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        "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"
      ],
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      "title": "Function hodge() in the stokes package",
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      "engine": "knitr::rmarkdown",
      "headings": [
        "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"
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      "title": "Function inner() in the stokes package",
      "author": "Robin K. S. Hankin",
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        "Alternating forms",
        "References"
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      "title": "Function kinner() in the stokes package",
      "author": "Robin K. S. Hankin",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Some simple examples",
        "Tidyup",
        "References"
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      "title": "Function phi() in the stokes package",
      "author": "Robin K. S. Hankin",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Distributivity",
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        "Function Alt()",
        "References"
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      "title": "Function tensorprod() in the stokes package",
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      "headings": [
        "The tensor cross product",
        "Verification",
        "Note on associativity",
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      "filename": "stokes.html",
      "title": "Exterior calculus with R",
      "author": "Robin K. S. Hankin",
      "engine": "knitr::rmarkdown",
      "headings": [
        "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"
      ],
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      "title": "Functions vector_cross_product() and vcp3() in the stokes package",
      "author": "Robin K. S. Hankin",
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      "headings": [
        "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"
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      "source": "volume.Rmd",
      "filename": "volume.html",
      "title": "Function volume() in the stokes package",
      "author": "Robin K. S. Hankin",
      "engine": "knitr::rmarkdown",
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        "References"
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      "created": "2022-09-18 09:57:40",
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    {
      "source": "wedge.Rmd",
      "filename": "wedge.html",
      "title": "Functions wedge() and wedge2() in the stokes package",
      "author": "Robin K. S. Hankin",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Digression: function spraycross()",
        "Cut to the chase: wedge2()",
        "Algebraic properties",
        "References"
      ],
      "created": "2019-04-01 02:51:02",
      "modified": "2026-04-23 09:42:13",
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