Package: stokes 1.2-4

keep() and discard() | References

Further properties of Alt() | Wedge product | Further further properties of Alt() | Argument give_kform | References

Wedge products | $$(\mathrm{d}x\wedge\mathrm{d}y)\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix}\right) | $$(\mathrm{d}x\wedge\mathrm{d}y\wedge\mathrm{d}z)\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix},\begin{pmatrix}w_1\w_2\w_3\end{pmatrix}\right) | The print method | $$(3\mathrm{d}y\wedge\mathrm{d}z)\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix}\right) | $$(1\mathrm{d}x\wedge\mathrm{d}y)\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix}\right) | $$X\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix}\right) | Configuring the print method | The Hodge dual | Creating elementary one-forms | Package dataset | References

Alternating forms | References

The tensor cross product | Verification | Note on associativity | References

R implementation | Verification | Orientation | Immediate properties | Vector products and the Hodge star operator | Vector cross products in 3 dimensions | Vector cross product identities | Edge-cases | References

References

Digression: function spraycross() | Cut to the chase: wedge2() | Algebraic properties | References

Distributivity | Reconstruction of a given tensor | Function Alt() | References

Some simple examples | Tidyup | References

The Hodge dual on basis elements of $\Lambda^k(V)$ | [\bigcup_ | More complicated examples | Small-dimensional vector spaces | Vector cross product identities | Non positive-definite metrics | Print methods for the Minkowski metric | Specifying the Minkowski metric | References

Package dataset | References

Contraction of products | Repeated contraction | Contraction from first principles | Worked example using contract_elementary() | The "meat" of contract() | References

The stokes package | Package idiom for evaluation of a tensor | Vector space structure of tensors | Numerical verification of multilinearity in the package | Tensor product of general tensors | Alternating forms | Wedge products and the exterior calculus | Formal definition of dx | Formal definition of wedge product | Print methods | Contractions | Transformations and pullback | Exterior derivatives | [ {d}\phi\left({v}i,\ldots,{v}{k+1}\right) | Differential of the differential, $d^2=0$ | Stokes's theorem | References