Table 1 List of functions implemented for each type of vector.

\({{\textbf {v}}} \cdot {{\textbf {u}}}\)

v.dot()

Dot product

\({{\textbf {v}}} \times {{\textbf {u}}}\)

v.cross(u)

Cross product

\(\sphericalangle ({{\textbf {v}}}, {{\textbf {u}}})\)

v.angle(u)

Angle between two vectors

\(\hat{{{\textbf {v}}}}\)

v.versor()

Versor associated

\(*\)

\(\hat{{{\textbf {v}}}}\)

v.versorDl()

Versor associated (dimensionless)

\(\pm |{{\textbf {v}}}|/|{{\textbf {u}}}| \text { if } {{\textbf {v}}}\parallel {{\textbf {u}}}\)

v.scale(u)

Ratio between parallel vectors

v.rotate(a,ax)

Rotate around z-axis (2D) or an arbitrary axis (3D)

\(*\)

\({{\textbf {v}}} \oplus {{\textbf {u}}}\)

v.directSum(u)

Direct sum

\({{\textbf {v}}} \odot {{\textbf {u}}}\)

v.elementwiseProduct()

Element-wise product

\({{\textbf {v}}} \oslash {{\textbf {u}}}\)

v.elementwiseDivision()

Element-wise division

\(|{{\textbf {v}}}|\)

v.norm()

Euclidean norm

\(|{{\textbf {v}}}|_{1}\)

v.normL1()

\(L_1\) norm

\(|{{\textbf {v}}}|_{p}\)

v.normL(p)

p norm

\(|{{\textbf {v}}}|_{\infty }\)

v.normLInf()

Infinity norm

\(|{{\textbf {v}}}|^2\)

v.normSquared()

Euclidean norm squared

\({{\textbf {v}}} \parallel {{\textbf {u}}}\)

v.isParallel(u)

Are parallel

\({{\textbf {v}}} \perp {{\textbf {u}}}\)

v.isPerpendicular(u)

Are perpendicular

\({{\textbf {v}}} \uparrow \uparrow {{\textbf {u}}}\)

v.isSameDirection(u)

Are parallel and have same directions

\({{\textbf {v}}} \uparrow \downarrow {{\textbf {u}}}\)

v.isOppositeDirection(u)

Are parallel and have opposite directions

\( {{\textbf {v}}} = {{\textbf {u}}}\)

v.isNear(u)

Are the same

\( {{\textbf {v}}} = 0\)

v.isNull()

Is zero

v.isNan()

Has any NaN component

v.isNormal()

Are all components neither infinity, NaN, zero or subnormal

\( {{\textbf {v}}} \ne \pm \infty \)

v.isFinite()

Are all components finite

\( {{\textbf {v}}} = \pm \infty \)

v.isInfinite()

Has any infinite component