Bug fix: Contourplot bugs

There are several bugs affecting contourplot in the plots package. The following two bugs can be remedied by using the procedure patchcontourplot from the Maple Advisor Database to install a patch.

• In Maple 6, contourplot does not work with an expression f involving a fraction with non-constant denominator (i.e. such that denom(f) returns a non-constant value): it just plots contours for the numerator numer(f) . This bug was fixed in Maple 6.01.

> with(plots,contourplot):

> contourplot(x/y,x=1..2,y=1..2);

• contourplot doesn't work when the bounds for the variable depend on the variable. This bug is present in both Maple 6 and Maple 6.01.

> contourplot(x+y,x=0..1,y=0..x,coloring=[red,blue]);

• For copyright reasons, patchcontourplot is a procedure that produces a new version of the original Maple library procedure `plots/contplot` and a modified version of `plot/iplot2d` under the name `plot/iplot2d/patch` , rather than being a new version of the Maple library procedure itself. Running patchcontourplot() once will save the new procedures into a library (which could be the Maple Advisor Database library - saving it into Maple's own "lib" library is not recommended). Then (as long as this library's directory is present in your libname before Maple's "lib" directory), the patched procedures will be used. The directory to be used is the value of the variable savelibname , if that has been assigned a value, otherwise the first one in libname . I recommend that your "advisor" directory containing the Maple Advisor Database files be the first member of libname , so in most cases the corrected procedure will go there. If necessary, assign a new value to savelibname before running patchcontourplot .

> savelibname:= "c:/advisor";

Now run patchcontourplot() . A warning will result if you attempt to install the patch in a directory whose name does not include the word "advisor", and you will be asked to confirm that this directory is the proper target. This is intended to prevent you from accidentally writing to Maple's own "lib" or "update" libraries.

> patchcontourplot();

Now the examples above should work:

> contourplot(x/y,x=1..2,y=1..2);

> contourplot(x+y,x=0..1,y=0..x,coloring=[red,blue]);

• The following bugs are not fixed by this patch.
• contourplot doesn't work with two-dimensional coordinate systems.

> contourplot(r*cos(theta),r=0..3,theta=0..Pi,coords=polar);

Error, (in plot/iplot2d/patch) cannot convert to coordinate system polar

Three-dimensional coordinate systems do work, but not in the way you might expect.

> contourplot(r*cos(theta),r=0..3,theta=0..Pi,coords=cylindrical,scaling=constrained);

It seems that contourplot(f(u,v), u=a..b, v=c..d, coords=cylindrical) actually plots the projection in the xy plane of the contours of the surface , i.e. the curves for different values of the constant .

To produce a contour plot in a two-dimensional coordinate system, use the Maple Advisor Database function changecoords2d .

> changecoords2d(contourplot(r*cos(theta),r=0..3, theta=0..2*Pi,scaling=constrained), polar);

To make a contour plot using a three-dimensional coordinate system such as cylindrical coordinates (plotting the level curves of ), you can use the parametric version of contourplot .

> contourplot([r,theta,r*cos(theta)], r=0..3, theta=0..2*Pi, coords=cylindrical, scaling=constrained);

• Strange results can occur if the expression being plotted becomes infinite somewhere in the rectangle. First of all, if this is the case you should use the contours option to specify the contour values as a list, as otherwise very large contour values are likely to be chosen. There is likely to be a strange "zig-zag" effect near a curve where the function has limits of both and , caused by the fact that linear interpolation across such a curve does not approximate the expression well. But a strange bug can be encountered if the values calculated at some grid points are very large. For example:

> contourplot((2*x+y)/(x^2-y),x=-3..3,y=-3..3,contours=[-1,0,1]);

A work-around for this is to change either the definition of the function or the rectangle very slightly so that grid points will not be so very close to (or exactly on) the curve.

> contourplot((2*x+y)/(x^2-y),x=-3..3,y=-3.00001..3.00002,contours=[-2,0,2],axes=box,grid=[40,40]);

Maple Advisor Database R. Israel, 2000