MFSolve

MFSolve is an equation solver that solves and evaluates expressions on the fly. It is based on Prof. D.E.Knuth's metafont. The goal of mfsolve is to make the solver useful in an interactive program, by enhancing the bidirectionality of the solver. Like metafont, it can solve linear equations, and evaluate nonlinear expressions. In addition to metafont, it also solves for angles, and makes the solution independend of the order of the equations.

The Expr type allows for calculations with constants and unknown variables.

Examples:

Let's define some variables. The SimpleVar type is a simple wrapper around String to provide nice output. The Dependencies datatype contains all dependencies and known equations.

let [x, y, t, a] = map (makeVariable . SimpleVar) ["x", "y", "t", "a"]

Solve linear equations:

showVars $ solveEqs emptyDeps
[ 2*x + y === 5,
  x - y   === 1]

x = 2.0
y = 1.0

Solve for angle (pi/4):

showVars $ solveEqs emptyDeps
[ sin(t) === 1/sqrt(2) ]

t = 0.7853981633974484

Solve for angle (pi/3) and amplitude:

showVars $ solveEqs emptyDeps
[ a*sin(x) === sqrt 3,
  a*cos(x) === 1 ]

x = 1.0471975511965979
a = 2.0

Allow nonlinear expression with unknown variables:

showVars $ solveEqs emptyDeps
[ sin(sqrt(x)) === y,
  x === 2]

x = 2.0
y = 0.9877659459927355

Find the angle and amplitude when using a rotation matrix:

showVars $ solveEqs emptyDeps
[ a*cos t*x - a*sin t*y === 30,
  a*sin t*x + a*cos t*y === 40,
  x === 10,
  y === 10 ]

x = 10.0
y = 10.0
t = 0.14189705460416402
a = 3.5355339059327373