public List <TrinomialSolutionDto> Square(int a = 1, int b = 1)
{
List <TrinomialSolutionDto> solution = new List <TrinomialSolutionDto>();
solution.Add(new TrinomialSolutionDto()
{
SolutionLine = ("(" + AssitUtilities.PlusAndKill(true, false, a) + "x " + AssitUtilities.PlusAndKill(false, false, b) + "y)²").ToString(),
Description = "Square Line first"
});
solution.Add(new TrinomialSolutionDto()
{
SolutionLine = AssitUtilities.PlusAndKill(true, true, a) + "²x² " + " +2(" + AssitUtilities.PlusAndKill(true, false, a) + "x)(" + AssitUtilities.PlusAndKill(true, false, b) + "y) " + AssitUtilities.PlusAndKill(false, true, b) + "²y²".ToString(),
Description = "Formula Applied"
});
int c = 2 * a * b;
a *= a;
b *= b;
solution.Add(new TrinomialSolutionDto()
{
SolutionLine = AssitUtilities.PlusAndKill(true, false, a) + "x²" + AssitUtilities.PlusAndKill(false, false, c) + "xy " + AssitUtilities.PlusAndKill(false, false, b) + "y²".ToString(),
Description = "Formula Applied"
});
int gcd = MathUtilities.GCD(new int[] { a, b, c });
if (gcd != 1)
{
solution.Add(new TrinomialSolutionDto()
{
SolutionLine = gcd + "( " + AssitUtilities.PlusAndKill(true, false, a / gcd) + "x²" + AssitUtilities.PlusAndKill(false, false, c / gcd) + "xy " + AssitUtilities.PlusAndKill(false, false, b / gcd) + "y²)".ToString(),
Description = "Formula Applied"
});
}
return(solution);
}
public List <TrinomialSolutionDto> Trinomial(string equation, int a = 1, int b = 1, int c = 0)
{
List <TrinomialSolutionDto> solution = new List <TrinomialSolutionDto>();
// var terms = equation.Split(new char[] {'+', '-'}).Select(t => t.Trim());
// char v = 'x';
// int a;
// int b;
// int c;
int d = a * c;
var factors = d.Divisors();
var pairFactor = AssitUtilities.MidTermFactorPair(factors, b, d);
if (pairFactor[0] != 0 && pairFactor[1] != 0)
{
solution.Add(new TrinomialSolutionDto()
{
SolutionLine = AssitUtilities.PlusAndKill(true, false, a) + "x^2"
+ AssitUtilities.PlusAndKill(false, false, pairFactor[0]) + "x"
+ AssitUtilities.PlusAndKill(false, false, pairFactor[1]) + "x"
+ AssitUtilities.PlusAndKill(false, true, c)
.ToString(),
Description = "xxxxxxxx"
});
}
else
{
solution.Add(new TrinomialSolutionDto()
{
SolutionLine = "There is no other factor but itselt!",
Description = "xxxxxxxxxxxxxx"
});
return(solution);
}
int gcd1 = MathUtilities.GCD(new int[] { pairFactor[0], a });
int gcd2 = MathUtilities.GCD(new int[] { pairFactor[1], c });
solution.Add(new TrinomialSolutionDto()
{
SolutionLine = (AssitUtilities.PlusAndKill(true, false, gcd1) + "x("
+ AssitUtilities.PlusAndKill(true, false, a / gcd1) + "x"
+ AssitUtilities.PlusAndKill(false, true, pairFactor[0] / gcd1) + ")"
+ AssitUtilities.PlusAndKill(false, true, gcd2) + "("
+ AssitUtilities.PlusAndKill(true, false, pairFactor[1] / gcd2) + "x"
+ AssitUtilities.PlusAndKill(false, true, c / gcd2) + ")")
.ToString(),
Description = "xxxxxxxx"
});
solution.Add(new TrinomialSolutionDto()
{
SolutionLine = ("("
+ AssitUtilities.PlusAndKill(true, false, a / gcd1) + "x"
+ AssitUtilities.PlusAndKill(false, true, pairFactor[0] / gcd1) + ")("
+ AssitUtilities.PlusAndKill(true, false, gcd1) + "x"
+ AssitUtilities.PlusAndKill(false, true, gcd2) + ")")
.ToString(),
Description = "xxxxxxxx"
});
return(solution);
}
public List <QuadraticSolutionDto> Qudratic(int a = 1, int b = 1, int c = 0, int d = 0)
{
List <QuadraticSolutionDto> solution = new List <QuadraticSolutionDto>();
c = c - d;
if (d != 0)
{
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = AssitUtilities.PlusAndKill(true, false, a) + "x^2"
+ AssitUtilities.PlusAndKill(false, false, b) + "x"
+ AssitUtilities.PlusAndKill(false, true, c) + " = 0"
.ToString(),
Description = "xxxxxxxx"
});
}
d = a * c;
var factors = d.Divisors();
var pairFactor = AssitUtilities.MidTermFactorPair(factors, b, d);
if (pairFactor[0] != 0 && pairFactor[1] != 0)
{
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = AssitUtilities.PlusAndKill(true, false, a) + "x^2"
+ AssitUtilities.PlusAndKill(false, false, pairFactor[0]) + "x"
+ AssitUtilities.PlusAndKill(false, false, pairFactor[1]) + "x"
+ AssitUtilities.PlusAndKill(false, true, c) + " = 0"
.ToString(),
Description = "xxxxxxxx"
});
}
else
{
//TODO
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = "x = ( - (" + b + ") + √(" + b + "² - 4*" + a + "*" + c + " )) / ( 2*" + a + " ) Or, x = ( - (" + b + ") - √(" + b + "² - 4*" + a + "*" + c + " )) / ( 2*" + a + " )",
Description = "A"
});
double result1 = ((-1 * b) + Math.Sqrt((b * b) - (4 * a * c))) / (a * 2);
double result2 = ((-1 * b) - Math.Sqrt((b * b) - (4 * a * c))) / (a * 2);
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = "x = " + Math.Round(result1, 2) + " Or, x = " + Math.Round(result2, 2),
Description = "AAA"
});
return(solution);
}
int gcd1 = MathUtilities.GCD(new int[] { pairFactor[0], a });
int gcd2 = MathUtilities.GCD(new int[] { pairFactor[1], c });
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = (AssitUtilities.PlusAndKill(true, false, gcd1) + "x("
+ AssitUtilities.PlusAndKill(true, false, a / gcd1) + "x"
+ AssitUtilities.PlusAndKill(false, true, pairFactor[0] / gcd1) + ")"
+ AssitUtilities.PlusAndKill(false, true, gcd2) + "("
+ AssitUtilities.PlusAndKill(true, false, pairFactor[1] / gcd2) + "x"
+ AssitUtilities.PlusAndKill(false, true, c / gcd2) + ")") + " = 0"
.ToString(),
Description = "xxxxxxxx"
});
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = ("("
+ AssitUtilities.PlusAndKill(true, false, a / gcd1) + "x"
+ AssitUtilities.PlusAndKill(false, true, pairFactor[0] / gcd1) + ")("
+ AssitUtilities.PlusAndKill(true, false, gcd1) + "x"
+ AssitUtilities.PlusAndKill(false, true, gcd2) + ")") + " = 0"
.ToString(),
Description = "xxxxxxxx"
});
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = ("Hence, ("
+ AssitUtilities.PlusAndKill(true, false, a / gcd1) + "x"
+ AssitUtilities.PlusAndKill(false, true, pairFactor[0] / gcd1) + ") = 0 or ("
+ AssitUtilities.PlusAndKill(true, false, gcd1) + "x"
+ AssitUtilities.PlusAndKill(false, true, gcd2) + ") = 0")
.ToString(),
Description = "xxxxxxxxxxxxx"
});
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = ("therefore, "
+ AssitUtilities.PlusAndKill(true, false, a / gcd1) + "x = "
+ AssitUtilities.PlusAndKill(true, true, -1 * pairFactor[0] / gcd1) + " or, "
+ AssitUtilities.PlusAndKill(true, false, gcd1) + "x = "
+ AssitUtilities.PlusAndKill(true, true, -1 * gcd2))
.ToString(),
Description = "xxxxxxxxxxxxx"
});
int nominatorA = -1 * pairFactor[0] / gcd1;
int denominatorA = a / gcd1;
int nominatorB = -1 * gcd2;
int denominatorB = gcd1;
string resultA = AssitUtilities.Fraction(nominatorA, denominatorA);
string resultB = AssitUtilities.Fraction(nominatorB, denominatorB);
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = ("x = "
+ resultA + " or, "
+ "x = "
+ resultB)
.ToString(),
Description = "xxxxxxxxxxxxx"
});
if (MathUtilities.GCD(nominatorA, denominatorA) == 1 || MathUtilities.GCD(nominatorB, denominatorB) == 1 ||
MathUtilities.GCD(nominatorA, denominatorA) == -1 || MathUtilities.GCD(nominatorB, denominatorB) == -1)
{
return(solution);
}
resultA = AssitUtilities.Katakati(nominatorA, denominatorA);
resultB = AssitUtilities.Katakati(nominatorB, denominatorB);
solution.Add(new QuadraticSolutionDto()
{
SolutionLine = ("x = "
+ resultA + " or, "
+ "x = "
+ resultB)
.ToString(),
Description = "xxxxxxxxxxxxx"
});
return(solution);
}
