Implicitplot problem

Posted on 2008-03-01 03:13 By scumath (

88)

Categories:

How do I ...? with Maple

I want to plot the astroid by the following code, but only the part in the first quadrant appears. I don't know that is wrong and how to solve the problem. Thanks.

with(plots):
a:=1:
implicitplot(x^(2/3)+y^(2/3)=a^(2/3),x=-a..a,y=-a..a);

The same problem with plot

Comment on 2008-03-01 03:45 from scumath (

88)

In fact, the same problem occurs in plotting explicit power functions with fractional powers. The following can only produce half of the whole graph. What can't Maple plot the whole graph in the domain of the function y=x^(1/3)?

with(plots):
plot(x^(1/3),x=-2..2,thickness=3);

principal root

Comment on 2008-03-01 04:00 from acer ( Maple Rating 4

1410)

If you read the help-page root, you'll see that it returns the "principal root", defined by the formula root(x,n) = exp(1/n * ln(x)). The help-page ?^ also summarizes this. In your example, x^(1/3) acts like root(x,3). For example,

> (-1.0)^(1/3);
                         0.5000000001 + 0.8660254037 I
 
> root(-1.0,3);
                         0.5000000001 + 0.8660254037 I

The complex values don't show up on your graph, as they are not numeric (real).

On the other hand, surd returns -(-x)^(1/n) for x<0 when n is an odd integer. See its help-page. So for your plot, try,

plot(surd(x,3),x=-2..2,thickness=3);

Reading the help-pages is generally a good idea.

acer

surd

Comment on 2008-03-01 03:43 from acer ( Maple Rating 4

1410)

In Maple 11.02,

with(plots):
a:=1:
implicitplot([surd(x^2,3)+surd(y^2,3)=a^(2/3)],x=-a..a,y=-a..a);

acer

How to solve it in Maple 8?

Comment on 2008-03-01 03:51 from scumath (

88)

Thanks. But how can I solve the problem in Maple 8?
It seems that Maple does not allow power functions with fractional powers or decimal powers to take negative values even if they are defined there like y=x^(1/3)..

works for me

Comment on 2008-03-01 04:05 from acer ( Maple Rating 4

1410)

These two examples below work for me in Maple 8,

plot(surd(x,3),x=-2..2,thickness=3);
with(plots):
a:=1:
implicitplot(surd(x^2,3)+surd(y^2,3)=a^(2/3),x=-a..a,y=-a..a);

acer

Ok in Maple 8

Comment on 2008-03-01 04:24 from scumath (

88)

Yes, both work very well in Maple 8.
So my problem is completely solved.
Thank you very much.

plot(surd(x,3),x=-2..2,thickness=3);
with(plots): a:=1:
implicitplot(surd(x^2,3)+surd(y^2,3)=a^(2/3),x=-a..a,y=-a..a);

surd

Comment on 2008-03-01 04:09 from scumath (

88)

Thank you, acer.

Using surd (which I don't know before) in Maple 8 can solve the second problem by the following code (which can produce the whole graph):

with(plots):
plot(surd(x,3),x=-1..1);