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John Fredsted

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20 years, 171 days
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These are replies submitted by John Fredsted

Quite correct...

John Fredsted 2238
January 21 2008
You are quite right, which is why I withdraw my post. I apologize.

One possible reason...

John Fredsted 2238
January 20 2008
Maybe the reason is the following (taken from the first page of the document previously referred to):
But also the substitution command can be executed more efficiently: the replacement of the same symbol (or number) in an expression occurs only once, even though the symbol (or number) may appear in several places in the expression.

Seconded...

John Fredsted 2238
January 20 2008
0 0
I also prefer consistency throughout the system above any nifty GUI's, especially if some of these GUI's make original behaviour noisy. Here, of course, I refer to the introduction of the 2D math notation which, if I have not fundamentally misunderstood something, relies heavily on XML coding, the result, unfortunately, being that something as trivial as tabbing, compare my earlier complaints, does not work consistently anymore.

Seconded...

John Fredsted 2238
January 20 2008
I also prefer consistency throughout the system above any nifty GUI's, especially if some of these GUI's make original behaviour noisy. Here, of course, I refer to the introduction of the 2D math notation which, if I have not fundamentally misunderstood something, relies heavily on XML coding, the result, unfortunately, being that something as trivial as tabbing, compare my earlier complaints, does not work consistently anymore.

Useful link...

John Fredsted 2238
January 20 2008
I found the following link useful: Maple Lecture 12. Representation of Expressions. Reading the first two pages, one gains an understanding as to why subs or eval can behave as seen above.

A different solution...

John Fredsted 2238
January 20 2008
Maybe you could use the following: 
split := proc(p::polynom(anything,[x,y]))
	if type(p,`+`) then map(split,p)
	else select(type,p,freeof([x,y])) * INT(degree(p,x),degree(p,y))
	end if
end proc:

Illuminating links...

John Fredsted 2238
January 20 2008
0 0
Thanks for those illuminating links.

Illuminating links...

John Fredsted 2238
January 20 2008
Thanks for those illuminating links.

Spherical coordinates...

John Fredsted 2238
January 20 2008
0 0
Thanks for making me aware of that important simplification, which, I suppose, I would have known myself if only I would learn to carefully read the associated help pages. However, your choice of theta and phi disagrees with the choice made in Maple itself, see ?spherical_coordinates.

Spherical coordinates...

John Fredsted 2238
January 20 2008
Thanks for making me aware of that important simplification, which, I suppose, I would have known myself if only I would learn to carefully read the associated help pages. However, your choice of theta and phi disagrees with the choice made in Maple itself, see ?spherical_coordinates.

Sphere with cylindrical hole...

John Fredsted 2238
January 19 2008
0 0
Parametrize the sphere, using spherical coordinates: 
xSphere := (theta,phi) -> 2*a*sin(theta)*cos(phi);
ySphere := (theta,phi) -> 2*a*sin(theta)*sin(phi);
zSphere := (theta,phi) -> 2*a*cos(theta);
Parametrize the cylinder, using cylindrical coordinates: 
xCylinder := (phi,z) -> a*cos(phi);
yCylinder := (phi,z) -> a*sin(phi);
zCylinder := (phi,z) -> z;
Plot them as follows, using some specific, but otherwise arbitrary, value for a: 
a := 1:
with(plots):
plot1 := plot3d(
	[xSphere(theta,phi),ySphere(theta,phi),zSphere(theta,phi)],
	theta = Pi/6..5*Pi/6,phi = 0..2*Pi
):
plot2 := plot3d(
	[xCylinder(phi,z),yCylinder(phi,z),zCylinder(phi,z)],
	phi = 0..2*Pi,z = -sqrt(3)*a..sqrt(3)*a
):
display(plot1,plot2,scaling = constrained);

Sphere with cylindrical hole...

John Fredsted 2238
January 19 2008
Parametrize the sphere, using spherical coordinates: 
xSphere := (theta,phi) -> 2*a*sin(theta)*cos(phi);
ySphere := (theta,phi) -> 2*a*sin(theta)*sin(phi);
zSphere := (theta,phi) -> 2*a*cos(theta);
Parametrize the cylinder, using cylindrical coordinates: 
xCylinder := (phi,z) -> a*cos(phi);
yCylinder := (phi,z) -> a*sin(phi);
zCylinder := (phi,z) -> z;
Plot them as follows, using some specific, but otherwise arbitrary, value for a: 
a := 1:
with(plots):
plot1 := plot3d(
	[xSphere(theta,phi),ySphere(theta,phi),zSphere(theta,phi)],
	theta = Pi/6..5*Pi/6,phi = 0..2*Pi
):
plot2 := plot3d(
	[xCylinder(phi,z),yCylinder(phi,z),zCylinder(phi,z)],
	phi = 0..2*Pi,z = -sqrt(3)*a..sqrt(3)*a
):
display(plot1,plot2,scaling = constrained);

Less than strikes again...

John Fredsted 2238
January 19 2008
0 0
In order to avoid that the browser interpretes < and > as the beginning and end of an HTML-tag, write them as &lt; and &gt;.

Less than strikes again...

John Fredsted 2238
January 19 2008
In order to avoid that the browser interpretes < and > as the beginning and end of an HTML-tag, write them as &lt; and &gt;.

Better late than never :-)...

John Fredsted 2238
January 19 2008
Thanks for that suggestion of yours - good to have you back. I have difficulties with the structured types in Maple, probably because there are so many possibilities, so, I guess, that is why I did not myself use anything like 'specfunc', etc.
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