mathematica

Solving symbolic equations with SymPy – Stéphane Caron

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SymPy has some routines to make formulas more palatable. For instance, it can print sympy.Expr objects (expressions) in LATEX:

The second argument of solve() indicates the set of “output” variables. Indeed, we have three equations for twelve variables. Each equation can be used to express one variable as function of the others. Thus, we can pick three variables and express them as functions of the remaining nine.

via Solving symbolic equations with SymPy – Stéphane Caron

mathematica graphing a 2 by 2 matrix as an object

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is there a possibility to “transform” a matrix (inheriting the input-output “weights”) into a graph object inheriting the matrix relations?

you can convert it to an edge-weighted graph using WeightedAdjacencyGraph. This will give you a complete graph (a Graph expression) in which each vertex is also connected to itself. I am not sure how much sense it makes treat this matrix as a graph, given the full connectivity.

Since you have a fully connected graph, it does not matter in your case, but be aware that WeightedAdjacencyGraph represents missing edges with Infinity, not with zero. This is somewhat annoying because it is inconsistent with WeightedAdjacencyMatrix, which uses 0. While Infinity does make sense in some (not all) applications, it is much more common to see data that uses 0.

 

 

 

via [✓] Convert matrix into “Graph object”? – Online Technical Discussion Groups—Wolfram Community

SliceDensityPlot3D—Wolfram Language Documentation

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SliceDensityPlot3D[f, surf, {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}] generates a density plot of f over the slice surface surf as a function of x, y, and z. SliceDensityPlot3D[f, surf, {x, y, z} \[Element] reg] restricts the surface to be within region reg. SliceDensityPlot3D[f, {surf1, surf2, …}, …] generates density plots over several slices.

Source: SliceDensityPlot3D—Wolfram Language Documentation