Changes between Initial Version and Version 4 of Ticket #16197


Ignore:
Timestamp:
04/22/14 06:48:16 (7 years ago)
Author:
rws
Comment:

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 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)

Legend:

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  • Ticket #16197

    • Property Summary changed from provide function expansions of power series (from Pari) to provide missing function expansions of power series
  • Ticket #16197 – Description

    initial v4  
    1 Not the same as `SR.taylor()`.
     1Some functions do not support rings/power-series*:
    22{{{
    33sage: R.<x> = PowerSeriesRing(ZZ)
     
    77...
    88TypeError: cannot coerce arguments: no canonical coercion from Power Series Ring in x over Integer Ring to Symbolic Ring
    9 sage: var('X')
    10 X
    11 sage: ex=sin(1+4*X^2)
    12 sage: ex.series()
    13 ...
    14 TypeError: series() takes exactly 2 positional arguments (0 given)
    159}}}
    16 What is missing and can be had from Pari:
    17 * `acos`, `acosh`, `agm`, `asin`, `asinh`, `atan`, `atanh`, `cos`, `cosh`, `cotanh`, `dilog`, `gamma`, `intformal`, `lngamma`, `psi`, `sin`, `sinh`, `tan`, `tanh`
    18 For example:
    19 {{{
    20 ? atan(4*x^2+1)
    21 %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)
    22 }}}
     10What is missing:
     11* `acos`, `acosh`, `asin`, `asinh`, `atan`, `atanh`, `cos`, `cosh`, `cotanh`, `dilog`, `gamma`, `intformal`, `lngamma`, `psi`, `sin`, `sinh`, `tan`, `tanh`