AngouriMath

Navigation

Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug Contacts

← Back to list of members

SolveSystem(System.Collections.Generic.IEnumerable{AngouriMath.Entity},System.ReadOnlySpan{AngouriMath.Entity.Variable})

Method (no overloads)

Summary

Solves a system of equations for vars, one row per solution, or
null where it cannot.

Remarks

Tried in order: a Gröbner basis, where the system is polynomial over Q; row reduction,
where a linear system has fewer equations than unknowns; once for each factor, where
an equation is a product in more than one unknown; NonSquareSystemSolver,
where the count is not square or an unknown is in no equation; and elimination.
Elimination solves one equation after another with substitution, e.g.
let { x - y + a = 0, y + 2a = 0 } be a system of equations for variables { x, y }
Then we first find y from the first equation,
y = x + a
then we substitute it to all others
x + a + 2a = 0
then we find x
x = -3a
Then we substitute back
y = -3a + a = -2a
and each row it answers is put back into the equations as they were written.

AngouriMath

Table of contents

AngouriMath

SolveSystem​(System.​Collections.​Generic.​IEnumerable{AngouriMath.​Entity},​System.​ReadOnlySpan{AngouriMath.​Entity.​Variable})

SolveSystem(System.Collections.Generic.IEnumerable{AngouriMath.Entity},System.ReadOnlySpan{AngouriMath.Entity.Variable})