## Documentation ¶

### Overview ¶

Package dualcmplx provides the anti-commutative dual complex numeric type and functions.

See https://arxiv.org/abs/1601.01754v1 for details.

Example
```Output:

square:
0 {x:0 y:0} -> {x:-4 y:3}
1 {x:0 y:1} -> {x:-5 y:3}
2 {x:1 y:0} -> {x:-4 y:4}
3 {x:1 y:1} -> {x:-5 y:4}

line segment:
0 {x:2 y:2} -> {x:2 y:2}
1 {x:2 y:3} -> {x:1 y:2}
```
Example (Displace)
```Output:

(7+7i)
```
Example (DisplaceAndRotate)
```Output:

(-7+7i)
```
Example (Rotate)
```Output:

(-4+3i)
```
Example (RotateAndDisplace)
```Output:

(0+6i)
```

### Constants ¶

This section is empty.

### Variables ¶

This section is empty.

### Functions ¶

#### func Abs ¶

`func Abs(d Number) float64`

Abs returns the absolute value of d.

### Types ¶

#### type Number ¶

```type Number struct {
Real, Dual complex128
}```

Number is a float64 precision anti-commutative dual complex number.

`func Add(x, y Number) Number`

Add returns the sum of x and y.

#### func Conj ¶

`func Conj(d Number) Number`

Conj returns the conjugate of d₁+d₂ϵ, d̅₁+d₂ϵ.

#### func Exp ¶

`func Exp(d Number) Number`

Exp returns e**q, the base-e exponential of d.

Special cases are:

```Exp(+Inf) = +Inf
Exp(NaN) = NaN
```

Very large values overflow to 0 or +Inf. Very small values underflow to 1.

#### func Inv ¶

`func Inv(d Number) Number`

Inv returns the dual inverse of d.

#### func Log ¶

`func Log(d Number) Number`

Log returns the natural logarithm of d.

Special cases are:

```Log(+Inf) = (+Inf+0ϵ)
Log(0) = (-Inf±Infϵ)
Log(x < 0) = NaN
Log(NaN) = NaN
```

#### func Mul ¶

`func Mul(x, y Number) Number`

Mul returns the dual product of x and y, x×y.

#### func Pow ¶

`func Pow(d, p Number) Number`

Pow returns d**p, the base-d exponential of p.

#### func PowReal ¶

`func PowReal(d Number, p float64) Number`

PowReal returns d**p, the base-d exponential of p.

Special cases are (in order):

```PowReal(NaN+xϵ, ±0) = 1+NaNϵ for any x
Pow(0+xϵ, y) = 0+Infϵ for all y < 1.
Pow(0+xϵ, y) = 0 for all y > 1.
PowReal(x, ±0) = 1 for any x
PowReal(1+xϵ, y) = 1+xyϵ for any y
Pow(Inf, y) = +Inf+NaNϵ for y > 0
Pow(Inf, y) = +0+NaNϵ for y < 0
PowReal(x, 1) = x for any x
PowReal(NaN+xϵ, y) = NaN+NaNϵ
PowReal(x, NaN) = NaN+NaNϵ
PowReal(-1, ±Inf) = 1
PowReal(x+0ϵ, +Inf) = +Inf+NaNϵ for |x| > 1
PowReal(x+yϵ, +Inf) = +Inf for |x| > 1
PowReal(x, -Inf) = +0+NaNϵ for |x| > 1
PowReal(x, +Inf) = +0+NaNϵ for |x| < 1
PowReal(x+0ϵ, -Inf) = +Inf+NaNϵ for |x| < 1
PowReal(x, -Inf) = +Inf-Infϵ for |x| < 1
PowReal(+Inf, y) = +Inf for y > 0
PowReal(+Inf, y) = +0 for y < 0
PowReal(-Inf, y) = Pow(-0, -y)
```

#### func Scale ¶

`func Scale(f float64, d Number) Number`

Scale returns d scaled by f.

#### func Sqrt ¶

`func Sqrt(d Number) Number`

Sqrt returns the square root of d.

Special cases are:

```Sqrt(+Inf) = +Inf
Sqrt(±0) = (±0+Infϵ)
Sqrt(x < 0) = NaN
Sqrt(NaN) = NaN
```

#### func Sub ¶

`func Sub(x, y Number) Number`

Sub returns the difference of x and y, x-y.

#### func (Number) Format ¶

`func (d Number) Format(fs fmt.State, c rune)`

Format implements fmt.Formatter.