273 Reputation

19 years, 274 days

Two questions...

1)  Which version of MapleTA are you using?  This has a major impact on how you can work around the difficulty.

If you are using a new enough version of MapleTA there is an equation editor in the question editor that can probably be used to get around this problem.

2)  Are you generating the expression t^3/t^2 randomly as the quotient of polynomials or is it a fixed expression?

This relates to the first question.  If you are randomly generating a rational function, you should be able to use the equation editor along with some tricks in Maple to get what you want.

@dkozlov Thank you.  Our IT people ...

@dkozlov Thank you.  Our IT people have already sent the request.  Just in case, I will send them the link to this page.

Is it a bug? #3...

@I am not trying to explain why implicit plot works in some cases.  My goal is to explain that I do not feel the assumption that implicitplot should work in cases that are basically singular is well founded.  Just because a routine works the way you want it to work in some cases does not mean that it should work that way in most cases.

Attached is an animation of implicitplot for (y-a*x)^2=0.

 > with(plots):
 > animate(implicitplot,[(y-a*x)^2=0,x=-5..5,y=-5..5,numpoints = 10^6, thickness = 5],a=-2..1);
 >

Is it a bug? #2...

I guess that I simply view this behavior differently.  All of the cases that are shown here appear to be "singular" in the sense that the are 0 derivatives of the function on the set of interest.  This is known to cause trouble, even for the fast convergence of Newton's method.

If you plot acer's example as the graphs of the functions f[a](x,y) = (x-y)^2+a intersecting with the xy-plane in three dimensions, this becomes clearer.  (The level sets, lines of intersection, disappear on one side of a=0.)  The difference between this and g[a](x,y)=x-y is stark.  (The level sets, lines of intersection, do not disappear near a=0 for g[a](x,y)=0.)

 > with(plots):
 > animate(plot3d,[[(x-y)^2+a,0],x=-10..10,y=-10..10,color=["LightGreen",red],view=[-5..5,-5..5,-5..5],orientation=[30,85,0],axes=boxed],a=-3..2);
 > animate(plot3d,[[x-y+a,0],x=-10..10,y=-10..10,color=["LightGreen",red],view=[-10..10,-10..10,-10..10],orientation=[15,75,0],axes=boxed],a=-5..5);
 >

Is it actually a bug?...

I have often observed this behavior in implicitplot3d.  I think the behavior is based on the fact that Maple is using a grid to look for solutions to the equation.  If the solution points are too far from grid points, I expect Maple to "miss" some of the solution set.

This example shows what Maple does in a simple case when one "adds" an important point to the grid.

 > with(plots):
 > implicitplot3d(z^2=x^2+y^2,x=-2..2,y=-2..2,z=-2..2,orientation=[25,75,0],axes=boxed); implicitplot3d(z^2=x^2+y^2,x=-2..2,y=-2..2,z=-2..2,orientation=[25,75,0],axes=boxed,          grid=[9,9,9]);
 >
 >

What are the a, b and x?...

What are you trying to do?  Without context, I am only guessing as to what your actual problem involves.  Are you trying to create a function of x and then integrate it?  Please write out an example showing what you really want.

Are a, b and x Vectors?

Did you mean "unapply" in your code?

Is your integral over a rectangle in two dimensions?

What are the a, b and x?...

What are you trying to do?  Without context, I am only guessing as to what your actual problem involves.  Are you trying to create a function of x and then integrate it?  Please write out an example showing what you really want.

Are a, b and x Vectors?

Did you mean "unapply" in your code?

Is your integral over a rectangle in two dimensions?

The name of the user is displayed...

The name of the user is displayed on the MapleTA window in the upper right below the Maplesoft logo.  My question still stands, when do you need  something beyond multi-part questions?

The name of the user is displayed...

The name of the user is displayed on the MapleTA window in the upper right below the Maplesoft logo.  My question still stands, when do you need  something beyond multi-part questions?

Maybe this is better?...

@Markiyan Hirnyk  Maybe switching to interface(prettyprint=2)?

 > p1 := proc () interface(prettyprint = 2); print(eval(thisproc)) end proc;
 (1)
 > p1();
 (2)
 >

or in document mode

 (1)

 (2)

Maybe this is better?...

@Markiyan Hirnyk  Maybe switching to interface(prettyprint=2)?

 > p1 := proc () interface(prettyprint = 2); print(eval(thisproc)) end proc;
 (1)
 > p1();
 (2)
 >

or in document mode

 (1)

 (2)

Maple is doing 10 decimal digit computat...

@Kitonum  I guess I was not clear enough.  Maple is doing the whole computation using 10 decimal digit arithmetic.  Maple is getting the correct answer for a computation done using 10 decimal digit arithmetic.

Mathematica is getting the correct answer for a different way of doing this computation.  Both answers are correct for the specific method of computation used.

If you read and understand the section on errors in numerical computations from a numerical analysis text, you should understand what is happening.  Good luck, it is not too difficult.

P.S.  At this link you will find some information on how Mathematica does numerical computations.  http://reference.wolfram.com/mathematica/guide/PrecisionAndAccuracyControl.html

@Adri vanderMeer van der Meer  ...

@Adri vanderMeer van der Meer   Excellent.  That will solve my problem. How did you find this work around?