Re: Taylor expansion does not expand well

[James Sherman Jr.]

On Thu, Dec 10, 2015 at 12:36 PM, Nicholas Jankowski
<address@hidden> wrote:
> On Thu, Dec 10, 2015 at 12:05 PM, Andy Buckle <address@hidden> wrote:
>>
>>
>>
>> On 10 December 2015 at 16:56, Jonathan Camilleri <address@hidden>
>> wrote:
>>>
>>> How does this work please?
>>>
>>> f=[1,3,3]
>>> f =
>>>
>>>    1   3   3
>>>
>>> octave:2> g = taylor(1,'expansionPoint',1,'order',4)
>>>
>>> Error:
>>> error: 'taylor' undefined near line 1 column 5
>>>
>>> What does this error mean please?
>>>
>>>
>>> I am using http://octave-online.net/.
>>>
>>> See post at
>>> http://math.stackexchange.com/questions/209320/where-do-the-factorials-come-from-in-the-taylor-series.
>>> See https://en.wikipedia.org/wiki/Taylor_series.
>>> Documentation at
>>> http://octave.sourceforge.net/symbolic/function/@sym/taylor.html would be
>>> helpful if it included more clear examples, preferably ones which are
>>> complete.
>>>
>>> You may use data sets to include tutorials if you wish, as I fail to see
>>> a complete implementation in place.
>>>
>>
>> "'taylor' undefined" means it can't find the function, taylor. Do you have
>> the symbolic package installed and loaded?
>>
>> If you do
>>
>> pkg list
>>
>> do you see a star next to symbolic?
>>
>>
>>
>> --
>> /* andy buckle */
>>
>> _______________________________________________
>> Help-octave mailing list
>> address@hidden
>> https://lists.gnu.org/mailman/listinfo/help-octave
>>
>
> I just checked out octave-online.net, and symbolic 2.1.0 should be installed
> and loaded by default. (list below).  I'm running a newer version (2,2,2).
> Jon, it is part of the symbolic package, and for it to work you have to call
> it with symbolically declared variables.  (try: help sym)
>
> Depending on how I try to call taylor, I get the same response. I'm not sure
> what the expected behavior is:
>
>>> a = sym('a')
> a = (sym) a
>
> taylor(a)
> a = (sym) a
>
>>> taylor(sin(a))
> ans = (sym)
>
>     5    3
>    a    a
>   --- - -- + a
>   120   6
>
> Alll good.
>
> now, calling with a nonsymbolically defined argument:
>
>>> b = [1:10];
>>> taylor(sin(b))
> error: 'taylor' undefined near line 1 column 1
>
> Seems like it should give a better answer than that, as this seems like it
> can't find taylor, when it's just called incorrectly. does that have
> something to do with how the interpreter looks for the package function?
>
> What's more, trying the same on octave-online.net:
>
> octave:10> a=sym ('a')
> a = (sym) a
>
> octave:11> taylor(a)
> error: structure has no member '
> '
> error: called from:
> error:   /usr/local/share/octave/packages/symbolic-2.1.0/@sym/symvar.m at
> line 98, column 14
> error:   /usr/local/share/octave/packages/symbolic-2.1.0/@sym/taylor.m at
> line 46, column 7
>
>
> Is this just a 2.1.0 bug?
>
> octave:2> pkg list
>
>  Package Name         | Version | Installation directory
> ---------------------+---------+-----------------------
>      communications *|   1.2.0 |
> .../share/octave/packages/communications-1.2.0
>             control *|   2.6.6 |
> /usr/local/share/octave/packages/control-2.6.6
>        econometrics *|   1.1.1 |
> .../share/octave/packages/econometrics-1.1.1
>           financial *|   0.4.0 |
> .../local/share/octave/packages/financial-0.4.0
> fuzzy-logic-toolkit *|   0.4.4 |
> .../octave/packages/fuzzy-logic-toolkit-0.4.4
>             general *|   1.3.4 |
> /usr/local/share/octave/packages/general-1.3.4
>            geometry *|   1.7.0 |
> /usr/local/share/octave/packages/geometry-1.7.0
>                  io *|   2.2.7 | /usr/local/share/octave/packages/io-2.2.7
>      linear-algebra *|   2.2.1 |
> .../share/octave/packages/linear-algebra-2.2.1
>           mechanics *|   1.3.1 |
> .../local/share/octave/packages/mechanics-1.3.1
>       miscellaneous *|   1.2.1 |
> .../share/octave/packages/miscellaneous-1.2.1
>                 nan  |   2.7.1 | /usr/local/share/octave/packages/nan-2.7.1
>              odepkg *|   0.8.4 |
> /usr/local/share/octave/packages/odepkg-0.8.4
>               optim *|   1.4.1 |
> /usr/local/share/octave/packages/optim-1.4.1
>         optiminterp *|   0.3.4 | .../share/octave/packages/optiminterp-0.3.4
>            parallel *|   2.2.0 |
> /usr/local/share/octave/packages/parallel-2.2.0
>              signal *|   1.3.0 |
> /usr/local/share/octave/packages/signal-1.3.0
>             splines *|   1.2.7 |
> /usr/local/share/octave/packages/splines-1.2.7
>          statistics *|   1.2.4 | .../share/octave/packages/statistics-1.2.4
>             strings *|   1.1.0 |
> /usr/local/share/octave/packages/strings-1.1.0
>              struct *|  1.0.10 |
> /usr/local/share/octave/packages/struct-1.0.10
>            symbolic *|   2.1.0 |
> /usr/local/share/octave/packages/symbolic-2.1.0
>
>
>
>
>
> _______________________________________________
> Help-octave mailing list
> address@hidden
> https://lists.gnu.org/mailman/listinfo/help-octave
>

Just to compare this to current MATLAB behavior, if you try and call
taylor with a matrix of doubles, you get the following error message:

> Undefined function 'taylor' for input arguments of type 'double'.

So, I guess its slightly better error message, since you might be able
to deduce from there that you're calling it incorrectly.