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Topic: Tips for writing correct, non trivial Mathematica Libraries
Replies: 4   Last Post: Jan 20, 2012 1:58 AM

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Andrzej Kozlowski

Posts: 2,112
Registered: 1/29/05
Re: Tips for writing correct, non trivial Mathematica Libraries
Posted: Jan 20, 2012 1:51 AM
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On 19 Jan 2012, at 15:55, Andrzej Kozlowski wrote:

>
> On 19 Jan 2012, at 14:14, Nehal Patel wrote:
>

>> On Jan 19, 2012, at 6:39 AM, Andrzej Kozlowski wrote:
>>

>>>
>>> On 19 Jan 2012, at 11:12, Bill Rowe wrote:
>>>

>>>>>
>>>>> geom[list_] := Apply[Times, list]^(1/Length[list])

>>>>
>>>>> So, this does a bad thing for geom[ x+ y] (returns (Sqrt[x y])
>>>>
>>>> What were you expecting here? This looks correct to me

>>>
>>> Clearly he sees what actually is a powerful feature of Mathematica

as a "bad thing". The feature is that a function whose arguments are not
restricted by pattern maching can be put to a more general use. I think
it's great and not "bad". If you want to restrict the function to work
on lists you can do this:
>>>
>>
>> Hi -- thanks for your comment. Actually I think the pattern matching

is the coolest thing. my point is that when combined with how
Mathematica treats + (and in general, Flat and Orderless operators) it
becomes a lot harder to reason about whether a function handles all
edge cases correctly. So for instance nobody would expect the geometric
mean of x + y to be Sqrt[x y], it should be (x + y)^1 = x+ y
>
> No, it shouldn't be. There is no such thing as a mean of a number or

an algebraic expression. What you would expect is
>
> In[7]:= geom[{x + y}]
>
> Out[7]= x + y
>
> which is indeed what you get.
>

>>
>> Separately, GeometricMean does do something reasonable for

GeometricMean[x + y] (give it a try), and I wish it were easier to see
what syntax it uses.
>
> It is very easy to do that, it in fact:
>
> Clear[geom]
>
> geom::nonlist =
> "The argument `1` is neither a non-empty vector nor a non-empty matrix";
>
> geom[ls_] /;If[Head[ls] === List, True, Message[geom::nonlist, x]; False] :=
> Apply[Times, ls]^(1/Length[ls])
>
> geom[{x + y}]
>
> x + y
>
> geom[x + y]
>
> The argument x is neither a non-empty vector nor a non-empty matrix
>
> geom[x + y]
>
> Andrzej Kozlowski
>



It should have been:

geom[ls_] /;
If[Head[ls] === List, True, Message[geom::nonlist, ls]; False] :=
Apply[Times, ls]^(1/Length[ls])

and then:

geom[x + y]

geom::nonlist: The argument x+y is neither a non-empty vector nor a non-empty matrix

geom[x + y]=




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