## Bug in Optimization

Maple 2016

Let us consider the linear integer programming problem:

```A := Matrix([[1, 7, 1, 3], [1, 6, 4, 6], [17, 1, 5, 1], [1, 6, 10, 4]]):
n := 4; z := add(add(A[i, j]*x[i, j], j = 1 .. n), i = 1 .. n):
restr := {seq(add(x[i, j], i = 1 .. n) = 1, j = 1 .. n), seq(add(x[i, j], j = 1 .. n) = 1, i = 1 .. n)}:
sol := Optimization[LPSolve](z, restr, assume = binary);

Error, (in Optimization:-LPSolve) no feasible integer point found;
use feasibilitytolerance option to adjust tolerance

sol1 := Optimization[LPSolve](z, restr, assume = binary, feasibilitytolerance = 100, integertolerance = 1);

Error, (in Optimization:-LPSolve) no feasible integer point found;
use feasibilitytolerance option to adjust tolerance
```

That was OK in Maple 16, outputting

.

The bug in one of the principal Maple commands lasts since Maple 2015, where the above code causes "Kernel connection has been lost". The SCRs about it were submitted three times (see http://www.mapleprimes.com/questions/204750-Bug-In-LPSolve-In-Maple-20151).

## How can I draw the solution of a 3d linear inequal...

Hi dears,

How can I draw the solution of the following 3d linear inequalities in Maple?

A:={-x-y+3*z >= 0, -x+2*y >= 0, 3*x-2*y-z >= 0, x > 0, y > 0, z > 0}

I am looking forward to hearing from you

Sincerely yours.

## How do I solve a first order linear PDE with two t...

Hello!

For the last couple of days I've been trying really hard to solve the linear PDE

. Where R is a function R(t,q(t),p(t)) and H is the hamiltonian H=   .

(dH/dp= p and dH/dq= -2q-2), q and p depends on the time t, and I'm supposed to solve the PDE and then plot the gaussian distribution (2D).

I tried doing this:

pde := diff(R(t, q1(t), p1(t)), t) = -(diff(R(t, q(t), p(t)), q(t)))*p(t)+(diff(R(t, q(t), p(t)), p(t)))*(-2*q(t)-2)

But pdsolve(pde) gives me:  "Error, (in pdsolve/info) the name of the indeterminate function must be given".

When I change q(t) to q and p(t) to p I get:

R(t, q, p) = _F1(p^2-2*q^2-4*q, -(1/2)*ln(sqrt(2)*q+p+sqrt(2))*sqrt(2)+t)

And then I'm lost. How do I solve this PDE in maple?

Thankful for any help

## Why does this computation hang?...

The following program hangs on the last command and a hard restart is required. The computation of a 2 x 2 matrix times a 2-vector is not that hard. Any ideas as to what is happening?

Another question: if v is a vector that depends on x and y say why does
>solve(v=0,{x,y})
not work?

It should only take a few lines of code to change v=0 to the system {components of v = 0}

## Numerical Solutions to Matrix/Lattice Based Proble...

Hi, so I have few problems here. I need to;

Create a MxN Matrix/Lattice, where N and M can be any positive integer, that contains a random selection of -1/1s at each entry.

Need to sum every entry, then multiply by -1 to find “H”.

Need to multiply each neighbour to find its bond energy, so if it’s the same you get 1 else -1, but only its direct neighbours once, so if it was a 2x2 matrix there would be only 4 values and then sum them.

I don’t seem to be able to set up the code so that it does it for any size matrix, as I only know how to write it out basic for a 2x2. Also, not so important, but I wanted to know if could create a loop that would find every iteration of possible setups i.e. for a 2x1 you can have 1.1, -1.1, 1.-1, -1.-1. And then give the solutions outlined earlier for each of the the possibilities [There being 2MxN ]

## Solving a matrix with LinearSolve ...

I have tried to solve a matrix with the function "LinearSolve" as seen in the picture, but instead of solving it just gives me back the operation i wrote (3). My which is to solve an equation system a quick as possible - have a templet fill in the matrix and press enter. I thought this "LinearSolve" function was the easiest way of doing. I know that I can right click and choose the function, but I want it as a command.

Any solutions on how to use the "LinearSolve" command to solve an equation system?

## Linear Instability Analysis ...

Hello Everyone,

May I ask you about this  "Error,   (in pdsolve/numeric/process_PDEs)  number of dependent variables and number of PDE must be the same". Does anyone have idea about solving linear instability equation (flow inside pipe, oscillating flow) ?

Thank you,

## Using Linsolve for large systems of linear equatio...

Hi,
I am solving large systems of linear equations (mod 2) which are of this form ,
systems:= {0 = f[[1, 4]]-f[[1, 3]], 0 = f[[1, 5]]-f[[1, 3]], 0 = f[[1, 5]]-f[[1, 4]], 0 = f[[1, 6]]-f[[1, 3]], 0 = f[[1, 6]]-f[[1, 4]], 0 = f[[1, 6]]-f[[1, 5]], 0 = f[[1, 7]]-f[[1, 3]], 0 = f[[1, 7]]-f[[1, 4]], 0 = f[[1, 7]]-f[[1, 5]], 0 = f[[1, 7]]-f[[1, 6]], 0 = f[[2, 4]]-f[[1, 3]], 0 = f[[2, 5]]-f[[1, 3]], 0 = f[[2, 5]]-f[[1, 4]], 0 = f[[2, 6]]-f[[1, 3]], 0 = f[[2, 6]]-f[[1, 4]], 0 = f[[2, 6]]-f[[1, 5]], 0 = f[[2, 6]]-f[[2, 4]], 0 = f[[2, 6]]-f[[2, 5]], 0 = f[[2, 7]]-f[[1, 3]], 0 = f[[2, 7]]-f[[1, 4]], 0 = f[[2, 7]]-f[[1, 5]], 0 = f[[2, 7]]-f[[1, 6]], 0 = f[[2, 7]]-f[[2, 4]], 0 = f[[2, 7]]-f[[2, 5]], 0 = f[[3, 1]]-f[[1, 4]], 0 = f[[3, 1]]-f[[1, 5]], 0 = f[[3, 1]]-f[[1, 6]], 0 = f[[3, 1]]-f[[2, 7]], 0 = f[[3, 5]]-f[[1, 4]], 0 = f[[3, 5]]-f[[1, 5]], 0 = f[[3, 5]]-f[[2, 4]], 0 = f[[3, 5]]-f[[2, 5]], 0 = f[[3, 6]]-f[[1, 3]], 0 = f[[3, 6]]-f[[1, 4]], 0 = f[[3, 6]]-f[[1, 5]], 0 = f[[3, 6]]-f[[1, 6]], 0 = f[[3, 6]]-f[[2, 4]], 0 = f[[3, 6]]-f[[2, 5]], 0 = f[[3, 6]]-f[[2, 6]], 0 = f[[3, 7]]-f[[1, 4]], 0 = f[[3, 7]]-f[[1, 5]], 0 = f[[3, 7]]-f[[1, 6]], 0 = f[[3, 7]]-f[[1, 7]], 0 = f[[3, 7]]-f[[2, 4]], 0 = f[[3, 7]]-f[[2, 5]], 0 = f[[3, 7]]-f[[2, 6]], 0 = f[[3, 7]]-f[[2, 7]], 0 = f[[3, 7]]-f[[3, 6]], 0 = f[[4, 1]]-f[[1, 5]], 0 = f[[4, 1]]-f[[1, 7]], 0 = f[[4, 1]]-f[[2, 7]], 0 = f[[4, 1]]-f[[3, 5]], 0 = f[[4, 1]]-f[[3, 7]], 0 = f[[4, 2]]-f[[2, 6]], 0 = f[[4, 2]]-f[[2, 7]], 0 = f[[4, 6]]-f[[1, 5]], 0 = f[[4, 6]]-f[[1, 6]], 0 = f[[4, 6]]-f[[2, 5]], 0 = f[[4, 6]]-f[[2, 6]], 0 = f[[4, 6]]-f[[3, 5]], 0 = f[[4, 6]]-f[[3, 6]], 0 = f[[4, 7]]-f[[1, 5]], 0 = f[[4, 7]]-f[[1, 6]], 0 = f[[4, 7]]-f[[1, 7]], 0 = f[[4, 7]]-f[[2, 5]], 0 = f[[4, 7]]-f[[2, 6]], 0 = f[[4, 7]]-f[[2, 7]], 0 = f[[4, 7]]-f[[3, 5]], 0 = f[[4, 7]]-f[[3, 6]], 0 = f[[4, 7]]-f[[4, 6]], 0 = f[[5, 1]]-f[[2, 6]], 0 = f[[5, 1]]-f[[2, 7]], 0 = f[[5, 1]]-f[[3, 6]], 0 = f[[5, 1]]-f[[4, 6]], 0 = f[[5, 2]]-f[[2, 7]], 0 = f[[5, 2]]-f[[3, 5]], 0 = f[[5, 2]]-f[[3, 6]], 0 = f[[5, 2]]-f[[3, 7]], 0 = f[[5, 2]]-f[[4, 6]], 0 = f[[5, 2]]-f[[4, 7]], 0 = f[[5, 3]]-f[[4, 7]], 0 = f[[5, 7]]-f[[1, 6]], 0 = f[[5, 7]]-f[[1, 7]], 0 = f[[5, 7]]-f[[2, 6]], 0 = f[[5, 7]]-f[[2, 7]], 0 = f[[5, 7]]-f[[3, 6]], 0 = f[[5, 7]]-f[[3, 7]], 0 = f[[5, 7]]-f[[4, 6]], 0 = f[[5, 7]]-f[[4, 7]], 0 = f[[6, 1]]-f[[1, 7]], 0 = f[[6, 1]]-f[[3, 6]], 0 = f[[6, 1]]-f[[4, 7]], 0 = f[[6, 1]]-f[[5, 7]], 0 = f[[6, 2]]-f[[3, 7]], 0 = f[[6, 2]]-f[[4, 7]], 0 = f[[6, 3]]-f[[4, 6]], 0 = f[[6, 3]]-f[[5, 7]], 0 = f[[6, 4]]-f[[5, 7]], 0 = f[[7, 2]]-f[[3, 7]], 0 = f[[7, 2]]-f[[5, 7]], 1 = f[[3, 1]]-f[[1, 7]], 1 = f[[3, 1]]-f[[2, 4]], 1 = f[[3, 1]]-f[[2, 5]], 1 = f[[3, 1]]-f[[2, 6]], 1 = f[[3, 1]]-f[[3, 6]], 1 = f[[4, 1]]-f[[1, 6]], 1 = f[[4, 1]]-f[[2, 5]], 1 = f[[4, 1]]-f[[2, 6]], 1 = f[[4, 1]]-f[[3, 6]], 1 = f[[4, 2]]-f[[3, 5]], 1 = f[[4, 2]]-f[[3, 6]], 1 = f[[4, 2]]-f[[3, 7]], 1 = f[[5, 1]]-f[[1, 6]], 1 = f[[5, 1]]-f[[1, 7]], 1 = f[[5, 1]]-f[[3, 5]], 1 = f[[5, 1]]-f[[3, 7]], 1 = f[[5, 1]]-f[[4, 7]], 1 = f[[5, 2]]-f[[2, 6]], 1 = f[[5, 3]]-f[[4, 6]], 1 = f[[6, 1]]-f[[2, 7]], 1 = f[[6, 1]]-f[[3, 7]], 1 = f[[6, 1]]-f[[4, 6]], 1 = f[[6, 2]]-f[[3, 6]], 1 = f[[6, 2]]-f[[4, 6]], 1 = f[[6, 2]]-f[[5, 7]], 1 = f[[6, 3]]-f[[3, 7]], 1 = f[[6, 3]]-f[[4, 7]], 1 = f[[6, 4]]-f[[4, 7]], 1 = f[[7, 1]]-f[[3, 7]], 1 = f[[7, 1]]-f[[4, 7]], 1 = f[[7, 1]]-f[[5, 7]], 1 = f[[7, 2]]-f[[4, 7]], 1 = f[[7, 3]]-f[[5, 7]], 1 = f[[7, 4]]-f[[5, 7]]};

I have been using msolve as follows; msolve(systems,2);  which returns NULL if there is no solution. This however takes a lot of my computer memory and also take a lot of time since the equations are very many.  I decided to try LinearSolve, but it doesn't give me any solutions even for the ones that I know that the solutions exist. My code was writen as follows:

systems:=as above..

vars := [f[[1, 3]], f[[1, 4]], f[[1, 5]], f[[1, 6]], f[[1, 7]], f[[2, 4]], f[[2, 5]], f[[2, 6]], f[[2, 7]], f[[3, 1]], f[[3, 5]], f[[3, 6]], f[[3, 7]], f[[4, 1]], f[[4, 2]], f[[4, 6]], f[[4, 7]], f[[5, 1]], f[[5, 2]], f[[5, 3]], f[[5, 7]], f[[6, 1]], f[[6, 2]], f[[6, 3]], f[[6, 4]], f[[7, 1]], f[[7, 2]], f[[7, 3]], f[[7, 4]]];

A,b:=GenerateMatrix(systems,var):
LinearSolve(A,b) mod 2;
what I'm I doing wrong? How can I make this fast and in such a way that the solution is computed without taking too much memory?

I also understand that LinearSolve returns the following when there is no solution, "Error, (in LinearAlgebra:-LinearSolve) inconsistent system
", in my case, if there is no solution, I don't want that error to be printed, but I want some variable (call it x) to be printed if a solution is found.

Any help is appreciated.

Vic.

## Initial value problem - dsolve does not give parti...

Trying to solve this IVP of the SHO  (second order linear costant-coefficient).

Everything works fine until I come to the solving even after using dsolve with initial conditions (even using the differential operator D in the initial conditions)  , the answer still contains _C1, an unknown constant.

The full worksheet is below.  The code for dsolve is:

sol3 := dsolve(subs(par1, {de1, D(x)*0 = 0, x(0) = 1}), x(t));

Hoping you can help with a solution.

## Want to solve system of linear equations...

Hello Dear!

I want to solve the system of linear equation but facing some problem please see the attachmen. I am waiting your positive response

1_(1).mw

## Parametric linear system ...

Hi,

I am trying to solve a simple system of the form AX=0, where A is a N*N matrix, X is an N*1 vector (and the right-hand side of the equation is an N*1 vector of zeros, I apologize for the inexact notation). The difficulty comes from the fact that the values of A are parameterized by 2*N parameters (that I will write as the 2*N vector P), and I would like to get a solution in the form X=f(P).

One solution is to try to use LinearAlgebra[LinearSolve], but it only returns the trivial solution X=0, which I am not interested in.

Another solution is to compute analytically the Moore-Penrose pseudoinverse Ag of A, as the general solution is of the form

(I - Ag A)f ;

where f is a vector of free parameters. However, even for a small matrix size (N=4), Maple is still computing after 3 hours on my (fairly powerful) machine, and it is taking more and more memory over time. As the results are polynomial/rational equations in the parameters P, I was actually expecting Maple to be more powerful than other softwares, but for this particular problem, Matlab's symbolic toolbox (muPAD) gives quick solutions until N=6. I need, in the end, to solve additional polynomial/rational equations that are derived from the solutions X=f(P), where Matlab fails. This is why I would really like to be able to solve the above-mentioned problem AX=0 with Maple in order to try to solve the subsequent step of the problem (polynomial system) with Maple.

Any suggestions on how to do this would be highly appreciated! Thank you very much for your time and help.

Laureline

## Matrix of linear system...

Hello..  I want to know if there is anny command to show the matrix of linear system.  I recently entred a 64 equations and i solved it by command solve,  but i want to show the matrix of system..  So plz. Help

## Error when solving linear ODE...

I have an equation eq := diff(y(x), x\$3)+3*diff(y(x), x\$2)+12*y(x);

dsolve(eq, y(x)); gave me a general solution.

I tried to get a particular solution using dsolve({eq, y(0) = a, y'(0)=0, y"(0) = 0}, y(x));

But I got Error, (in dsolve) not a system with respect to the unknowns [y(x)].

Thank you for any help.

Heather

## Extract Linear Graph...

Does any one know if you can extract the linear graph from a Maple Sim model?  And by linear graph I mean the alternative to a a bond graph, not a type of plot.

## How is basis chosen?...

I solve a linear system of equations which is rank deficient. Naturally, when Maple solves it symbolically, it chooses some of its variables to use them as a basis to express the solution.

In a specific problem I'm solving, the basis chosen by Maple is -very- smart, showing a good exploitation of the problem structure.

I'm curious as to what kind of factorization is used by default, or if there's a lot of by hand "black magic" involved, what are its general characteristics.

Best regards

Claudio

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