 addcoords - Maple Programming Help

add a new coordinate system, and/or default information

 Calling Sequence addcoords(coord_name, v, in_cart, con, dlist)

Parameters

 coord_name - name of the coordinate system v - list of variables (in either 2 or 3 dimensions) in_cart - list of expressions defining the cartesian coordinates x, y, z in terms of the new coordinates con - list of names of constants in in_cart dlist - list of default values for coordplot or coordplot3d

Description

 • The function addcoords adds a new coordinate system which can be used to plot a function or to provide default information used by coordplot or coordplot3d for generating plots of the coordinate system.
 Note: To add a new coordinate system for use with the differential operators (Divergence, Gradient, Curl, and Laplacian) of the VectorCalculus package, use the VectorCalculus[AddCoordinates] command.
 • In the two-dimensional case, v and in_cart are lists of two elements. For the three-dimensional case, they are lists of three elements.
 • When con is required, it must be specified AFTER v.
 • When adding default information, the coordinate system must be previously defined (either internally to Maple or by addcoords), or defined in the same call to addcoords.
 • For two-dimensional systems, default information for coordplot is defined in dlist by

$\left[\mathrm{range1},\mathrm{range2},\mathrm{grid1},\mathrm{grid2},\mathrm{view1},\mathrm{view2}\right]$

 range1, range2 specify the variable ranges to be used in the transformation.
 grid1, grid2 are the two integer grid values.
 view1, view2 are real ranges specifying the dimensions of the view box to be used by coordplot.
 • For three-dimensional systems, default information for coordplot3d is defined in dlist by

$\left[\mathrm{values1},\mathrm{values2},\mathrm{values3},\left[\mathrm{range1},\mathrm{range2},\mathrm{range3}\right],\left[\mathrm{view1},\mathrm{view2},\mathrm{view3}\right]\right]$

 values1, values2, values3 are lists of constant values, each list corresponding to a single coordinate.  At least one constant value must appear in each list.
 range1, range2, range3 are range values for each of the coordinates.
 view1, view2, view3 are real ranges specifying the dimensions of the view box to be used by coordplot3d.
 • See plots[coordplot] or plots[coordplot3d] for details about each of the above parameters.
 • See coords or plot3d[coords] for details of the coordinate systems currently implemented in Maple.

Examples

 > $\mathrm{addcoords}\left(\mathrm{me1},\left[\mathrm{e1},\mathrm{e2}\right],\left[\frac{{\mathrm{e1}}^{2}-{\mathrm{e2}}^{2}}{2},2\mathrm{e1}\mathrm{e2}\right]\right)$
 > $\mathrm{plot}\left(1,\mathrm{coords}=\mathrm{me1}\right)$ > $\mathrm{addcoords}\left(\mathrm{newcylinder},\left[r,\mathrm{\theta },z\right],\left[r\mathrm{cos}\left(\mathrm{\theta }\right),r\mathrm{sin}\left(\mathrm{\theta }\right),z\right],\left[\left[1.5\right],\left[\frac{\mathrm{\pi }}{3}\right],\left[0.5\right],\left[0..2,0..2\mathrm{\pi },-1..1\right],\left[-4..4,-4..4,-1..1\right]\right]\right):$
 > $f≔r\mathrm{sin}\left(\mathrm{\theta }\right){z}^{2}:$$v≔\left[r,\mathrm{\theta },z\right]$
 ${v}{≔}\left[{r}{,}{\mathrm{\theta }}{,}{z}\right]$ (1)
 > $\mathrm{plot3d}\left(z\mathrm{cos}\left(\mathrm{\theta }\right),z=0..10,\mathrm{\theta }=0..2\mathrm{\pi },\mathrm{style}=\mathrm{PATCH},\mathrm{shading}=\mathrm{ZGREYSCALE},\mathrm{coords}=\mathrm{newcylinder}\right)$ > $\mathrm{plots}\left[\mathrm{coordplot3d}\right]\left(\mathrm{newcylinder}\right)$ 