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cl3test.lpr
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cl3test.lpr
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program cl3test;
{$mode objfpc}{$h+}
uses
Cl3, DateUtils, Math, SysUtils;
var
k : longint;
a : double;
v, v1, v2, v3 : TVector;
B, B1, B2, B3 : TBivector;
I, I1, I2, I3 : TTrivector;
M, M1, M2, M3 : TMultivector;
StartTime : TDateTime;
function Rnd: double;
var
i: longint;
begin
i := RandomRange(-MaxSmallint, MaxSmallint);
while (i = 0) do
begin
i := RandomRange(-MaxSmallint, MaxSmallint);
end;
result := i;
end;
begin
StartTime := Now;
Randomize;
Writeln('CL3 TEST: begin');
for k := 0 to 1000000 do
begin
a := Rnd;
v := Rnd*e1 + Rnd*e2 + Rnd*e3;
B := Rnd*e12 + Rnd*e13 + Rnd*e23;
I := Rnd*e123;
M := a + v + B + I;
// TTrivector
M := I.ToMultivector;
if I.Dot (I) <> M.Dot (M) then Writeln('TEST-101: NOT PASSED');
if I.Dot (M) <> M.Dot (I) then Writeln('TEST-102: NOT PASSED');
if I.Wedge (I) <> M.Wedge (M) then Writeln('TEST-103: NOT PASSED');
if I.Wedge (M) <> M.Wedge (I) then Writeln('TEST-104: NOT PASSED');
if (I*M) <> (M*I) then Writeln('TEST-105: NOT PASSED');
if (I*I) <> (M*M) then Writeln('TEST-106: NOT PASSED');
if I.Reciprocal <> M.Reciprocal then Writeln('TEST-107: NOT PASSED');
if I.Conjugate <> M.Conjugate then Writeln('TEST-108: NOT PASSED');
if I.Inverse <> M.Inverse then Writeln('TEST-109: NOT PASSED');
if I.Dual <> M.Dual then Writeln('TEST-110: NOT PASSED');
if I.Norm <> M.ExtractTrivector.Norm then Writeln('TEST-111: NOT PASSED');
if I.SquaredNorm <> M.SquaredNorm then Writeln('TEST-112: NOT PASSED');
if I.Reverse <> M.Reverse then Writeln('TEST-113: NOT PASSED');
if not SameValue(I/I, 1) then Writeln('TEST-114: NOT PASSED');
if (I.Projection(u1 ) <> M.Projection(u1 .ToMultivector)) then Writeln('TEST-114: NOT PASSED');
if (I.Projection(u2 ) <> M.Projection(u2 .ToMultivector)) then Writeln('TEST-115: NOT PASSED');
if (I.Projection(u3 ) <> M.Projection(u3 .ToMultivector)) then Writeln('TEST-116: NOT PASSED');
if (I.Projection(u12 ) <> M.Projection(u12 .ToMultivector)) then Writeln('TEST-117: NOT PASSED');
if (I.Projection(u13 ) <> M.Projection(u13 .ToMultivector)) then Writeln('TEST-119: NOT PASSED');
if (I.Projection(u23 ) <> M.Projection(u23 .ToMultivector)) then Writeln('TEST-118: NOT PASSED');
if (I.Projection(u123) <> M.Projection(u123.ToMultivector)) then Writeln('TEST-120: NOT PASSED');
if (I.Rejection (u1 ) <> M.Rejection (u1 .ToMultivector)) then Writeln('TEST-121: NOT PASSED');
if (I.Rejection (u2 ) <> M.Rejection (u2 .ToMultivector)) then Writeln('TEST-122: NOT PASSED');
if (I.Rejection (u3 ) <> M.Rejection (u3 .ToMultivector)) then Writeln('TEST-123: NOT PASSED');
if (I.Rejection (u12 ) <> M.Rejection (u12 .ToMultivector)) then Writeln('TEST-124: NOT PASSED');
if (I.Rejection (u13 ) <> M.Rejection (u13 .ToMultivector)) then Writeln('TEST-126: NOT PASSED');
if (I.Rejection (u23 ) <> M.Rejection (u23 .ToMultivector)) then Writeln('TEST-125: NOT PASSED');
if (I.Rejection (u123) <> M.Rejection (u123.ToMultivector)) then Writeln('TEST-127: NOT PASSED');
if (I.Reflection(u1 ) <> M.Reflection(u1 .ToMultivector)) then Writeln('TEST-128: NOT PASSED');
if (I.Reflection(u2 ) <> M.Reflection(u2 .ToMultivector)) then Writeln('TEST-129: NOT PASSED');
if (I.Reflection(u3 ) <> M.Reflection(u3 .ToMultivector)) then Writeln('TEST-130: NOT PASSED');
if (I.Reflection(u12) <> M.Reflection(u12.ToMultivector)) then Writeln('TEST-131: NOT PASSED');
if (I.Reflection(u13) <> M.Reflection(u13.ToMultivector)) then Writeln('TEST-133: NOT PASSED');
if (I.Reflection(u23) <> M.Reflection(u23.ToMultivector)) then Writeln('TEST-132: NOT PASSED');
if (I.Rotation(u1 , u2 ) <> M.Rotation(u1 .ToMultivector, u2 .ToMultivector)) then Writeln('TEST-134: NOT PASSED');
if (I.Rotation(u2 , u3 ) <> M.Rotation(u2 .ToMultivector, u3 .ToMultivector)) then Writeln('TEST-135: NOT PASSED');
if (I.Rotation(u3 , u1 ) <> M.Rotation(u3 .ToMultivector, u1 .ToMultivector)) then Writeln('TEST-136: NOT PASSED');
if (I.Rotation(u12, u13) <> M.Rotation(u12.ToMultivector, u13.ToMultivector)) then Writeln('TEST-137: NOT PASSED');
if (I.Rotation(u13, u23) <> M.Rotation(u13.ToMultivector, u23.ToMultivector)) then Writeln('TEST-139: NOT PASSED');
if (I.Rotation(u23, u12) <> M.Rotation(u23.ToMultivector, u12.ToMultivector)) then Writeln('TEST-138: NOT PASSED');
// TBivector
M := B.ToMultivector;
if B.Dot (B) <> M.Dot (M) then Writeln('TEST-201: NOT PASSED');
if B.Dot (M) <> M.Dot (B) then Writeln('TEST-202: NOT PASSED');
if B.Wedge (B) <> M.Wedge (M) then Writeln('TEST-203: NOT PASSED');
if B.Wedge (M) <> M.Wedge (B) then Writeln('TEST-204: NOT PASSED');
if (B*M) <> (M*B) then Writeln('TEST-205: NOT PASSED');
if (B*B) <> (M*M) then Writeln('TEST-206: NOT PASSED');
if B.Reciprocal <> M.Reciprocal then Writeln('TEST-208: NOT PASSED');
if B.Conjugate <> M.Conjugate then Writeln('TEST-209: NOT PASSED');
if B.Inverse <> M.Inverse then Writeln('TEST-210: NOT PASSED');
if B.Dual <> M.Dual then Writeln('TEST-211: NOT PASSED');
if B.Norm <> M.ExtractBivector.Norm then Writeln('TEST-212: NOT PASSED');
if B.SquaredNorm <> M.SquaredNorm then Writeln('TEST-213: NOT PASSED');
if B.Reverse <> M.Reverse then Writeln('TEST-214: NOT PASSED');
if not (B/B).SameValue(1) then Writeln('TEST-215: NOT PASSED');
if (B.Projection(u1 ) <> M.Projection(u1 .ToMultivector)) then Writeln('TEST-215: NOT PASSED');
if (B.Projection(u2 ) <> M.Projection(u2 .ToMultivector)) then Writeln('TEST-216: NOT PASSED');
if (B.Projection(u3 ) <> M.Projection(u3 .ToMultivector)) then Writeln('TEST-217: NOT PASSED');
if (B.Projection(u12 ) <> M.Projection(u12 .ToMultivector)) then Writeln('TEST-218: NOT PASSED');
if (B.Projection(u13 ) <> M.Projection(u13 .ToMultivector)) then Writeln('TEST-219: NOT PASSED');
if (B.Projection(u23 ) <> M.Projection(u23 .ToMultivector)) then Writeln('TEST-220: NOT PASSED');
if (B.Projection(u123) <> M.Projection(u123.ToMultivector)) then Writeln('TEST-221: NOT PASSED');
if (B.Rejection (u1 ) <> M.Rejection (u1 .ToMultivector)) then Writeln('TEST-222: NOT PASSED');
if (B.Rejection (u2 ) <> M.Rejection (u2 .ToMultivector)) then Writeln('TEST-223: NOT PASSED');
if (B.Rejection (u3 ) <> M.Rejection (u3 .ToMultivector)) then Writeln('TEST-224: NOT PASSED');
if (B.Rejection (u12 ) <> M.Rejection (u12 .ToMultivector)) then Writeln('TEST-225: NOT PASSED');
if (B.Rejection (u13 ) <> M.Rejection (u13 .ToMultivector)) then Writeln('TEST-226: NOT PASSED');
if (B.Rejection (u23) <> M.Rejection (u23 .ToMultivector)) then Writeln('TEST-227: NOT PASSED');
if (B.Rejection (u123) <> M.Rejection (u123.ToMultivector)) then Writeln('TEST-228: NOT PASSED');
if (B.Reflection(u1 ) <> M.Reflection(u1 .ToMultivector)) then Writeln('TEST-229: NOT PASSED');
if (B.Reflection(u2 ) <> M.Reflection(u2 .ToMultivector)) then Writeln('TEST-230: NOT PASSED');
if (B.Reflection(u3 ) <> M.Reflection(u3 .ToMultivector)) then Writeln('TEST-231: NOT PASSED');
if (B.Reflection(u12 ) <> M.Reflection(u12 .ToMultivector)) then Writeln('TEST-232: NOT PASSED');
if (B.Reflection(u13 ) <> M.Reflection(u13 .ToMultivector)) then Writeln('TEST-233: NOT PASSED');
if (B.Reflection(u23 ) <> M.Reflection(u23 .ToMultivector)) then Writeln('TEST-234: NOT PASSED');
if (B.Reflection(u123) <> M.Reflection(u123.ToMultivector)) then Writeln('TEST-235: NOT PASSED');
if (B.Rotation(u1 , u2 ) <> M.Rotation(u1 .ToMultivector, u2 .ToMultivector)) then Writeln('TEST-236: NOT PASSED');
if (B.Rotation(u2 , u3 ) <> M.Rotation(u2 .ToMultivector, u3 .ToMultivector)) then Writeln('TEST-237: NOT PASSED');
if (B.Rotation(u3 , u1 ) <> M.Rotation(u3 .ToMultivector, u1 .ToMultivector)) then Writeln('TEST-238: NOT PASSED');
if (B.Rotation(u12, u13) <> M.Rotation(u12.ToMultivector, u13.ToMultivector)) then Writeln('TEST-239: NOT PASSED');
if (B.Rotation(u13, u23) <> M.Rotation(u13.ToMultivector, u23.ToMultivector)) then Writeln('TEST-240: NOT PASSED');
if (B.Rotation(u23, u12) <> M.Rotation(u23.ToMultivector, u12.ToMultivector)) then Writeln('TEST-241: NOT PASSED');
// TVector
M := v.ToMultivector;
if v.Dot (v) <> M.Dot (M) then Writeln('TEST-301: NOT PASSED');
if v.Dot (M) <> M.Dot (v) then Writeln('TEST-302: NOT PASSED');
if v.Wedge (v) <> M.Wedge (M) then Writeln('TEST-303: NOT PASSED');
if v.Wedge (M) <> M.Wedge (v) then Writeln('TEST-304: NOT PASSED');
if (v*M) <> (M*v) then Writeln('TEST-305: NOT PASSED');
if (v*v) <> (M*M) then Writeln('TEST-306: NOT PASSED');
if v.Reciprocal <> M.Reciprocal then Writeln('TEST-307: NOT PASSED');
if v.Conjugate <> M.Conjugate then Writeln('TEST-308: NOT PASSED');
if v.Inverse <> M.Inverse then Writeln('TEST-309: NOT PASSED');
if v.Dual <> M.Dual then Writeln('TEST-310: NOT PASSED');
if v.Norm <> M.ExtractVector.Norm then Writeln('TEST-311: NOT PASSED');
if v.SquaredNorm <> M.SquaredNorm then Writeln('TEST-312: NOT PASSED');
if v.Reverse <> M.Reverse then Writeln('TEST-313: NOT PASSED');
if not (v/v).SameValue(1) then Writeln('TEST-314: NOT PASSED');
if (v.Projection(u1 ) <> M.Projection(u1 .ToMultivector)) then Writeln('TEST-314: NOT PASSED');
if (v.Projection(u2 ) <> M.Projection(u2 .ToMultivector)) then Writeln('TEST-315: NOT PASSED');
if (v.Projection(u3 ) <> M.Projection(u3 .ToMultivector)) then Writeln('TEST-316: NOT PASSED');
if (v.Projection(u12 ) <> M.Projection(u12 .ToMultivector)) then Writeln('TEST-317: NOT PASSED');
if (v.Projection(u13 ) <> M.Projection(u13 .ToMultivector)) then Writeln('TEST-318: NOT PASSED');
if (v.Projection(u23 ) <> M.Projection(u23 .ToMultivector)) then Writeln('TEST-319: NOT PASSED');
if (v.Projection(u123) <> M.Projection(u123.ToMultivector)) then Writeln('TEST-320: NOT PASSED');
if (v.Rejection (u1 ) <> M.Rejection (u1 .ToMultivector)) then Writeln('TEST-321: NOT PASSED');
if (v.Rejection (u2 ) <> M.Rejection (u2 .ToMultivector)) then Writeln('TEST-322: NOT PASSED');
if (v.Rejection (u3 ) <> M.Rejection (u3 .ToMultivector)) then Writeln('TEST-323: NOT PASSED');
if (v.Rejection (u12 ) <> M.Rejection (u12 .ToMultivector)) then Writeln('TEST-324: NOT PASSED');
if (v.Rejection (u13 ) <> M.Rejection (u13 .ToMultivector)) then Writeln('TEST-325: NOT PASSED');
if (v.Rejection (u23 ) <> M.Rejection (u23 .ToMultivector)) then Writeln('TEST-326: NOT PASSED');
if (v.Rejection (u123) <> M.Rejection (u123.ToMultivector)) then Writeln('TEST-327: NOT PASSED');
if (v.Reflection(u1 ) <> M.Reflection(u1 .ToMultivector)) then Writeln('TEST-328: NOT PASSED');
if (v.Reflection(u2 ) <> M.Reflection(u2 .ToMultivector)) then Writeln('TEST-329: NOT PASSED');
if (v.Reflection(u3 ) <> M.Reflection(u3 .ToMultivector)) then Writeln('TEST-330: NOT PASSED');
if (v.Reflection(u12 ) <> M.Reflection(u12 .ToMultivector)) then Writeln('TEST-331: NOT PASSED');
if (v.Reflection(u13 ) <> M.Reflection(u13 .ToMultivector)) then Writeln('TEST-332: NOT PASSED');
if (v.Reflection(u23 ) <> M.Reflection(u23 .ToMultivector)) then Writeln('TEST-333: NOT PASSED');
if (v.Reflection(u123) <> M.Reflection(u123.ToMultivector)) then Writeln('TEST-334: NOT PASSED');
if (v.Rotation(u1 , u2 ) <> M.Rotation(u1 .ToMultivector, u2 .ToMultivector)) then Writeln('TEST-335: NOT PASSED');
if (v.Rotation(u2 , u3 ) <> M.Rotation(u2 .ToMultivector, u3 .ToMultivector)) then Writeln('TEST-336: NOT PASSED');
if (v.Rotation(u3 , u1 ) <> M.Rotation(u3 .ToMultivector, u1 .ToMultivector)) then Writeln('TEST-337: NOT PASSED');
if (v.Rotation(u12, u13) <> M.Rotation(u12.ToMultivector, u13.ToMultivector)) then Writeln('TEST-338: NOT PASSED');
if (v.Rotation(u13, u23) <> M.Rotation(u13.ToMultivector, u23.ToMultivector)) then Writeln('TEST-339: NOT PASSED');
if (v.Rotation(u23, u12) <> M.Rotation(u23.ToMultivector, u12.ToMultivector)) then Writeln('TEST-340: NOT PASSED');
end;
Writeln('CL3 TEST: end.');
v1 := Rnd*e1 + Rnd*e2 + Rnd*e3;
v2 := Rnd*e1 + Rnd*e2 + Rnd*e3;
v3 := Rnd*e1 + Rnd*e2 + Rnd*e3;
B1 := Rnd*e12 + Rnd*e13 + Rnd*e23;
B2 := Rnd*e12 + Rnd*e13 + Rnd*e23;
B3 := Rnd*e12 + Rnd*e13 + Rnd*e23;
I1 := Rnd*e123;
I2 := Rnd*e123;
I3 := Rnd*e123;
M1 := Rnd + Rnd*e1 + Rnd*e2 + Rnd*e3 + Rnd*e12 + Rnd*e13 + Rnd*e23 + Rnd*e123;
M2 := Rnd + Rnd*e1 + Rnd*e2 + Rnd*e3 + Rnd*e12 + Rnd*e13 + Rnd*e23 + Rnd*e123;
M3 := Rnd + Rnd*e1 + Rnd*e2 + Rnd*e3 + Rnd*e12 + Rnd*e13 + Rnd*e23 + Rnd*e123;
writeln;
Writeln(Format('v1 = %s (Norm = %s)', [v1.ToString, v1.Norm.ToString]));
Writeln(Format('v2 = %s (Norm = %s)', [v2.ToString, v2.Norm.ToString]));
Writeln(Format('v3 = %s (Norm = %s)', [v3.ToString, v3.Norm.ToString]));
Writeln(Format('v1/v1 = %s', [(v1/v1).ToString]));
Writeln(Format('v2/v2 = %s', [(v2/v2).ToString]));
Writeln(Format('v3/v3 = %s', [(v3/v3).ToString]));
Writeln(Format('B1 = %s (Norm = %s)', [B1.ToString, B1.Norm.ToString]));
Writeln(Format('B2 = %s (Norm = %s)', [B2.ToString, B2.Norm.ToString]));
Writeln(Format('B3 = %s (Norm = %s)', [B3.ToString, B3.Norm.ToString]));
Writeln(Format('B1/B1 = %s', [(B1/B1).ToString]));
Writeln(Format('B2/B2 = %s', [(B2/B2).ToString]));
Writeln(Format('B3/B3 = %s', [(B3/B3).ToString]));
Writeln(Format('I1 = %s (Norm = %s)', [I1.ToString, I1.Norm.ToString]));
Writeln(Format('I2 = %s (Norm = %s)', [I2.ToString, I2.Norm.ToString]));
Writeln(Format('I3 = %s (Norm = %s)', [I3.ToString, I2.Norm.ToString]));
Writeln(Format('I1/I1 = %s', [(I1/I1).ToString]));
Writeln(Format('I2/I2 = %s', [(I2/I2).ToString]));
Writeln(Format('I3/I3 = %s', [(I3/I3).ToString]));
Writeln(Format('M1 = %s (Norm = %s)', [M1.ToString, M1.Norm.ToString]));
Writeln(Format('M2 = %s (Norm = %s)', [M2.ToString, M2.Norm.ToString]));
Writeln(Format('M3 = %s (Norm = %s)', [M3.ToString, M3.Norm.ToString]));
Writeln(Format('M1/M1 = %s', [(M1/M1).ToString]));
Writeln(Format('M2/M2 = %s', [(M2/M2).ToString]));
Writeln(Format('M3/M3 = %s', [(M3/M3).ToString]));
Writeln(Format(' 1/M3 = (%s)', [(M3.Reciprocal ).ToString]));
Writeln(Format(' 1/M3 = (%s)', [(M3.Reverse/M3.SquaredNorm).ToString]));
Writeln(Format('M.Normalized = %s', [(M3.Normalized ).ToString]));
Writeln(Format('M.Normalized.Norm = %s', [(M3.Normalized.Norm).ToString]));
writeln;
writeln('TVECTOR');
writeln('Dot : vector & vector : ', v1.ToMultivector.Dot(v2.ToMultivector).IsA);
writeln('Dot : vector & bivector : ', v1.ToMultivector.Dot(B2.ToMultivector).IsA);
writeln('Dot : vector & trivector : ', v1.ToMultivector.Dot(I2.ToMultivector).IsA);
writeln('Dot : vector & multivector : ', v1.ToMultivector.Dot(M2 ).IsA);
writeln;
writeln('Wedge : vector & vector : ', v1.ToMultivector.Wedge(v2.ToMultivector).IsA);
writeln('Wedge : vector & bivector : ', v1.ToMultivector.Wedge(B2.ToMultivector).IsA);
writeln('Wedge : vector & trivector : ', v1.ToMultivector.Wedge(I2.ToMultivector).IsA);
writeln('Wedge : vector & multivector : ', v1.ToMultivector.Wedge(M2 ).IsA);
writeln;
writeln('Geometric : vector & vector : ', (v1.ToMultivector*v2.ToMultivector).IsA);
writeln('Geometric : vector & bivector : ', (v1.ToMultivector*B2.ToMultivector).IsA);
writeln('Geometric : vector & trivector : ', (v1.ToMultivector*I2.ToMultivector).IsA);
writeln('Geometric : vector & multivector : ', (v1.ToMultivector*M2 ).IsA);
writeln;
writeln('Projection: vector & vector : ', v1.ToMultivector.Projection(v2.ToMultivector).IsA);
writeln('Projection: vector & bivector : ', v1.ToMultivector.Projection(B2.ToMultivector).IsA);
writeln('Projection: vector & trivector : ', v1.ToMultivector.Projection(I2.ToMultivector).IsA);
writeln('Projection: vector & multivector : ', v1.ToMultivector.Projection(M2 ).IsA);
writeln;
writeln('Rejection : vector & vector : ', v1.ToMultivector.Rejection(v2.ToMultivector).IsA);
writeln('Rejection : vector & bivector : ', v1.ToMultivector.Rejection(B2.ToMultivector).IsA);
writeln('Rejection : vector & trivector : ', v1.ToMultivector.Rejection(I2.ToMultivector).IsA);
writeln('Rejection : vector & multivector : ', v1.ToMultivector.Rejection(M2 ).IsA);
writeln;
writeln('Reflection: vector & vector : ', v1.ToMultivector.Reflection(v2.ToMultivector).IsA);
writeln('Reflection: vector & bivector : ', v1.ToMultivector.Reflection(B2.ToMultivector).IsA);
writeln('Reflection: vector & trivector : ', v1.ToMultivector.Reflection(I2.ToMultivector).IsA);
writeln('Reflection: vector & multivector : ', v1.ToMultivector.Reflection(M2 ).IsA);
writeln;
writeln('Rotation : vector & vectors : ', v1.ToMultivector.Rotation(v2.ToMultivector, v3.ToMultivector).IsA);
writeln('Rotation : vector & bivectors : ', v1.ToMultivector.Rotation(B2.ToMultivector, B3.ToMultivector).IsA);
writeln('Rotation : vector & trivectors : ', v1.ToMultivector.Rotation(I2.ToMultivector, I3.ToMultivector).IsA);
writeln('Rotation : vector & multivectors : ', v1.ToMultivector.Rotation(M2 , M3).IsA);
writeln;
writeln('TBIVECTOR');
writeln('Dot : bivector & vector : ', B1.ToMultivector.Dot(v2.ToMultivector).IsA);
writeln('Dot : bivector & bivector : ', B1.ToMultivector.Dot(B2.ToMultivector).IsA);
writeln('Dot : bivector & trivector : ', B1.ToMultivector.Dot(I2.ToMultivector).IsA);
writeln('Dot : bivector & multivector : ', B1.ToMultivector.Dot(M2 ).IsA);
writeln;
writeln('Wedge : bivector & vector : ', B1.ToMultivector.Wedge(v2.ToMultivector).IsA);
writeln('Wedge : bivector & bivector : ', B1.ToMultivector.Wedge(B2.ToMultivector).IsA);
writeln('Wedge : bivector & trivector : ', B1.ToMultivector.Wedge(I2.ToMultivector).IsA);
writeln('Wedge : bivector & multivector : ', B1.ToMultivector.Wedge(M2 ).IsA);
writeln;
writeln('Geometric : bivector & vector : ', (B1.ToMultivector*v2.ToMultivector).IsA);
writeln('Geometric : bivector & bivector : ', (B1.ToMultivector*B2.ToMultivector).IsA);
writeln('Geometric : bivector & trivector : ', (B1.ToMultivector*I2.ToMultivector).IsA);
writeln('Geometric : bivector & multivector : ', (B1.ToMultivector*M2 ).IsA);
writeln;
writeln('Projection: bivector & vector : ', B1.ToMultivector.Projection(v2.ToMultivector).IsA);
writeln('Projection: bivector & bivector : ', B1.ToMultivector.Projection(B2.ToMultivector).IsA);
writeln('Projection: bivector & trivector : ', B1.ToMultivector.Projection(I2.ToMultivector).IsA);
writeln('Projection: bivector & multivector : ', B1.ToMultivector.Projection(M2 ).IsA);
writeln;
writeln('Rejection : bivector & vector : ', B1.ToMultivector.Rejection(v2.ToMultivector).IsA);
writeln('Rejection : bivector & bivector : ', B1.ToMultivector.Rejection(B2.ToMultivector).IsA);
writeln('Rejection : bivector & trivector : ', B1.ToMultivector.Rejection(I2.ToMultivector).IsA);
writeln('Rejection : bivector & multivector : ', B1.ToMultivector.Rejection(M2 ).IsA);
writeln;
writeln('Reflection: bivector & vector : ', B1.ToMultivector.Reflection(v2.ToMultivector).IsA);
writeln('Reflection: bivector & bivector : ', B1.ToMultivector.Reflection(B2.ToMultivector).IsA);
writeln('Reflection: bivector & trivector : ', B1.ToMultivector.Reflection(I2.ToMultivector).IsA);
writeln('Reflection: bivector & multivector : ', B1.ToMultivector.Reflection(M2 ).IsA);
writeln;
writeln('Rotation : bivector & vectors : ', B1.ToMultivector.Rotation(v2.ToMultivector, v3.ToMultivector).IsA);
writeln('Rotation : bivector & bivectors : ', B1.ToMultivector.Rotation(B2.ToMultivector, B3.ToMultivector).IsA);
writeln('Rotation : bivector & trivectors : ', B1.ToMultivector.Rotation(I2.ToMultivector, I3.ToMultivector).IsA);
writeln('Rotation : bivector & multivectors : ', B1.ToMultivector.Rotation(M2 , M3).IsA);
writeln;
writeln('TTRIVECTOR');
writeln('Dot : trivector & vector : ', I1.ToMultivector.Dot(v2.ToMultivector).IsA);
writeln('Dot : trivector & bivector : ', I1.ToMultivector.Dot(B2.ToMultivector).IsA);
writeln('Dot : trivector & trivector : ', I1.ToMultivector.Dot(I2.ToMultivector).IsA);
writeln('Dot : trivector & multivector : ', I1.ToMultivector.Dot(M2 ).IsA);
writeln;
writeln('Wedge : trivector & vector : ', I1.ToMultivector.Wedge(v2.ToMultivector).IsA);
writeln('Wedge : trivector & bivector : ', I1.ToMultivector.Wedge(B2.ToMultivector).IsA);
writeln('Wedge : trivector & trivector : ', I1.ToMultivector.Wedge(I2.ToMultivector).IsA);
writeln('Wedge : trivector & multivector : ', I1.ToMultivector.Wedge(M2 ).IsA);
writeln;
writeln('Geometric : trivector & vector : ', (I1.ToMultivector*v2.ToMultivector).IsA);
writeln('Geometric : trivector & bivector : ', (I1.ToMultivector*B2.ToMultivector).IsA);
writeln('Geometric : trivector & trivector : ', (I1.ToMultivector*I2.ToMultivector).IsA);
writeln('Geometric : trivector & multivector : ', (I1.ToMultivector*M2 ).IsA);
writeln;
writeln('Projection: trivector & vector : ', I1.ToMultivector.Projection(v2.ToMultivector).IsA);
writeln('Projection: trivector & bivector : ', I1.ToMultivector.Projection(B2.ToMultivector).IsA);
writeln('Projection: trivector & trivector : ', I1.ToMultivector.Projection(I2.ToMultivector).IsA);
writeln('Projection: trivector & multivector : ', I1.ToMultivector.Projection(M2 ).IsA);
writeln;
writeln('Rejection : trivector & vector : ', I1.ToMultivector.Rejection(v2.ToMultivector).IsA);
writeln('Rejection : trivector & bivector : ', I1.ToMultivector.Rejection(B2.ToMultivector).IsA);
writeln('Rejection : trivector & trivector : ', I1.ToMultivector.Rejection(I2.ToMultivector).IsA);
writeln('Rejection : trivector & multivector : ', I1.ToMultivector.Rejection(M2 ).IsA);
writeln;
writeln('Reflection: trivector & vector : ', I1.ToMultivector.Reflection(v2.ToMultivector).IsA);
writeln('Reflection: trivector & bivector : ', I1.ToMultivector.Reflection(B2.ToMultivector).IsA);
writeln('Reflection: trivector & trivector : ', I1.ToMultivector.Reflection(I2.ToMultivector).IsA);
writeln('Reflection: trivector & multivector : ', I1.ToMultivector.Reflection(M2 ).IsA);
writeln;
writeln('Rotation : trivector & vectors : ', I1.ToMultivector.Rotation(v2.ToMultivector, v3.ToMultivector).IsA);
writeln('Rotation : trivector & bivectors : ', I1.ToMultivector.Rotation(B2.ToMultivector, B3.ToMultivector).IsA);
writeln('Rotation : trivector & trivectors : ', I1.ToMultivector.Rotation(I2.ToMultivector, I3.ToMultivector).IsA);
writeln('Rotation : trivector & multivectors : ', I1.ToMultivector.Rotation(M2 , M3).IsA);
writeln;
writeln('TMULTIVECTOR');
writeln('Dot : multivector & vector : ', M1.Dot(v2.ToMultivector).IsA);
writeln('Dot : multivector & bivector : ', M1.Dot(B2.ToMultivector).IsA);
writeln('Dot : multivector & trivector : ', M1.Dot(I2.ToMultivector).IsA);
writeln('Dot : multivector & multivector : ', M1.Dot(M2 ).IsA);
writeln;
writeln('Wedge : multivector & vector : ', M1.Wedge(v2.ToMultivector).IsA);
writeln('Wedge : multivector & bivector : ', M1.Wedge(B2.ToMultivector).IsA);
writeln('Wedge : multivector & trivector : ', M1.Wedge(I2.ToMultivector).IsA);
writeln('Wedge : multivector & multivector : ', M1.Wedge(M2 ).IsA);
writeln;
writeln('Geometric : multivector & vector : ', (M1*v2.ToMultivector).IsA);
writeln('Geometric : multivector & bivector : ', (M1*B2.ToMultivector).IsA);
writeln('Geometric : multivector & trivector : ', (M1*I2.ToMultivector).IsA);
writeln('Geometric : multivector & multivector : ', (M1*M2 ).IsA);
writeln;
writeln('Projection: multivector & vector : ', M1.Projection(v2.ToMultivector).IsA);
writeln('Projection: multivector & bivector : ', M1.Projection(B2.ToMultivector).IsA);
writeln('Projection: multivector & trivector : ', M1.Projection(I2.ToMultivector).IsA);
writeln('Projection: multivector & multivector : ', M1.Projection(M2 ).IsA);
writeln;
writeln('Rejection : multivector & vector : ', M1.Rejection(v2.ToMultivector).IsA);
writeln('Rejection : multivector & bivector : ', M1.Rejection(B2.ToMultivector).IsA);
writeln('Rejection : multivector & trivector : ', M1.Rejection(I2.ToMultivector).IsA);
writeln('Rejection : multivector & multivector : ', M1.Rejection(M2 ).IsA);
writeln;
writeln('Reflection: multivector & vector : ', M1.Reflection(v2.ToMultivector).IsA);
writeln('Reflection: multivector & bivector : ', M1.Reflection(B2.ToMultivector).IsA);
writeln('Reflection: multivector & trivector : ', M1.Reflection(I2.ToMultivector).IsA);
writeln('Reflection: multivector & multivector : ', M1.Reflection(M2 ).IsA);
writeln;
writeln('Rotation : multivector & vectors : ', M1.Rotation(v2.ToMultivector, v3.ToMultivector).IsA);
writeln('Rotation : multivector & bivectors : ', M1.Rotation(B2.ToMultivector, B3.ToMultivector).IsA);
writeln('Rotation : multivector & trivectors : ', M1.Rotation(I2.ToMultivector, I3.ToMultivector).IsA);
writeln('Rotation : multivector & multivectors : ', M1.Rotation(M2 , M3).IsA);
writeln;
writeln(Format('Time elapsed : %ds', [SecondsBetween(Now, StartTime)]));
end.