Carl Love

Carl Love

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10 years, 58 days
Natick, Massachusetts, United States
My name was formerly Carl Devore.

MaplePrimes Activity


These are replies submitted by Carl Love

@acer I was very careful to remove any need for manual extraction of the reduced constraints (returned by solve) from my solution. I just decided the display the results at that point so the reader could "catch a breather"---kinda like a dramatic pause. The remaining code works regardless of what those reduced constraints are or how many there are. All that matters is each constraint set eliminates one variable and gives numeric bounds for the other.

Also, I did use Im or any other complex-number commands.

@acer I was very careful to remove any need for manual extraction of the reduced constraints (returned by solve) from my solution. I just decided the display the results at that point so the reader could "catch a breather"---kinda like a dramatic pause. The remaining code works regardless of what those reduced constraints are or how many there are. All that matters is each constraint set eliminates one variable and gives numeric bounds for the other.

Also, I did use Im or any other complex-number commands.

I want to point out that my solution above gets the exact answer with purely symbolic techniques. It does not require plots. It does not require any initial guess. It uses only basic Maple commands, no packages. It does not use any complex-number commands such as evalc, Re, Im. It does not use any assumptions or RealDomain or Student. Each command runs quickly. In short, it is accessible to the average student. The apparent complexity with indets, etc., was only because I wanted to ensure that it would run the same regardless of the order that solutions are returned by solve. That would not be a concern to a student running Maple as a "desk calculator". 

I want to point out that my solution above gets the exact answer with purely symbolic techniques. It does not require plots. It does not require any initial guess. It uses only basic Maple commands, no packages. It does not use any complex-number commands such as evalc, Re, Im. It does not use any assumptions or RealDomain or Student. Each command runs quickly. In short, it is accessible to the average student. The apparent complexity with indets, etc., was only because I wanted to ensure that it would run the same regardless of the order that solutions are returned by solve. That would not be a concern to a student running Maple as a "desk calculator". 

@Kitonum Yes, thanks for spotting that. I should've compared the whole list of pairs before posting.

@Kitonum Yes, thanks for spotting that. I should've compared the whole list of pairs before posting.

I believe that Preben's method here is called the "shooting method" for BVPs. See http://en.wikipedia.org/wiki/Shooting_method. I have a hunch (with no real evidence yet) that Maple's BVP solver was trying this. My hunch is based on the error message about the Newton iteration convergence.

I believe that Preben's method here is called the "shooting method" for BVPs. See http://en.wikipedia.org/wiki/Shooting_method. I have a hunch (with no real evidence yet) that Maple's BVP solver was trying this. My hunch is based on the error message about the Newton iteration convergence.

Minimal polynomials are not necessarily square free. Consider a matrix which is all 0 except for a single off-diagonal nonzero. Clearly the minimal polynomial is x2.

Minimal polynomials are not necessarily square free. Consider a matrix which is all 0 except for a single off-diagonal nonzero. Clearly the minimal polynomial is x2.

Must be a oversight in the documentation. The help link to SquareFreePart is dead, nor does my Maple 16 have the help file; although I can see that my Maple's PolynomialTools does indeed export a SquareFreePart.

Must be a oversight in the documentation. The help link to SquareFreePart is dead, nor does my Maple 16 have the help file; although I can see that my Maple's PolynomialTools does indeed export a SquareFreePart.

@pagan I played around a bit with your suggestion. I noticed that the :: syntax can only be used as an argument to showstat (or to its low-level companion debugopts). Thus, it can only be used to view procedures. To view the contents of other module locals, one still needs to use the kernelopts setting. This may be needed to fully understand module code. For example, isprime is implemented as a ModuleApply. After showstat(isprime), we see between statements 6 and 7 that a reference is made to a set special_primes. This is a local of module isprime. (Do eval(isprime) to view the header of isprime as a module.) To view special_primes, do

kernelopts(opaquemodules= false);

eval(isprime:-special_primes);

(The eval is redundant in this case, special_primes being a set; I just include it to cover the other cases.)

This would a good time to mention that one often needs to also issue the command interface(verboseproc= 3) before viewing the code and remember table of a procedure with eval.

@pagan I played around a bit with your suggestion. I noticed that the :: syntax can only be used as an argument to showstat (or to its low-level companion debugopts). Thus, it can only be used to view procedures. To view the contents of other module locals, one still needs to use the kernelopts setting. This may be needed to fully understand module code. For example, isprime is implemented as a ModuleApply. After showstat(isprime), we see between statements 6 and 7 that a reference is made to a set special_primes. This is a local of module isprime. (Do eval(isprime) to view the header of isprime as a module.) To view special_primes, do

kernelopts(opaquemodules= false);

eval(isprime:-special_primes);

(The eval is redundant in this case, special_primes being a set; I just include it to cover the other cases.)

This would a good time to mention that one often needs to also issue the command interface(verboseproc= 3) before viewing the code and remember table of a procedure with eval.

Upload a worksheet with an example.

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