       Re: Polar coordinates - ReplaceAll issue

• To: mathgroup at smc.vnet.net
• Subject: [mg107490] Re: [mg107479] Polar coordinates - ReplaceAll issue
• From: "David Park" <djmpark at comcast.net>
• Date: Sun, 14 Feb 2010 08:17:03 -0500 (EST)
• References: <7611287.1266146114246.JavaMail.root@n11>

```You don't want to use \[RightArrow]! The arrow that is used in rules is
entered as "->" (but without the quotes) and Mathematica automatically
converts it to an arrow (but not a \[RightArrow]).

omega = {x1 -> r Cos[theta], x2 -> r Sin[theta]}
% // FullForm

{x1 -> r Cos[theta], x2 -> r Sin[theta]}
List[Rule[x1, Times[r, Cos[theta]]], Rule[x2, Times[r, Sin[theta]]]]

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: Andrej [mailto:andrej.kastrin at gmail.com]

Hi,

this is my first post to this group. Yes, I'm a newbie in Mathematica.
I'm trying to compute the probability of circular disc (in R^2).
Suppose that vertical and horizontal deviations from the center of the
disc follows bivariate normal distribution. I hope that the code below
is self explained. The main issue is the transformation from Cartesian
to polar coordinates as follows:

# First I set up the appropriate bivariate normal distribution:
Needs["MultivariateStatistics`"]
X = {x1, x2};
mu = {0, 0};
Sigma = sigma^2 ({{1,rho}, {rho,1}});
dist = MultinormalDistribution[mu, Sigma];
cond = {sigma > 0, -1 < rho < 1, r > 0, 0 < theta < 2 \[Pi]};
f = Simplify[PDF[dist, X], cond]
domain[f] = {{x1, -\[Infinity], \[Infinity]}, {x2, -\[Infinity], \
[Infinity]}} && cond;

# Transformation to polar coordinates:
Omega = {x1 \[RightArrow] r Cos[theta], x2 \[RightArrow] r
Sin[theta]};
g = Simplify[(f /. Omega) Jacob[X /. Omega, {r, theta}], cond]

And the message I get:

ReplaceAll::reps: {x1\[RightArrow]r Cos[theta],x2\[RightArrow]r
Sin[theta]} is neither a list of replacement rules nor a valid
dispatch table, and so cannot be used for replacing. >>

Thanks in advance for any suggestions or pointers.

Best, Andrej

```

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