public void Space()
{
var S = new Space(2, 3, 4);
Assert.AreEqual(2, S.PositiveDimension);
Assert.AreEqual(3, S.NegativeDimension);
Assert.AreEqual(4, S.NilpotentDimension);
Assert.AreEqual(9, S.Dimension);
Assert.AreEqual(0b000, S.IndexFromBladeBasis(0, 0));
Assert.AreEqual(0b001, S.IndexFromBladeBasis(1, 0));
Assert.AreEqual(0b010, S.IndexFromBladeBasis(1, 1));
Assert.AreEqual(0b100, S.IndexFromBladeBasis(1, 2));
Assert.AreEqual(0b011, S.IndexFromBladeBasis(2, 0));
Assert.AreEqual(0b101, S.IndexFromBladeBasis(2, 1));
Assert.AreEqual(0b110, S.IndexFromBladeBasis(2, 8));
Assert.AreEqual(0b111, S.IndexFromBladeBasis(3, 0));
Assert.AreEqual(0b111111111, S.IndexFromBladeBasis(9, 0));
Assert.AreEqual((0, 0), S.BladeBasisFromIndex(0b000));
Assert.AreEqual((1, 0), S.BladeBasisFromIndex(0b001));
Assert.AreEqual((1, 1), S.BladeBasisFromIndex(0b010));
Assert.AreEqual((1, 2), S.BladeBasisFromIndex(0b100));
Assert.AreEqual((2, 0), S.BladeBasisFromIndex(0b011));
Assert.AreEqual((2, 1), S.BladeBasisFromIndex(0b101));
Assert.AreEqual((2, 8), S.BladeBasisFromIndex(0b110));
Assert.AreEqual((3, 0), S.BladeBasisFromIndex(0b111));
Assert.AreEqual((9, 0), S.BladeBasisFromIndex(0b111111111));
Assert.AreEqual(new Multivector(S), S.Zero);
Assert.AreEqual(1, S.BasisSquared(0, 0));
Assert.AreEqual(1, S.BasisSquared(1, 0));
Assert.AreEqual(1, S.BasisSquared(1, 1));
Assert.AreEqual(-1, S.BasisSquared(1, 2));
Assert.AreEqual(-1, S.BasisSquared(1, 3));
Assert.AreEqual(-1, S.BasisSquared(1, 4));
Assert.AreEqual(0, S.BasisSquared(1, 5));
Assert.AreEqual(0, S.BasisSquared(1, 6));
Assert.AreEqual(0, S.BasisSquared(1, 7));
Assert.AreEqual(0, S.BasisSquared(1, 8));
Assert.Throws <IndexOutOfRangeException>(() => S.BasisSquared(1, 9), "Base number out of range");
for (uint i = 0; i < 1 << 9; i++)
{
Assert.AreEqual(
(0, S.BasisSquared(i)),
S.BasisMultiply(i, i)
);
}
Assert.AreEqual(1, S.BasisSquared(0b000010111));
Assert.AreEqual(-1, S.BasisSquared(0b000011001));
Assert.AreEqual(-1, S.BasisSquared(0b000001101));
Assert.AreEqual(0, S.BasisSquared(0b110100110));
Assert.AreEqual(0, S.BasisSquared(0b010010001));
Assert.AreEqual((0b011111, 1), S.BasisMultiply(0b001101, 0b010010));
Assert.AreEqual((0b100110, 1), S.BasisMultiply(0b110101, 0b010011));
Assert.AreEqual(0, S.BasisMultiply(0b101110, 0b110101).Sign);
}