I would like to transform these Cartesian coordinates to Cylindrical
0≤x≤1,-
1-
2
x
≤y≤
1-
2
x
,
2
x
+
2
y
≤z≤1
1
∫
2
x
+
2
y
1-
2
x
∫
-
1-
2
x
1
∫
0
1xyz
After the transformation, the coordinates still appear to be in Cartesian and not Cylindrical ≠ {x,y,z} →{r, θ, z}.
​
What is the recommended way in Mathematica to perform this transformation?
In[]:=
CoordinateTransform"Cartesian""Cylindrical",0,-
1-
2
x
,
2
x
+
2
y
,1,
1-
2
x
,1
Out[]=

1-
2
x
,ArcTan0,-
1-
2
x
,
2
x
+
2
y
,
2-
2
x
,ArcTan1,
1-
2
x
,1
CoordinateTransform"Cartesian""Cylindrical",0,-
1-
2
x
,
2
x
+
2
y
​​CoordinateTransform"Cartesian""Cylindrical",1,
1-
2
x
,1
Out[]=

1-
2
x
,ArcTan0,-
1-
2
x
,
2
x
+
2
y

Out[]=

2-
2
x
,ArcTan1,
1-
2
x
,1