Is there a module in Sage to solve 2 unknowns in diophantine equations?
For instance, ax+by=c where a,b,c are known
I tried basic extended euclidean algorithm but my numbers are too large.
Two ways of solving diophantine equations in Sage are
using the Smith normal form of matrices over ZZ
using polytopes
See the answers to these two Ask Sage questions:
Ask Sage question 10364: Linear diophantine equations
Ask Sage question 23666: Solving system of linear Diophantine equations
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Suppose i have system of equations. Lets consider simple example
x1+2x2=3
4x1+5x2=6
I screened my steps of solving
I can solve this equations during 5 minutes.
Here result which solved manually
Then
From the 1st equation, we express x1 in terms of the remaining variables
tnen Substitute x1 into equation 2
after simplification we get
then Divide the 2nd equation by -3
and my solve
Now, moving from the last equation to the first, you can find the values of the remaining variables
As you can see, with such simple steps, I solved this equation. So the question is, is there a way to enter these equations and also get the steps of solving this equation?
If there is no such way, then at least just get a solution.
I have a mathematical optimization which I wish to solve in R consider this system/problem:
How Can I solve this problem in R?
In this model Budget, p_l for all l and mu_target are fixed constants while muis a given m-dimensional vector and R is a given n by m matrix.
I have looked into constrOptim and lp but I don't have the imagination to implement the constraints
Those functions require that I have a "constraint" matrix but my problem is that I simply don't know how to design that constraint matrix. There are not many examples with decision variables on both sides of the equations.
Have a look on the nloptr package. It has quite extensive documentation with examples. Lots of algorithms to choose from, depending what problem you are trying to resolve.
NLoptr link
My idea is to start using lp solve in order to solve a linear programming model. As a result, I studied the lp function and his components.
However, one thing which is not clear to me is how do I display all possible optimal solutions using lp solve in R without my variables be binary?
I would appreciate an easy example to better understand.
Thanks,
David
I know that it's quite simple to solve the equation in Matlab. But is there a way to solve it in R as well? I need it for my Kalman filter implementations.
I need to solve a linear program in R where the variables are matrices.
More specifically, my optimizing function looks like this.
Max X(A+B)Y - x - y,
where X,Y,A,B are matrices and x,y are scalars. Solve for X,Y,x,y
Subject to bunch of constraints like any linear program
Is there a way to solve this in R?
I checked out linprog and limsolve packages in R. They solve linear programs of scalars.
Is there a way to do the same for matrices in R.
Thanks for your help.
Googling for R linear programming matrices yielded a number of interesting links, of which the following might be interesting:
Simplex Method for Linear Programming Problems, for the boot package.