SBG Horizontal Sorting

[Kalashnikovni]

As GiNaC only needs the equation and the desired unknown to solve from it, this process must shield a list of pairs of equations and variables, without modifying the input equations. There's no need to transform the equation to something like:

unknown := solved_expression

However, if it is a ForEq the indices may need modifications if the calculated matching is not the same for every element of the array.

[Kalashnikovni]

For the time being, horizontal sorting is supported only if the equation array is matched with the same occurrence of the same variable. For example in:

for i in 1:N loop
    L*der(iL[i])=uL[i];
  end for;

if der(iL[i]) is matched from 1, ..., N, then it is supported in the current version. If the indices of the array equation need modifications the execution will end with ERROR.
We will open a new issue to develop a new version of HorizontalSorting::sortEquation that support a general matching. For example, if

for i in 1:N loop
  L*der(iL[i])=uL[i];
end for;

matches with uL[1:N/2] and der(iL[N/2+1:N]), then we need to split the equation as follows:

for i in 1:N/2 loop
  L*der(iL[i])=uL[i];
end for;
for i in N/2+1:N loop
  L*der(iL[i])=uL[i];
end for;