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julialinear-algebra

How to perform row reduction whilst keeping variables in fraction form in Julia?

I am trying to perform Gaussian elimination on a matrix in Julia to then extract the solutions in fraction form, rather than decimal. For example, I would want 3/4 rather than 0.75 as a solution.

My current code for row-reducing a matrix and expressing the solutions as decimals is as follows:

using RowEchelon

A = [1 2 3;
     4 5 6;
     7 8 10]

A_reduced rref(A)

print(A_reduced)

Is there a way I can modify this code to obtain fractions rather than floating-point solutions?

Solution

  • Maybe you're looking for

    Rational{Int}.(rand())

    on your data either cast the initial matrix

    a = Rational{Int}.(A)
3×3 Matrix{Rational{Int64}}:
 1  2   3
 4  5   6
 7  8  10

a[1]
1//1

rref(a)
3×3 Matrix{Rational{Int64}}:
 1  0  0
 0  1  0
 0  0  1

    or just the result

    Rational{Int}.(rref(A))
3×3 Matrix{Rational{Int64}}:
 1  0  0
 0  1  0
 0  0  1