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NonSquareSystemSolver

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Description

Summary

A system with more or fewer equations than unknowns that neither the triangularisation nor
LinearSystemSolver takes, such as x^2 + y^2 = 1 for x and
y, or sin(x) = 0 and x = 0 for x. Each unknown is eliminated in
turn, an unknown that nothing is left to constrain becomes a parameter, and every family
found is substituted back into every equation.
#212

Remarks

An answer is given only where it is shown to hold. The elimination trusts each solve
it makes, and a solve can answer for a case its equation does not cover: sqrt(y) = x is solved for y as x^2, which is no solution where x is negative. So
each family is kept only where every equation, with the family substituted, simplifies to
0. sqrt(t^2) - t does not, and that system is declined.
A decline declines the whole system. An equation left with no unknown in it is zero,
a number away from zero, or neither as far as can be told, like (a + b)/2 - c. A
branch where one is away from zero has no solutions and is dropped. A branch where one
cannot be told gives no answer for the system, rather than leaving the other branches to
read as all of its solutions.
 A square system does not come here. It is the eliminator's in
InSolveSystem(System.Collections.Generic.List{AngouriMath.Entity},System.ReadOnlySpan{AngouriMath.Entity.Variable},AngouriMath.Entity,AngouriMath.Core.Budgets.BudgetLedger), whose answers this would change.

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