic Functions
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Calling Sequence
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sinp(ex, p, s) or evalp(sin(ex, p, s))
sinp(ex, p) or evalp(sin(ex, p))
sinp(ex)
...
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Parameters
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ex
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-
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expression of rational numbers and p-adic numbers
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p
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-
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prime number or positive integer
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s
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-
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positive integer
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Description
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The following functions evaluate the p-adic version of the corresponding real-valued function (obtained by dropping the final p from the name).
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sinp
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cosp
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tanp
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cscp
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secp
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cotp
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sinhp
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coshp
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tanhp
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cschp
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sechp
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cothp
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arcsinp
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arccosp
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arctanp
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arccscp
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arcsecp
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arccotp
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arcsinhp
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arccoshp
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arctanhp
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arccschp
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arcsechp
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arccothp
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expp
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logp
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sqrtp
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sinp is a short form for evalp@sin, and similarly for each of the other functions above.
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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.
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The expression ex can contain any of the operations +, -, *, /, ^, and any of the functions defined in the padic package.
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If the second and third arguments are omitted, then the expression ex must be a p-adic number.
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If the result of the computation is not convergent in the p-adic field, then the routine returns FAIL.
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See padic[evalp] for an explanation of the representation of p-adic numbers in Maple.
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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>).
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Examples
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