Bivector{V,T} <: TensorGraded{V,2,T}

Graded bivector elements of a Manifold instance V with scalar field T.

GradedVector{V,T} <: TensorGraded{V,1,T}

Graded vector elements of a Manifold instance V with scalar field T.

Manifold{V,T} <: TensorAlgebra{V,T}

Basis parametrization locally homeomorphic to T^n product topology.

Scalar{V,T} <: TensorGraded{V,0,T}

Graded scalar elements of a Manifold instance V with scalar field T.

TensorAlgebra{V,T} <: Number

Universal root tensor type with Manifold instance V with scalar field T.

TensorGraded{V,G,T} <: Manifold{V,T} <: TensorAlgebra

Grade G elements of a Manifold instance V with scalar field T.

TensorMixed{V,T} <: TensorAlgebra{V,T}

Elements of Manifold instance V having non-homogenous grade with scalar field T.

TensorTerm{V,G,T} <: TensorGraded{V,G,T}

Single coefficient for grade G of a Manifold instance V with scalar field T.

Trivector{V,T} <: TensorGraded{V,3,T}

Graded trivector elements of a Manifold instance V with scalar field T.

antisandwich(x::TensorAlgebra,R::TensorAlgebra)

Defined as complementleft(complementright(R)>>>complementright(x)).

bivector(::TensorAlgebra)

Return the bivector (rank 2) part of any TensorAlgebra element.

gdims(t::TensorGraded{V,G})

Dimensionality of the grade G of V for that TensorAlgebra.

geomabs(t::TensorAlgebra)

Geometric norm defined as geomabs(t) = abs(t) + pseudoabs(t).

mdims(t::TensorAlgebra{V})

Dimensionality of the pseudoscalar V of that TensorAlgebra.

pseudoabs(t::TensorAlgebra)

Complemented abs defined as complementleft(abs(complementright(t))).

pseudoabs2(t::TensorAlgebra)

Complemented abs2 defined as complementleft(abs2(complementright(t))).

pseudocbrt(t::TensorAlgebra)

Complemented cbrt defined as complementleft(cbrt(complementright(t))).

pseudocos(t::TensorAlgebra)

Complemented cos defined as complementleft(cos(complementright(t))).

pseudocosh(t::TensorAlgebra)

Complemented cosh defined as complementleft(cosh(complementright(t))).

pseudoexp(t::TensorAlgebra)

Complemented exp defined as complementleft(exp(complementright(t))).

pseudoinv(t::TensorAlgebra)

Complemented inv defined as complementleft(inv(complementright(t))).

pseudolog(t::TensorAlgebra)

Complemented log defined as complementleft(log(complementright(t))).

pseudosandwich(x::TensorAlgebra,R::TensorAlgebra)

Defined as complementleft(sandwich(complementright(x),complementright(R))).

pseudoscalar(::TensorAlgebra), volume(::TensorAlgebra)

Return the pseudoscalar (full rank) part of any TensorAlgebra element.

pseudosin(t::TensorAlgebra)

Complemented sin defined as complementleft(sin(complementright(t))).

pseudosinh(t::TensorAlgebra)

Complemented sinh defined as complementleft(sinh(complementright(t))).

pseudosqrt(t::TensorAlgebra)

Complemented sqrt defined as complementleft(sqrt(complementright(t))).

pseudotan(t::TensorAlgebra)

Complemented tan defined as complementleft(tan(complementright(t))).

pseudotanh(t::TensorAlgebra)

Complemented tanh defined as complementleft(tanh(complementright(t))).

scalar(::TensorAlgebra)

Return the scalar (rank 0) part of any TensorAlgebra element.

tdims(t::TensorAlgebra{V})

Dimensionality of the superalgebra of V for that TensorAlgebra.

trivector(::TensorAlgebra)

Return the trivector (rank 3) part of any TensorAlgebra element.

unit(t::Number)

Normalization defined as unit(t) = t/abs(t).

unitize(t::TensorAlgebra)

Pseudo-normalization defined as unitize(t) = t/value(pseudoabs(t)).

unitnorm(t::TensorAlgebra)

Geometric normalization defined as unitnorm(t) = t/norm(geomabs(t)).

value(::TensorAlgebra)

Returns the internal Values representation of a TensorAlgebra element.

valuetype(t::TensorAlgebra{V,T}) where {V,T} = T

Returns type of a TensorAlgebra element value's internal representation.

vector(::TensorAlgebra)

Return the vector (rank 1) part of any TensorAlgebra element.

rank(::Manifold{n})

Dimensionality n of the Manifold subspace representation.

@pseudo fun(args...)

Use the macro @pseudo to make a pseudoscalar complement variant of any functions:

julia> @pseudo myfun(x)
pseudomyfun (generic function with 1 method)

Now pseudomyfun(x) = complementleft(myfun(complementright(x))) is defined.

julia> @pseudo myproduct(a,b)
pseudomyproduct (generic function with 1 method)

Now pseudomyproduct(a,b) = complementleft(myproduct(!a,!b)) is defined.