/** This tests solving systems of linear equations using Matrix.frink.
*/

use Matrix.frink
use formatEquation.frink

symbolicMode[true]

a = new Matrix[[[noEval[r], noEval[s]], [noEval[t], noEval[u]]]]
println[formatTable[[["a = ", a.formatMatrixCompact[]]]]]

bb = noEval[[y,z]]
b = new Matrix[noEval[bb.transpose[]]]
println[]
println[formatTable[[["b = ", b.formatMatrixCompact[]]]]]

c = a.augment[b]
c.reduceRows[]
println[c.formatMatrix[]]
c.simplifySymbolic[]
println[c.formatMatrix[]]

sol = c.getColumnAsArray[3]
println["\nsol:"]
println[formatMatrix[sol]]

println["\nsol:"]
println[formatMatrixCompact[sol]]

println["\nsol:"]
println[formatMatrixVeryCompact[sol]]


xn = 1
for s = sol
{
   println["\n"]
   println[formatTable[[["x$xn = ", formatExpression[s]]]]]
   xn = xn + 1
}

sm = new Matrix[noEval[sol]]
println[]
println[formatMatrixCompact[sm.array]]