Possible Bug in LinearSolveFunction with Sparse Vectors

Question

Bug introduced in 5.0 and fixed in 11.0
LinearSolveFunction is new in 5.0

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Consider the following set of equations and corresponding variables:

eqns1 ={2 x == 2 - 4 y, 3 y == 4 z, 2 z + 4 t == 3, 3 t + 2 z == 5};
vars = {x, y, z, t};

We can use CoefficientArrays to get the array of coefficient of the variables, and use that to solve the set of equations:

{v1, m1} = CoefficientArrays[eqns1, vars];
LinearSolve[m1][-v1] (* This creates a LinearSolveFunction then applies it to -v1 *)

$ \{-\frac{41}{3}, \frac{22}{3}, \frac{11}{2}, -2\} $

Now we make the set of equations symbolic and repeat the process:

eqns2 = {b x == 2 - c y, a y == c z, b z + c t == 3, a t + b z == 5};
{v2, m2} = CoefficientArrays[eqns2, vars];

Now we solve the equations:

LinearSolve[m2][-v2]

And Mathematica just crashes as if you typed Quit[].

Note that LinearSolveFunction is the culprit because you can still get the answer without crashing Mathematica by just using regular LinearSolve (without first creating a LinearSolveFunction) as follows:

LinearSolve[m2, -v2]

$\{\frac{2 a^2 b - 2 a b c - 3 a c^2 + 5 c^3}{a b^2 (a - c)}, \frac{ 3 a c - 5 c^2}{a b (a - c)}, \frac{3 a - 5 c}{b (a - c)}, \frac{2}{a - c}\}$

Also, note that if we pass the vector as a List, it also works fine

ls = LinearSolve[m2]; (* create a LinearSolveFunction *)
ls[{2, 0, 3, 5}] // ExpandAll // Together

Can anyone reproduce this? I get the same behavior on both Mathematica 10.3.1 and 10.4. OS is Windows 10 64-bit.

Answer 1

This bug has been fixed in the just released Mathematica 11.0:

eqns2 = {b x == 2 - c y, a y == c z, b z + c t == 3, a t + b z == 5};
vars = {x, y, z, t};
{v2, m2} = CoefficientArrays[eqns2, vars];
LinearSolve[m2][-v2]

(* {(2 - (c^2 (3 - (2 c)/(a - c)))/(a b))/b, (c (3 - (2 c)/(a - c)))/(a b),
    (3 - (2 c)/(a - c))/b, 2/(a - c)} *)