Sergio Parreiras

Dr. Sergio Parreiras

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14 years, 261 days
UNC Chapel Hill
Associate Professor

MaplePrimes Activity


These are answers submitted by Sergio Parreiras

The textbook "A First Course in Computational Algebraic Geometry" by  Wolfram Decker and Gerhard Pfister has a section/chapter where they  solve a Sudoko game using Groebner basis BUT if I understood it correctly, their method only works for a small class of Sudoko games. I don't remember exactly but I think the Sudoko game must have only one solution.

I did not have a chance to see the worksheet but try setting Digits:=20; and run fsolve

with the option fulldigits. Do you still get "strange" answers?

No output from pdsolve, solve or dsolve usually means there is no solution.

Let's just consider a subset of the initial boundary conditions.

pdsolve returns the solution:

now if you try to impose

as an additional boudary condition, the system will not have a solution unless the function f is a constant,.

But if Maple is treating f as a given/arbitrary  function then clearly the set of solutions is empty.

  1. Perhaps you may want to read pdsolve[boundaryconditons] in the Help section.
  2. To see what type of initial data a linear PDE system  (without boundary conditions) requires, you may use: with(DEtools); initialdata(rifsimp(sys)).
  1. Also DEtools[rifsimp] is useful to check if the system is consistent.

Hope this helps, S.

 

This equation is too non-linear for Maple to compute an explicit solution. You may try changing variables but if you just want an answer to this system, use fsolve for a numeric answer.  You may also want to increase the precision by changing the variable Digits. Also with fsolve you can specify the range where you want Maple to look for solutions.

Using fsolve you get:

You can also specify the range where you want fsolve to find your solution:

Gives you:

 

You can also set the starting point where fsolve should look for the solution, please read fsolve/details in the help windown.

Again with larger systems, setting Digits:=20 may help to get a more accurate answer.

I was no able to replicated your problem:

> f := 1/((x1-x3)^2+(x2-x4)^2);



> diff(f, x1);



From Maplesoft website:

sol := solve({`<=`(0, `+`(`-`(`*`(`^`(y, 2))), x)), `<`(0, `+`(`-`(y), `*`(3, `*`(x)), `-`(2))), `<`(`+`(`*`(`^`(x, 2)), `*`(`^`(y, 2))), 9)}, [x, y])

> plots[inequal](sol, x = 0 .. 3, y = -2 .. 2)

Maple 16 plots[inequal] was able to handle only linear inequalities but in the new shiny Maple 17, we can plot non-linear inequalities (not sure if it is restricted to polynomial inequalities -- I am getting Maple 17 only in few weeks, so happy!

u*w^2/(u*w^2)^(2/3) is not a polynomial

2. is a floating point representation while 2 is the exact representation. Usually if you use fsolve or evalf to obtain numerical results, the result is expressed in floating point arithmetic. The dot is there to remind you that perhaps 2. is actually 1.999999999999 and not really 2 ... To solve you problem try convert (2.,rational) to obtain a rational representation.

As Preben Alsholm I am also not sure what do you want but if I take literally your question, that is, you just want to add the two functions, I think the problem is that you are using " : " instead of " ; " so the result is not displayed, instead type S1+S2 ;

  1. If the bounded region you want to plot is given by linear inequalities, you are lucky and you can use the command inequal with the plots package.
  2. If you want the area between two curves, there is this work-around: http://www.mapleprimes.com/posts/40006-An-Easy-Way-To-Plot-The-Region-Between-Two-Curves
  3. You should also look at the reference that Hirnyk gave above about the option, filled.
  4. There is another mathematical software program that has a command called RegionPlot... But to the best of my knowledge I do not know of any similar command in Maple besides the above options I listed. The inability of being able to plot regions defined by the composition (with logical operands AND, OR, NOT) of non-linear inequalities is the only reason I use other math. apps besides Maple.

plot(sin(Pi*x)*exp(A*x),x=a..b) works for A=100 and all values of a and b I tried so Maple does plot it; I guess your question is really why we can not visualize this function well:

for large A, if you pick a narrow domain (a close to b), you can visualize well but you are essentially plotting the exponential function only as sin(Pi*x) does not vary that much for a close to b;

but if you pick a large domain, the highest (or lowest) peak of the function will be way higher than the other peaks (so you will not be able to see them because of the scale, all the other peaks are way closer to zero the to the top peak.

for some functions you can solve this type of problem by using a log scale, see logplot or loglogplot commands with the plots package but in your case I do not think that it would help without additional modifications...

if I had to present this function in a paper, I would present two plots, say one with a from 0 to 3, showing a peak at 2x10^128 and another plot with range from 0 to 1 with a peak at 3x10^41.

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