public static void FromEquatableTest(int x, int y)
{
var r = PartialOrder.FromEquatable <int>();
Assert.Equal(x == y, r.Leq(x, y));
}
public static void PartiallyOrderedTest()
{
var order = Group.IntAdd.WithPartialOrder <int, Group.IntAddGroup, IPartialOrder <int> >(PartialOrder.FromEquatable <int>());
Assert.Equal(0, order.Zero <int, Group.IntAddGroup>());
Assert.Equal(7, order.Plus(3, 4));
Assert.Equal(1, order.Minus(3, 2));
Assert.Equal(-3, order.Negate(3));
Assert.True(order.Leq(3, 3));
Assert.False(order.Leq(5, 3));
var order2 = EuclideanDomain.Integers.WithPartialOrder <int, EuclideanDomain.IntegerEuclideanDomain, Group.IntAddGroup, Monoid.IntMultMonoid, IPartialOrder <int> >(PartialOrder.Make <int>((x, y) => Maybe.Just(x <= y)));
Assert.Equal(0, order2.Zero <int, Group.IntAddGroup>());
Assert.Equal(1, order2.One <int, Monoid.IntMultMonoid>());
Assert.Equal(7, order2.Plus(3, 4));
Assert.Equal(1, order2.Minus(3, 2));
Assert.Equal(12, order2.Mult(3, 4));
Assert.Equal(-3, order2.Negate(3));
Assert.Equal((2, 1), order2.EuclideanDivide <int, EuclideanDomain.IntegerEuclideanDomain, Group.IntAddGroup, Monoid.IntMultMonoid>(5, 2));
Assert.Equal(1, order2.Mod <int, EuclideanDomain.IntegerEuclideanDomain, Group.IntAddGroup, Monoid.IntMultMonoid>(5, 2));
Assert.Equal(5, order2.Gcd <int, EuclideanDomain.IntegerEuclideanDomain, Group.IntAddGroup, Monoid.IntMultMonoid>(5, 15));
Assert.Equal(15, order2.Lcm <int, EuclideanDomain.IntegerEuclideanDomain, Group.IntAddGroup, Monoid.IntMultMonoid>(5, 15));
Assert.True(order2.Leq(3, 3));
Assert.False(order2.Leq(5, 3));
var order3 = Field.Double.WithPartialOrder <double, Field.DoubleField, Group.DoubleAddGroup, Group.DoubleMultGroup, IPartialOrder <double> >(PartialOrder.Make <double>((x, y) => Maybe.Just(x <= y)));
Assert.Equal(0D, order3.Zero <double, Group.DoubleAddGroup>());
Assert.Equal(1D, order3.One <double, Group.DoubleMultGroup>());
Assert.Equal(7D, order3.Plus(3D, 4D));
Assert.Equal(1.5D, order3.Minus(5D, 3.5D));
Assert.Equal(12D, order3.Mult(3D, 4D));
Assert.Equal(2D, order3.Divide(6D, 3D));
Assert.Equal(-3D, order3.Negate(3D));
Assert.Equal(1 / 3D, order3.Reciprocal(3D));
Assert.Equal(2D, new double[] { 1, 2, 3 }.Average <double, Field.DoubleField, Group.DoubleAddGroup, Group.DoubleMultGroup>(order3));
Assert.Equal(2D, new (double, double)[] { (1, 1), (2, 1), (3, 1) }.WeightedAverage <double, Field.DoubleField, Group.DoubleAddGroup, Group.DoubleMultGroup>(order3));