Cayley methods
Cayley stores an exact complex value as magnitude and a rational direction coordinate. It is useful for multiplication, division, and integer powers.
Method reference
| Full syntax | Result | Meaning |
|---|---|---|
cayley.Cartesian() |
exact Cartesian value | Convert back to Cartesian form. |
cayley.Cayley() |
Cayley |
Return the receiver unchanged. |
cayley.Conjugate() |
Cayley |
Conjugate by negating the direction. |
cayley.Re() |
exact value | Return the real component. |
cayley.Im() |
exact value | Return the imaginary component. |
cayley.NormSquared() |
exact value | Return the square of the magnitude. |
cayley.Magnitude() |
exact value | Return the magnitude coordinate. |
cayley.Direction() |
exact value | Return the direction coordinate; a negative real may use Infinity. |
cayley.Inverse() |
Cayley |
Return the exact multiplicative inverse. |
cayley.CheckTraits() |
1 \| null |
Validate attached semantic traits. |
Checked examples
c := .Complex.Cayley(3 + 4~{i});
c.Cartesian() ##@ == 3 + 4~{i};
c.Cayley() ##@ == c;
c.Conjugate().Cartesian() ##@ == 3 - 4~{i};
c.Re() ##@ == c.Cartesian().Re();
c.Im() ##@ == c.Cartesian().Im();
c.NormSquared().CheckTraits() ##@ == 1;
c.Magnitude() ##@ == 5;
c.Direction() ##@ == 1/2;
c.Inverse().Magnitude() ##@ == 1/5;
c.CheckTraits() ##@ == 1;Direction is an exact rational parametrization rather than an angle measured by a floating-point transcendental function.