private IEnumerable <SolutionItem> GetSolution()
{
var a = _mainModel.ParameterA;
var b = _mainModel.ParameterB;
var c = _mainModel.ParameterC;
var complex = _mainModel.AcceptComplexNumberSolutions;
yield return(SolutionItem.WithEquation("initial equation", true, new[]
{
EquationItem.With("{0}x²", a),
EquationItem.With("{0}x", b),
EquationItem.With("{0}", c)
}));
if (a == 0 || b == 0 || c == 0 || Math.Abs(a) == 1 || Math.Abs(b) == 1 || Math.Abs(c) == 1)
{
yield return(SolutionItem.WithEquation("simplify equation", new[]
{
EquationItem.With("{0}x²", a),
EquationItem.With("{0}x", b),
EquationItem.With("{0}", c)
}));
}
if (a == 0 && b == 0)
{
if (c == 0)
{
yield return(SolutionItem.WithString("solve", "x = any number"));
}
else
{
yield return(SolutionItem.WithString("different constant values", "impossible equation"));
}
yield break;
}
if (c != 0)
{
yield return(SolutionItem.WithEquation("constant term to right hand side", new[]
{
EquationItem.With("{0}x²", a),
EquationItem.With("{0}x", b)
}, new[]
{
EquationItem.With("{0}", -c)
}));
}
if (a == 0)
{
if (b != 1)
{
yield return(SolutionItem.WithEquation("divide both sides by coeficient of x", new[]
{
EquationItem.With("({0} / {1})x", b, b)
}, new[]
{
EquationItem.With("{0} / {1}", -c, b)
}));
yield return(SolutionItem.WithEquation("simplify equation", new[]
{
EquationItem.With("x")
}, new[]
{
EquationItem.With("{0} / {1}", -c, b)
}));
}
var r = -c / b;
yield return(SolutionItem.WithEquation("solve", new[]
{
EquationItem.With("x")
}, new[]
{
EquationItem.With("{0}", r)
}));
yield break;
}
if (a != 1)
{
if (b == 0)
{
yield return(SolutionItem.WithEquation("divide both sides by coeficient of x²", new[]
{
EquationItem.With("({0} / {1})x²", a, a)
}, new[]
{
EquationItem.With("{0} / {1}", -c, a)
}));
}
else
{
yield return(SolutionItem.WithEquation("divide both sides by coeficient of x²", new[]
{
EquationItem.With("({0} / {1})x²", a, a),
EquationItem.With("({0} / {1})x", b, a)
}, new[]
{
EquationItem.With("{0} / {1}", -c, a)
}));
}
b /= a;
c /= a;
a = 1;
yield return(SolutionItem.WithEquation("simplify equation", new[]
{
EquationItem.With("x²", a),
EquationItem.With("{0}x", b)
}, new[]
{
EquationItem.With("{0}", -c)
}));
}
var e = b / 2;
var d = Math.Pow(e, 2);
if (b != 0)
{
yield return(SolutionItem.With("calculate half of the coefficient of x and square it", new FormattableItem[]
{
TextItem.With("d = "),
Equation.With(new[]
{
EquationItem.With("({0} / 2)²", b)
}, new[]
{
EquationItem.With("{0}", d)
})
}));
yield return(SolutionItem.WithEquation("add it to both sides of equation", new[]
{
EquationItem.With("x²", a),
EquationItem.With("{0}x", b),
EquationItem.With("{0}", d)
}, new[]
{
EquationItem.With("{0}", -c),
EquationItem.With("{0}", d)
}));
}
var f = -c + d;
if (e != 0)
{
yield return(SolutionItem.WithEquation("complete the square and simplify", new[]
{
EquationItem.With("(x + {0})²", e),
}, new[]
{
EquationItem.With("{0}", f)
}));
}
if (f < 0)
{
if (!complex)
{
yield return(SolutionItem.WithString("square on left equals negative value on right", "impossible equation"));
yield break;
}
}
else
{
complex = false;
}
if (e != 0 || f != 0)
{
yield return(SolutionItem.WithEquation("square root both sides", new[]
{
EquationItem.With("x"),
EquationItem.With("{0}", e),
}, new[]
{
EquationItem.With("±√({0})", f)
}));
}
if (e != 0)
{
yield return(SolutionItem.WithEquation("isolate x", new[]
{
EquationItem.With("x"),
}, new[]
{
EquationItem.With("{0}", -e),
EquationItem.With("±√({0})", f)
}));
}
var g = Math.Sqrt(Math.Abs(f));
if (e != 0 && g != 0)
{
yield return(SolutionItem.WithEquation("simplify equation", new[]
{
EquationItem.With("x"),
}, new[]
{
EquationItem.With("{0}", -e),
EquationItem.With("±{0}", complex, g)
}));
}
if (complex)
{
if (g == 0)
{
yield return(SolutionItem.WithEquation("solve", new[]
{
EquationItem.With("x")
}, new[]
{
EquationItem.With("{0}", -e),
}));
}
else
{
yield return(SolutionItem.With("solve", new FormattableItem[]
{
Equation.With(new[]
{
EquationItem.With("x")
}, new[]
{
EquationItem.With("{0}", -e),
EquationItem.With("{0}", complex, g)
}),
TextItem.With(", "),
Equation.With(new[]
{
EquationItem.With("x")
}, new[]
{
EquationItem.With("{0}", -e),
EquationItem.With("-{0}", complex, g)
})
}));
}
yield break;
}
var rs = new[] { -e - g, -e + g }
.OrderBy(x => x)
.ToArray();
if (g == 0)
{
yield return(SolutionItem.WithEquation("solve", new[]
{
EquationItem.With("x")
}, new[]
{
EquationItem.With("{0}", complex, rs[0])
}));
}
else
{
yield return(SolutionItem.With("solve", new FormattableItem[]
{
Equation.With(new[]
{
EquationItem.With("x")
}, new[]
{
EquationItem.With("{0}", complex, rs[0])
}),
TextItem.With(", "),
Equation.With(new[]
{
EquationItem.With("x")
}, new[]
{
EquationItem.With("{0}", complex, rs[1])
})
}));
}
}
