Convert a system of linear equations to matrix-form

Questions
1

Is there a simply function in WL which converts some given system eqns of linear equations in vars into the standard matrix form A.x == b ?

As an example:

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I have such a function but it’s non-trivial. It uses the CoefficientList-tensors. I suspect that there must be something better.

2

You may have a look at CoefficientArrays:

In[1]:= CoefficientArrays[{a + x - y - z == 0, 
   b + x + 2 y + z == 0}, {x, y, z}] // Normal

Out[1]= {{a, b}, {{1, -1, -1}, {1, 2, 1}}}
3

I Know. I use the CoeffientList-tensors, which are easier to use.

4

One of the more tricky tasks is to verify that the given equations are linear indeed and contain no mixed terms with respect to the given variables.

5

For verification, there is LinearFunctionQ in the Wolfram Function Repository. For the actual conversion of equations to matrix-vector, CoefficientArays is the recommended method (that is to say, it’s what we use in-house).

6

Oh thanks, Daniel. I did not know this LinearFunctionQ. I will examine it.

7

Daniel, I examined LinearFunctionQ and found:

  • It handles expressions written with normal symbols x, y, … correctly
  • It does respect variables written as Indexed (say Indexed[x,1])
  • It does respect variables written as Subscript(ed) (say Subscript[x,1])

Hence your function is perfect (BTW: Is the source code available?).

My code may be overloaded, since it outputs detailed messages to tell the user exactly what is wrong with which equation. For simplicity, I think I’ll throw that out and use your function.

Thanks for that hint!

8

It seems the source code is not available for this particular function.