## AngouriMath

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# Solve​(AngouriMath.​Entity.​Variable)

Summary

Solves a Statement Statement is an Entity such that its value is true for
any x in X, where X is the result of this method.

Parameter "var"

Over which variable to solve

Example

using System;
using static AngouriMath.MathS;

var (x, y) = Var("x", "y");
var eq = Sin(x).Equalizes(0.5);
Console.WriteLine(eq);
Console.WriteLine(eq.Solve(x));
Console.WriteLine("-----------------");
var eq2 = (Sqr(x) + 2 * x * y - y).Equalizes(0);
Console.WriteLine(eq2);
Console.WriteLine(eq2.Solve(x));
Console.WriteLine("-----------------");
var eq3 = ((x - 3) * (x - 6)).Equalizes(0) & ((x - 3) * (x - 7)).Equalizes(0);
Console.WriteLine(eq3);
Console.WriteLine(eq3.Solve(x));
Console.WriteLine("-----------------");
var eq4 = ((x - 3) * (x - 6)).Equalizes(0) | ((x - 3) * (x - 7)).Equalizes(0);
Console.WriteLine(eq4);
Console.WriteLine(eq4.Solve(x));
Console.WriteLine("-----------------");
var eq6 = GreaterThan((x - 3) * (x + 6), 0);
Console.WriteLine(eq6);
Console.WriteLine(eq6.Solve(x));
Console.WriteLine("-----------------");
var eq7 = LessThan((x - 3) * (x + 6), 0);
Console.WriteLine(eq7);
Console.WriteLine(eq7.Solve(x));
Console.WriteLine("-----------------");
var eq8 = (Sin(x) * x - 3).Equalizes(0);
Console.WriteLine(eq8);
Console.WriteLine(eq8.Solve(x));
Console.WriteLine("-----------------");
using var _ = Settings.AllowNewton.Set(false);
var eq9 = (Sin(x) * x - 3).Equalizes(0);
Console.WriteLine(eq9);
Console.WriteLine(eq9.Solve(x));


Prints
sin(x) = 1/2
{ arcsin(1/2) + 2 * pi * n_1, pi - arcsin(1/2) + 2 * pi * n_1 }
-----------------
x ^ 2 + 2 * x * y - y = 0
{ (-2 * y - sqrt((2 * y) ^ 2 - 4 * -y)) / 2, (-2 * y + sqrt((2 * y) ^ 2 - 4 * -y)) / 2 }
-----------------
(x - 3) * (x - 6) = 0 and (x - 3) * (x - 7) = 0
{ 3 }
-----------------
(x - 3) * (x - 6) = 0 or (x - 3) * (x - 7) = 0
{ 3, 6, 7 }
-----------------
(x - 3) * (x + 6) > 0
(-oo; -6) \/ (3; +oo)
-----------------
(x - 3) * (x + 6) < 0
(-6; 3)
-----------------
sin(x) * x - 3 = 0
{ 9.08837698687877... }
-----------------
sin(x) * x - 3 = 0
{  }

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