Re: Incorrect (unexpected) output from TransformedField

• To: mathgroup at smc.vnet.net
• Subject: [mg131462] Re: Incorrect (unexpected) output from TransformedField
• From: Itai Seggev <itais at wolfram.com>
• Date: Mon, 29 Jul 2013 23:20:27 -0400 (EDT)
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```On Tuesday, July 23, 2013 4:16:40 PM UTC-5, ZdenÄ?k HurÃ¡k wrote:
> Hello,
>
>
>
> I seem to have troubles to understand the correct usage of TransformedField
function (in version 9). Or the function contains a bug :-) Here goes a simple
code with the source of my confusion
>
>
>
> ===================================================
>
> In[22]:= TransformedField[
>
>  "Polar" -> "Cartesian", {r, 0}, {r, \[Theta]} -> {x, y}]
>
>
>
> Out[22]= {x, y}
>
> ===================================================
>
>
>
> What I would expect as the cartesian description of a vector field originally
given in polar coordinates as {r,theta} is {Abs[x],0}. Have I missed anything
here? Thanks.

Hi Zdenek.

The output is correct.  I would encourage you read the tutorial, which you can
do by typing tutorial/ChangingCoordinateSystems into the Documentation Center.
Briefly, this input is interpreted as "change the vector field r e_r + 0
e_theta to Cartesian coordinates (x,y), which gives the radial vector field x
e_x + y e_y".  The tutorial explains seveal other operations you can perform;
perhaps this one is what you had in mind?

In[1]:= Map[
TransformedField["Polar" -> "Cartesian", #, {r, \[Theta]} -> {x, y}] &,
{r, 0}
]

Out[1]= {Sqrt[x^2 + y^2], 0}

I hope this helps.

--
Itai Seggev
Mathematica Algorithms R&D
217-398-0700

```

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