Georgios,

In your example, Maple is not doing any numeric integration. It is computing a single antiderivative, which it then plots. You were just lucky that the constant of integration was what you wanted.

Jay,

Your first example (in the Answer) is not numeric integration either. The quotes are making Maple compute the antiderivative separately for each point it plots.

Georgios,

In your example, Maple is not doing any numeric integration. It is computing a single antiderivative, which it then plots. You were just lucky that the constant of integration was what you wanted.

Jay,

Your first example (in the Answer) is not numeric integration either. The quotes are making Maple compute the antiderivative separately for each point it plots.

@Heeka The GraphTheory package that I have been using throughout your two most recent threads does not exist in Maple 11.

The only other techniques for enumerating the Eulerian circuits that I can think of would be ad hoc---they would only work for a very small graph like this. Without loss of generality, we can assume that all Eulerian circuits begin with edges CA and AT.

@Heeka The GraphTheory package that I have been using throughout your two most recent threads does not exist in Maple 11.

The only other techniques for enumerating the Eulerian circuits that I can think of would be ad hoc---they would only work for a very small graph like this. Without loss of generality, we can assume that all Eulerian circuits begin with edges CA and AT.

@Heeka Note that there is a one-to-one correspondence between the Eulerian circuits in the original graph and in my enlarged graph.

@Heeka Note that there is a one-to-one correspondence between the Eulerian circuits in the original graph and in my enlarged graph.

@Markiyan Hirnyk My first answer was to a question that you deleted---a question about the examples on the help page ?LinearAlgebra,Modular,LinearSolve . I have since posted an answer to your second question.

@Markiyan Hirnyk My first answer was to a question that you deleted---a question about the examples on the help page ?LinearAlgebra,Modular,LinearSolve . I have since posted an answer to your second question.

@Markiyan Hirnyk There are two problems with your command

B:= LinearAolve(2, A, 2);

The first is that the return value of LinearSolve with the default inplace is NULL. So even if the command worked, B would just be NULL. 

The second is that the second 2 in your command says that the rightmost two columns of A are "augmented". In other words, the matrix A represents a linear system C.X = D where C is 3x2 and D is 3x2, the leftmost two columns of A being the C and the rightmost two columns being the D. This system is clearly inconsistent, its bottom row being < 0 0 | 1 1 >. If LinearSolve chooses to call that "singular" rather than "inconsistent", I am willing to forgive it. If it is to be considered a bug, it is only because of the choice of words in the error message.

@Markiyan Hirnyk There are two problems with your command

B:= LinearAolve(2, A, 2);

The first is that the return value of LinearSolve with the default inplace is NULL. So even if the command worked, B would just be NULL. 

The second is that the second 2 in your command says that the rightmost two columns of A are "augmented". In other words, the matrix A represents a linear system C.X = D where C is 3x2 and D is 3x2, the leftmost two columns of A being the C and the rightmost two columns being the D. This system is clearly inconsistent, its bottom row being < 0 0 | 1 1 >. If LinearSolve chooses to call that "singular" rather than "inconsistent", I am willing to forgive it. If it is to be considered a bug, it is only because of the choice of words in the error message.

@Markiyan Hirnyk The examples all seem consistent with what I said. With option inplace, the default, the result is obtained by re-examining the input matrix rather than by using the direct output of the command, which is NULL.

@Markiyan Hirnyk The examples all seem consistent with what I said. With option inplace, the default, the result is obtained by re-examining the input matrix rather than by using the direct output of the command, which is NULL.

@Markiyan Hirnyk Yes, of course, what I have created does not represent the original graph internally in Maple. This is a workaround required to create an approximate visualization of the Asker's original, which seemed to be what she wanted.

@Markiyan Hirnyk Yes, of course, what I have created does not represent the original graph internally in Maple. This is a workaround required to create an approximate visualization of the Asker's original, which seemed to be what she wanted.

@erik10 What is the maximum number of dintinct entries in A? It can't be 10000 because you wouldn't be able to visualize 10000 distinct vertical lines on one plot.

I multiplied by 1000 because I thought that that would cover any perceivable visual differences.

I don't understand what you're saying about no repetitions in the A vector. My code does not rely on there being repetitions.

If only the frequencies the given, then A could default to [$1..nops(B)] (i.e. [1, 2, ..., |B|]).