#16197: provide function expansions of power series (from Pari)
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Reporter: rws | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: calculus | Keywords: function, series expansion
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Not the same as `SR.taylor()`.
{{{
sage: R.<x> = PowerSeriesRing(ZZ)
sage: sqrt(1-4*x^2)
1 - 2*x^2 - 2*x^4 - 4*x^6 - 10*x^8 - 28*x^10 - 84*x^12 - 264*x^14 -
858*x^16 - 2860*x^18 + O(x^20)
sage: sin(1+4*x^2)
...
TypeError: cannot coerce arguments: no canonical coercion from Power
Series Ring in x over Integer Ring to Symbolic Ring
sage: var('X')
X
sage: ex=sin(1+4*X^2)
sage: ex.series()
...
TypeError: series() takes exactly 2 positional arguments (0 given)
}}}
What is missing and can be had from Pari:
* `acos`, `acosh`, `agm`, `asin`, `asinh`, `atan`, `atanh`, `cos`, `cosh`,
`cotanh`, `dilog`, `gamma`, `intformal`, `lngamma`, `psi`, `sin`, `sinh`,
`tan`, `tanh`
For example:
{{{
? atan(4*x^2+1)
%1 = 0.78539816339744830961566084581987572105 + 2*x^2 - 4*x^4 + 16/3*x^6 -
128/5*x^10 + 256/3*x^12 - 1024/7*x^14 + O(x^16)
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16197>
Sage <http://www.sagemath.org>
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