#16197: provide missing function expansions of power series
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Reporter: rws | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: calculus | Resolution:
Keywords: function, series expansion | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Old description:
> 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)
> }}}
New description:
Some functions do not support rings/power-series*:
{{{
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
}}}
What is missing:
* `acos`, `acosh`, `asin`, `asinh`, `atan`, `atanh`, `cos`, `cosh`,
`cotanh`, `dilog`, `gamma`, `intformal`, `lngamma`, `psi`, `sin`, `sinh`,
`tan`, `tanh`
--
Comment (by rws):
I wrote earlier:
> The rest of the ticket concerns possibly missing functions and I will
move this to another ticket.
Nothing missing there except the a.g.m., fortunately.
Replying to [comment:3 kcrisman]:
> Hmm, that's an interesting suggestion. One could imagine it's a bug the
other way around, but I have no vested interest in this - I think a
default for either one could be useful, in principle, and (importantly)
wouldn't be backward-incompatible. But what would the default be? It's
hard to imagine one non-arbitrary... hmm.
This is now #16201
> What do Mathematica and/or Maple and/or Magma do with this? If there is
a standard one could use that.
If I ask for "cosine power series" in Wolfram Alpha I get
`1-x^2/2+x^4/24-x^6/720+O(x^7)`
--
Ticket URL: <http://trac.sagemath.org/ticket/16197#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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