Certainly, I didn't want to say anything bad about Rosen's text. I didn't use it in my Discrete Math courses, but I might use it in the future. I was commenting on the code in the texts (and supplements) that I used, in Numerical Analysis, Linear Algebra, Probability and Statistics etc. In some cases the code was written by students and in some cases I don't know who wrote the code. Perhaps, it worked in Maple V Rel. 3 or 4 - I don't have any experience with them. The first version of Maple that I knew was Maple V Release 5. Also, I know some texts with good Maple code - Robert Israel's Calculus the Maple Way, for instance. I just didn't have a chance to use it (Calculus texts should be the same in all sections, and in the places where I taught, Stewart's Calculus was used - a very good text, by the way.) I could write good Maple (or Mathematica, or any other CAS, or Matlab) supplements (or textbooks) if I get paid for that (including benefits.) That would be a good idea, since I don't have a job since May. Unfortunately, nobody offered me such kind (or any other kind) of work. __________ Alec Mihailovs http://mihailovs.com/Alec/

There is one problem with what you (Scott03) were trying to do. The intersection of the circle and of the ellipse doesn't necessary happen at the same value of parameter. It worked with your example only because you changed it. It doesn't work in the original example. Here is how that should be done. I use the original example.

cirkelx := theta -> cos(theta):
cirkely:=theta->1+1*sin(theta):
ellipsx:=theta->2*cos(theta):
ellipsy:=theta->1*sin(theta):

plot([[cirkelx,cirkely,0..2*Pi],[ellipsx,ellipsy,0..2*Pi]],scaling=constrained);

EnvExplicit:=true:

RealDomain:-solve({cirkelx(a)=ellipsx(b),cirkely(a)=ellipsy(b)});

                /          1/2\                 /          1/2\
                |        13   |                 |        13   |
              3 |- 1/3 + -----|               3 |- 4/3 + -----|
                \          3  /                 \          3  /
  {b = arctan(-----------------), a = arctan(-------------------)}, {
                        1/2 1/2                          1/2 1/2
              (-5 + 2 13   )                 2 (-5 + 2 13   )

                      /          1/2\
                      |        13   |
                    3 |- 1/3 + -----|
                      \          3  /
        b = -arctan(-----------------) + Pi,
                              1/2 1/2
                    (-5 + 2 13   )

                       /          1/2\
                       |        13   |
                     3 |- 4/3 + -----|
                       \          3  /
        a = -arctan(-------------------) - Pi}
                                1/2 1/2
                    2 (-5 + 2 13   )

seq(simplify(eval([cirkelx(a),cirkely(a)],i)),i=%);

               1/2 1/2            1/2
   2 (-5 + 2 13   )             13
  [-------------------, - 1/3 + -----],
            3                     3

                       1/2 1/2            1/2
           2 (-5 + 2 13   )             13
        [- -------------------, - 1/3 + -----]
                    3                     3

evalf([%])[];

     [0.9913184374, 0.8685170917], [-0.9913184374, 0.8685170917]

__________ Alec Mihailovs http://mihailovs.com/Alec/

There is one problem with what you (Scott03) were trying to do. The intersection of the circle and of the ellipse doesn't necessary happen at the same value of parameter. It worked with your example only because you changed it. It doesn't work in the original example. Here is how that should be done. I use the original example.

cirkelx := theta -> cos(theta):
cirkely:=theta->1+1*sin(theta):
ellipsx:=theta->2*cos(theta):
ellipsy:=theta->1*sin(theta):

plot([[cirkelx,cirkely,0..2*Pi],[ellipsx,ellipsy,0..2*Pi]],scaling=constrained);

EnvExplicit:=true:

RealDomain:-solve({cirkelx(a)=ellipsx(b),cirkely(a)=ellipsy(b)});

                /          1/2\                 /          1/2\
                |        13   |                 |        13   |
              3 |- 1/3 + -----|               3 |- 4/3 + -----|
                \          3  /                 \          3  /
  {b = arctan(-----------------), a = arctan(-------------------)}, {
                        1/2 1/2                          1/2 1/2
              (-5 + 2 13   )                 2 (-5 + 2 13   )

                      /          1/2\
                      |        13   |
                    3 |- 1/3 + -----|
                      \          3  /
        b = -arctan(-----------------) + Pi,
                              1/2 1/2
                    (-5 + 2 13   )

                       /          1/2\
                       |        13   |
                     3 |- 4/3 + -----|
                       \          3  /
        a = -arctan(-------------------) - Pi}
                                1/2 1/2
                    2 (-5 + 2 13   )

seq(simplify(eval([cirkelx(a),cirkely(a)],i)),i=%);

               1/2 1/2            1/2
   2 (-5 + 2 13   )             13
  [-------------------, - 1/3 + -----],
            3                     3

                       1/2 1/2            1/2
           2 (-5 + 2 13   )             13
        [- -------------------, - 1/3 + -----]
                    3                     3

evalf([%])[];

     [0.9913184374, 0.8685170917], [-0.9913184374, 0.8685170917]

__________ Alec Mihailovs http://mihailovs.com/Alec/

Well, we already can't edit our comments if somebody replied to them. Why that should be different for the first post in the thread? __________ Alec Mihailovs http://mihailovs.com/Alec/

I also couldn't find it. My procedure's name was f, I just compared it with Maple's procedure SearchAll. As far as I recall, I first posted a comment with that procedure, then somebody from Maplesoft posted a comment that it is also possible to do that with SearchAll instead of f, but he wasn't sure about the efficiency, and then I posted a comment with time comparison for searching of long lists, with f doing search in something like 0.35 sec and SearchAll doing the same search in more than 150 sec. The only explanation that I see is that the person started the thread, deleted it, including all comments. I think that the possibility of doing that is a flaw in this site's design. In many cases the original posts are just questions, or contain errors, and comments with answers and with corrections of the errors are much more important. Another example of that kind is with integrals similar to I responded about a month ago. The author of that question posted a year ago a very similar question, just with cosh(x) instead of sinh(x), and I posted a long comment then about the different ways of doing that in Maple. Now I wanted to make a reference to it, but couldn't find the older post in his 'track'. That means that he deleted it. The difference between posting on Usenet and here is not only that Usenet posts can not be deleted, but also that they are saved in Sent Mail. My posts here are not saved in any form on my computer, so if they are deleted, they are gone, and it is not that easy to restore many of them, because my code usually has plenty of tricks in it. May I suggest that the originators of the thread were not able to delete other people comments? If they delete their original post, the first comment should start a thread instead of all comments being deleted. __________ Alec Mihailovs http://mihailovs.com/Alec/

Yes, both eludom and yrt work now. It was, probably, not yet indexed when I tried it. I usually have same problems as Axel, trying to find my old posts. They are usually comments and the thread name is not very descriptive, so I can't find them from the 'track'. Here is an example: SearchAll I remember posting a procedure working much faster than the procedure with that name in ListTools (while this site was in beta), and my comment had a title close to "The efficiency of SearchAll" as far as I recall, so it should have even higher search priority. __________ Alec Mihailovs http://mihailovs.com/Alec/

I tried a few different tricks, but couldn't get the answer with Pauli matrices. I would try SAGE. __________ Alec Mihailovs http://mihailovs.com/Alec/

I tried a few different tricks, but couldn't get the answer with Pauli matrices. I would try SAGE. __________ Alec Mihailovs http://mihailovs.com/Alec/

maplemint is not unique debugging command crashing mserver. From time to time, tracelast crashes mserver, too. I don't have a reproducible example though. It looks as if that doesn't depend on a particular error - more like on a some combination of errors. __________ Alec Mihailovs http://mihailovs.com/Alec/

Axes ranges are for x and y, while the range in the plot command is for theta. It looks as a cusp on a much wider range of x and y - even if the theta range changes only slightly, x and y ranges change significantly. The methods that Maple is using (rkf45 and rosenbrock) are somewhat old, but many other software alternatives, Matlab including, are also using them. While not being perfect, Maple often produces better results than its competitors, and the differential equations solver is one of the strongest parts of Maple. __________ Alec Mihailovs http://mihailovs.com/Alec/

Axes ranges are for x and y, while the range in the plot command is for theta. It looks as a cusp on a much wider range of x and y - even if the theta range changes only slightly, x and y ranges change significantly. The methods that Maple is using (rkf45 and rosenbrock) are somewhat old, but many other software alternatives, Matlab including, are also using them. While not being perfect, Maple often produces better results than its competitors, and the differential equations solver is one of the strongest parts of Maple. __________ Alec Mihailovs http://mihailovs.com/Alec/

I used settings

_EnvAllSolutions:=true:
_EnvExplicit:=true:

and got an opposite situation - an answer in the first case and a different answer in the second case, with a warning, solutions may have been lost. That may change after a restart. The problem may be in the ordering of the equations in solve. A different order leads to different steps in the solution. solve uses a set of equations, and the order of set elements is not uniquely predetermined. Besides, the number of equations is 13... __________ Alec Mihailovs http://mihailovs.com/Alec/

I used settings

_EnvAllSolutions:=true:
_EnvExplicit:=true:

and got an opposite situation - an answer in the first case and a different answer in the second case, with a warning, solutions may have been lost. That may change after a restart. The problem may be in the ordering of the equations in solve. A different order leads to different steps in the solution. solve uses a set of equations, and the order of set elements is not uniquely predetermined. Besides, the number of equations is 13... __________ Alec Mihailovs http://mihailovs.com/Alec/

As far as I can tell, this is a typical situation. Every time when I tried to use a textbook with either a Maple supplement, or a Maple code in it in one of my courses, the code was extremely crappy and unusable. __________ Alec Mihailovs http://mihailovs.com/Alec/

As far as I can tell, this is a typical situation. Every time when I tried to use a textbook with either a Maple supplement, or a Maple code in it in one of my courses, the code was extremely crappy and unusable. __________ Alec Mihailovs http://mihailovs.com/Alec/