I really like my geometric integer arithmetic systems of linear equation solver so far, it’s just that the problem is that it can only solve in up to three dimensions, the limit being that I don’t know how to compute cross products in n dimensions. I know it should be possible: a vector is a restriction to one dimension, so n - 1 vectors in n dimensions should define the perpendicular vector to all of them. And indeed, right in the introduction to the Wikipedia article on the cross product, this is stated right there. Now I just need to figure out the details of the math solution that they presented.
20200507/https://en.wikipedia.org/wiki/Cross_product
20200507/https://en.wikipedia.org/wiki/Exterior_algebra
20200507/https://en.wikipedia.org/wiki/Hodge_star_operator
20200507/https://en.wikipedia.org/wiki/Differential_form