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eric-wiesereric-wieser
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Do not clobber sympy.Basic.__str__ (#258)
Instead we modify `print`, because at least nothing within sympy should be depending on that. This fixes `simplify(expr)` behaving differently depending on whether latex printing was enabled or disabled when `simplify(expr)` was called for the _first_ time. This is a horrible bug, and you could argue we deserved it for doing horrible things to sympy internals. Ideally we would not replace `print` either, but that would be an API change, so should come as a future commit. The notebook changes are a result of our printer no longer affecting sympy's default sort order for terms. It's not clear to me why the formatting of the matrix output changed, but it seems harmless in any case.
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‎examples/ipython/LaTeX.ipynb‎

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‎examples/ipython/Terminal.ipynb‎

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"A.lt_dict[e0]= \u001b[0;34me0\u001b[0m + 2*\u001b[0;34me1\u001b[0m + 3*\u001b[0;34me2\u001b[0m\n",
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"A.lt_dict[e1]= 4*\u001b[0;34me0\u001b[0m + 5*\u001b[0;34me1\u001b[0m + 6*\u001b[0;34me2\u001b[0m\n",
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"A.lt_dict[e2]= 7*\u001b[0;34me0\u001b[0m + 8*\u001b[0;34me1\u001b[0m + 9*\u001b[0;34me2\u001b[0m\n",
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"Matrix([[1, 4, 7], [2, 5, 8], [3, 6, 9]])\n",
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"Matrix([\n",
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"[1, 4, 7],\n",
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"[2, 5, 8],\n",
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"[3, 6, 9]])\n",
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" v__x*\u001b[0;34me0\u001b[0m\n",
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" + v__y*\u001b[0;34me1\u001b[0m\n",
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" + v__z*\u001b[0;34me2\u001b[0m\n",

‎examples/ipython/dop.ipynb‎

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"\\begin{equation*} \\nabla^{2} = \\frac{1}{r^{2} \\tan{\\left (\\theta \\right )}} \\frac{\\partial}{\\partial \\theta } + \\frac{2}{r} \\frac{\\partial}{\\partial r} + \\frac{1}{r^{2} {\\sin{\\left (\\theta \\right )}}^{2}} \\frac{\\partial^{2}}{\\partial \\phi ^{2}} + r^{-2} \\frac{\\partial^{2}}{\\partial \\theta ^{2}} + \\frac{\\partial^{2}}{\\partial r^{2}} \\end{equation*}"
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"\\begin{equation*} \\nabla^{2} = \\frac{2}{r} \\frac{\\partial}{\\partial r} + \\frac{1}{r^{2} \\tan{\\left (\\theta \\right )}} \\frac{\\partial}{\\partial \\theta } + \\frac{1}{r^{2} {\\sin{\\left (\\theta \\right )}}^{2}} \\frac{\\partial^{2}}{\\partial \\phi ^{2}} + \\frac{\\partial^{2}}{\\partial r^{2}} + r^{-2} \\frac{\\partial^{2}}{\\partial \\theta ^{2}} \\end{equation*}"
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"text/plain": [
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"\\frac{1}{r^{2} \\tan{\\left (\\theta \\right )}} \\frac{\\partial}{\\partial \\theta } + \\frac{2}{r} \\frac{\\partial}{\\partial r} + \\frac{1}{r^{2} {\\sin{\\left (\\theta \\right )}}^{2}} \\frac{\\partial^{2}}{\\partial \\phi ^{2}} + r^{-2} \\frac{\\partial^{2}}{\\partial \\theta ^{2}} + \\frac{\\partial^{2}}{\\partial r^{2}}"
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"\\frac{2}{r} \\frac{\\partial}{\\partial r} + \\frac{1}{r^{2} \\tan{\\left (\\theta \\right )}} \\frac{\\partial}{\\partial \\theta } + \\frac{1}{r^{2} {\\sin{\\left (\\theta \\right )}}^{2}} \\frac{\\partial^{2}}{\\partial \\phi ^{2}} + \\frac{\\partial^{2}}{\\partial r^{2}} + r^{-2} \\frac{\\partial^{2}}{\\partial \\theta ^{2}}"
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.2"
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"version": "3.8.0"
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‎examples/ipython/inner_product.ipynb‎

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"\\begin{equation*} \\left ( A^{x} a^{x} + A^{y} a^{y} + A^{z} a^{z}\\right ) + \\left ( A a^{x} - A^{xy} a^{y} - A^{xz} a^{z}\\right ) \\boldsymbol{e}_{x} + \\left ( A a^{y} + A^{xy} a^{x} - A^{yz} a^{z}\\right ) \\boldsymbol{e}_{y} + \\left ( A a^{z} + A^{xz} a^{x} + A^{yz} a^{y}\\right ) \\boldsymbol{e}_{z} + \\left ( A^{xyz} a^{z} - A^{x} a^{y} + A^{y} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{xyz} a^{y} - A^{x} a^{z} + A^{z} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xyz} a^{x} - A^{y} a^{z} + A^{z} a^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xy} a^{z} - A^{xz} a^{y} + A^{yz} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}"
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"\\begin{equation*} \\left ( A^{x} a^{x} + A^{y} a^{y} + A^{z} a^{z}\\right ) + \\left ( A a^{x} - A^{xy} a^{y} - A^{xz} a^{z}\\right ) \\boldsymbol{e}_{x} + \\left ( A a^{y} + A^{xy} a^{x} - A^{yz} a^{z}\\right ) \\boldsymbol{e}_{y} + \\left ( A a^{z} + A^{xz} a^{x} + A^{yz} a^{y}\\right ) \\boldsymbol{e}_{z} + \\left ( - A^{x} a^{y} + A^{xyz} a^{z} + A^{y} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{x} a^{z} - A^{xyz} a^{y} + A^{z} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xyz} a^{x} - A^{y} a^{z} + A^{z} a^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xy} a^{z} - A^{xz} a^{y} + A^{yz} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}"
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"\\left ( A^{x} a^{x} + A^{y} a^{y} + A^{z} a^{z}\\right ) + \\left ( A a^{x} - A^{xy} a^{y} - A^{xz} a^{z}\\right ) \\boldsymbol{e}_{x} + \\left ( A a^{y} + A^{xy} a^{x} - A^{yz} a^{z}\\right ) \\boldsymbol{e}_{y} + \\left ( A a^{z} + A^{xz} a^{x} + A^{yz} a^{y}\\right ) \\boldsymbol{e}_{z} + \\left ( A^{xyz} a^{z} - A^{x} a^{y} + A^{y} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{xyz} a^{y} - A^{x} a^{z} + A^{z} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xyz} a^{x} - A^{y} a^{z} + A^{z} a^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xy} a^{z} - A^{xz} a^{y} + A^{yz} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}"
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"\\left ( A^{x} a^{x} + A^{y} a^{y} + A^{z} a^{z}\\right ) + \\left ( A a^{x} - A^{xy} a^{y} - A^{xz} a^{z}\\right ) \\boldsymbol{e}_{x} + \\left ( A a^{y} + A^{xy} a^{x} - A^{yz} a^{z}\\right ) \\boldsymbol{e}_{y} + \\left ( A a^{z} + A^{xz} a^{x} + A^{yz} a^{y}\\right ) \\boldsymbol{e}_{z} + \\left ( - A^{x} a^{y} + A^{xyz} a^{z} + A^{y} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{x} a^{z} - A^{xyz} a^{y} + A^{z} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xyz} a^{x} - A^{y} a^{z} + A^{z} a^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xy} a^{z} - A^{xz} a^{y} + A^{yz} a^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}"
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"\\begin{equation*} \\left ( A B - A^{xyz} B^{xyz} - A^{xy} B^{xy} - A^{xz} B^{xz} + A^{x} B^{x} - A^{yz} B^{yz} + A^{y} B^{y} + A^{z} B^{z}\\right ) + \\left ( A B^{x} - A^{xyz} B^{yz} + A^{xy} B^{y} + A^{xz} B^{z} + A^{x} B - A^{yz} B^{xyz} - A^{y} B^{xy} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A B^{y} + A^{xyz} B^{xz} - A^{xy} B^{x} + A^{xz} B^{xyz} + A^{x} B^{xy} + A^{yz} B^{z} + A^{y} B - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( A B^{z} - A^{xyz} B^{xy} - A^{xy} B^{xyz} - A^{xz} B^{x} + A^{x} B^{xz} - A^{yz} B^{y} + A^{y} B^{yz} + A^{z} B\\right ) \\boldsymbol{e}_{z} + \\left ( A B^{xy} + A^{xyz} B^{z} + A^{xy} B - A^{xz} B^{yz} + A^{x} B^{y} + A^{yz} B^{xz} - A^{y} B^{x} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( A B^{xz} - A^{xyz} B^{y} + A^{xy} B^{yz} + A^{xz} B + A^{x} B^{z} - A^{yz} B^{xy} - A^{y} B^{xyz} - A^{z} B^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A B^{yz} + A^{xyz} B^{x} - A^{xy} B^{xz} + A^{xz} B^{xy} + A^{x} B^{xyz} + A^{yz} B + A^{y} B^{z} - A^{z} B^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( A B^{xyz} + A^{xyz} B + A^{xy} B^{z} - A^{xz} B^{y} + A^{x} B^{yz} + A^{yz} B^{x} - A^{y} B^{xz} + A^{z} B^{xy}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}"
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"\\begin{equation*} \\left ( A B + A^{x} B^{x} - A^{xy} B^{xy} - A^{xyz} B^{xyz} - A^{xz} B^{xz} + A^{y} B^{y} - A^{yz} B^{yz} + A^{z} B^{z}\\right ) + \\left ( A B^{x} + A^{x} B + A^{xy} B^{y} - A^{xyz} B^{yz} + A^{xz} B^{z} - A^{y} B^{xy} - A^{yz} B^{xyz} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A B^{y} + A^{x} B^{xy} - A^{xy} B^{x} + A^{xyz} B^{xz} + A^{xz} B^{xyz} + A^{y} B + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( A B^{z} + A^{x} B^{xz} - A^{xy} B^{xyz} - A^{xyz} B^{xy} - A^{xz} B^{x} + A^{y} B^{yz} - A^{yz} B^{y} + A^{z} B\\right ) \\boldsymbol{e}_{z} + \\left ( A B^{xy} + A^{x} B^{y} + A^{xy} B + A^{xyz} B^{z} - A^{xz} B^{yz} - A^{y} B^{x} + A^{yz} B^{xz} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( A B^{xz} + A^{x} B^{z} + A^{xy} B^{yz} - A^{xyz} B^{y} + A^{xz} B - A^{y} B^{xyz} - A^{yz} B^{xy} - A^{z} B^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A B^{yz} + A^{x} B^{xyz} - A^{xy} B^{xz} + A^{xyz} B^{x} + A^{xz} B^{xy} + A^{y} B^{z} + A^{yz} B - A^{z} B^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( A B^{xyz} + A^{x} B^{yz} + A^{xy} B^{z} + A^{xyz} B - A^{xz} B^{y} - A^{y} B^{xz} + A^{yz} B^{x} + A^{z} B^{xy}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}"
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"\\left ( A B - A^{xyz} B^{xyz} - A^{xy} B^{xy} - A^{xz} B^{xz} + A^{x} B^{x} - A^{yz} B^{yz} + A^{y} B^{y} + A^{z} B^{z}\\right ) + \\left ( A B^{x} - A^{xyz} B^{yz} + A^{xy} B^{y} + A^{xz} B^{z} + A^{x} B - A^{yz} B^{xyz} - A^{y} B^{xy} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A B^{y} + A^{xyz} B^{xz} - A^{xy} B^{x} + A^{xz} B^{xyz} + A^{x} B^{xy} + A^{yz} B^{z} + A^{y} B - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( A B^{z} - A^{xyz} B^{xy} - A^{xy} B^{xyz} - A^{xz} B^{x} + A^{x} B^{xz} - A^{yz} B^{y} + A^{y} B^{yz} + A^{z} B\\right ) \\boldsymbol{e}_{z} + \\left ( A B^{xy} + A^{xyz} B^{z} + A^{xy} B - A^{xz} B^{yz} + A^{x} B^{y} + A^{yz} B^{xz} - A^{y} B^{x} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( A B^{xz} - A^{xyz} B^{y} + A^{xy} B^{yz} + A^{xz} B + A^{x} B^{z} - A^{yz} B^{xy} - A^{y} B^{xyz} - A^{z} B^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A B^{yz} + A^{xyz} B^{x} - A^{xy} B^{xz} + A^{xz} B^{xy} + A^{x} B^{xyz} + A^{yz} B + A^{y} B^{z} - A^{z} B^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( A B^{xyz} + A^{xyz} B + A^{xy} B^{z} - A^{xz} B^{y} + A^{x} B^{yz} + A^{yz} B^{x} - A^{y} B^{xz} + A^{z} B^{xy}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}"
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"\\left ( A B + A^{x} B^{x} - A^{xy} B^{xy} - A^{xyz} B^{xyz} - A^{xz} B^{xz} + A^{y} B^{y} - A^{yz} B^{yz} + A^{z} B^{z}\\right ) + \\left ( A B^{x} + A^{x} B + A^{xy} B^{y} - A^{xyz} B^{yz} + A^{xz} B^{z} - A^{y} B^{xy} - A^{yz} B^{xyz} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A B^{y} + A^{x} B^{xy} - A^{xy} B^{x} + A^{xyz} B^{xz} + A^{xz} B^{xyz} + A^{y} B + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( A B^{z} + A^{x} B^{xz} - A^{xy} B^{xyz} - A^{xyz} B^{xy} - A^{xz} B^{x} + A^{y} B^{yz} - A^{yz} B^{y} + A^{z} B\\right ) \\boldsymbol{e}_{z} + \\left ( A B^{xy} + A^{x} B^{y} + A^{xy} B + A^{xyz} B^{z} - A^{xz} B^{yz} - A^{y} B^{x} + A^{yz} B^{xz} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( A B^{xz} + A^{x} B^{z} + A^{xy} B^{yz} - A^{xyz} B^{y} + A^{xz} B - A^{y} B^{xyz} - A^{yz} B^{xy} - A^{z} B^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A B^{yz} + A^{x} B^{xyz} - A^{xy} B^{xz} + A^{xyz} B^{x} + A^{xz} B^{xy} + A^{y} B^{z} + A^{yz} B - A^{z} B^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( A B^{xyz} + A^{x} B^{yz} + A^{xy} B^{z} + A^{xyz} B - A^{xz} B^{y} - A^{y} B^{xz} + A^{yz} B^{x} + A^{z} B^{xy}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}"
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"\\begin{equation*} \\left ( - A^{xyz} B^{xyz} - A^{xy} B^{xy} - A^{xz} B^{xz} + A^{x} B^{x} - A^{yz} B^{yz} + A^{y} B^{y} + A^{z} B^{z}\\right ) + \\left ( - A^{xyz} B^{yz} + A^{xy} B^{y} + A^{xz} B^{z} - A^{yz} B^{xyz} - A^{y} B^{xy} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A^{xyz} B^{xz} - A^{xy} B^{x} + A^{xz} B^{xyz} + A^{x} B^{xy} + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{xy} - A^{xy} B^{xyz} - A^{xz} B^{x} + A^{x} B^{xz} - A^{yz} B^{y} + A^{y} B^{yz}\\right ) \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{z} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{y} - A^{y} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{x} + A^{x} B^{xyz}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}"
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"\\begin{equation*} \\left ( A^{x} B^{x} - A^{xy} B^{xy} - A^{xyz} B^{xyz} - A^{xz} B^{xz} + A^{y} B^{y} - A^{yz} B^{yz} + A^{z} B^{z}\\right ) + \\left ( A^{xy} B^{y} - A^{xyz} B^{yz} + A^{xz} B^{z} - A^{y} B^{xy} - A^{yz} B^{xyz} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A^{x} B^{xy} - A^{xy} B^{x} + A^{xyz} B^{xz} + A^{xz} B^{xyz} + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( A^{x} B^{xz} - A^{xy} B^{xyz} - A^{xyz} B^{xy} - A^{xz} B^{x} + A^{y} B^{yz} - A^{yz} B^{y}\\right ) \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{z} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{y} - A^{y} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{x} B^{xyz} + A^{xyz} B^{x}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}"
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"\\left ( - A^{xyz} B^{xyz} - A^{xy} B^{xy} - A^{xz} B^{xz} + A^{x} B^{x} - A^{yz} B^{yz} + A^{y} B^{y} + A^{z} B^{z}\\right ) + \\left ( - A^{xyz} B^{yz} + A^{xy} B^{y} + A^{xz} B^{z} - A^{yz} B^{xyz} - A^{y} B^{xy} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A^{xyz} B^{xz} - A^{xy} B^{x} + A^{xz} B^{xyz} + A^{x} B^{xy} + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{xy} - A^{xy} B^{xyz} - A^{xz} B^{x} + A^{x} B^{xz} - A^{yz} B^{y} + A^{y} B^{yz}\\right ) \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{z} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{y} - A^{y} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{x} + A^{x} B^{xyz}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}"
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"\\left ( A^{x} B^{x} - A^{xy} B^{xy} - A^{xyz} B^{xyz} - A^{xz} B^{xz} + A^{y} B^{y} - A^{yz} B^{yz} + A^{z} B^{z}\\right ) + \\left ( A^{xy} B^{y} - A^{xyz} B^{yz} + A^{xz} B^{z} - A^{y} B^{xy} - A^{yz} B^{xyz} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A^{x} B^{xy} - A^{xy} B^{x} + A^{xyz} B^{xz} + A^{xz} B^{xyz} + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( A^{x} B^{xz} - A^{xy} B^{xyz} - A^{xyz} B^{xy} - A^{xz} B^{x} + A^{y} B^{yz} - A^{yz} B^{y}\\right ) \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{z} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{y} - A^{y} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{x} B^{xyz} + A^{xyz} B^{x}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}"
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{
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"\\begin{equation*} \\left ( A B - 2 A^{xyz} B^{xyz} - 2 A^{xy} B^{xy} - 2 A^{xz} B^{xz} + 2 A^{x} B^{x} - 2 A^{yz} B^{yz} + 2 A^{y} B^{y} + 2 A^{z} B^{z}\\right ) + \\left ( - A^{xyz} B^{yz} + A^{xy} B^{y} + A^{xz} B^{z} - A^{yz} B^{xyz} - A^{y} B^{xy} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A^{xyz} B^{xz} - A^{xy} B^{x} + A^{xz} B^{xyz} + A^{x} B^{xy} + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{xy} - A^{xy} B^{xyz} - A^{xz} B^{x} + A^{x} B^{xz} - A^{yz} B^{y} + A^{y} B^{yz}\\right ) \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{z} + A^{xz} B^{yz} - A^{x} B^{y} - A^{yz} B^{xz} + A^{y} B^{x} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{y} - A^{xy} B^{yz} - A^{x} B^{z} + A^{yz} B^{xy} - A^{y} B^{xyz} + A^{z} B^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{x} + A^{xy} B^{xz} - A^{xz} B^{xy} + A^{x} B^{xyz} - A^{y} B^{z} + A^{z} B^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( - A^{xy} B^{z} + A^{xz} B^{y} - A^{x} B^{yz} - A^{yz} B^{x} + A^{y} B^{xz} - A^{z} B^{xy}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}"
458+
"\\begin{equation*} \\left ( A B + 2 A^{x} B^{x} - 2 A^{xy} B^{xy} - 2 A^{xyz} B^{xyz} - 2 A^{xz} B^{xz} + 2 A^{y} B^{y} - 2 A^{yz} B^{yz} + 2 A^{z} B^{z}\\right ) + \\left ( A^{xy} B^{y} - A^{xyz} B^{yz} + A^{xz} B^{z} - A^{y} B^{xy} - A^{yz} B^{xyz} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A^{x} B^{xy} - A^{xy} B^{x} + A^{xyz} B^{xz} + A^{xz} B^{xyz} + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( A^{x} B^{xz} - A^{xy} B^{xyz} - A^{xyz} B^{xy} - A^{xz} B^{x} + A^{y} B^{yz} - A^{yz} B^{y}\\right ) \\boldsymbol{e}_{z} + \\left ( - A^{x} B^{y} + A^{xyz} B^{z} + A^{xz} B^{yz} + A^{y} B^{x} - A^{yz} B^{xz} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{x} B^{z} - A^{xy} B^{yz} - A^{xyz} B^{y} - A^{y} B^{xyz} + A^{yz} B^{xy} + A^{z} B^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{x} B^{xyz} + A^{xy} B^{xz} + A^{xyz} B^{x} - A^{xz} B^{xy} - A^{y} B^{z} + A^{z} B^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( - A^{x} B^{yz} - A^{xy} B^{z} + A^{xz} B^{y} + A^{y} B^{xz} - A^{yz} B^{x} - A^{z} B^{xy}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}"
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],
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"text/plain": [
461-
"\\left ( A B - 2 A^{xyz} B^{xyz} - 2 A^{xy} B^{xy} - 2 A^{xz} B^{xz} + 2 A^{x} B^{x} - 2 A^{yz} B^{yz} + 2 A^{y} B^{y} + 2 A^{z} B^{z}\\right ) + \\left ( - A^{xyz} B^{yz} + A^{xy} B^{y} + A^{xz} B^{z} - A^{yz} B^{xyz} - A^{y} B^{xy} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A^{xyz} B^{xz} - A^{xy} B^{x} + A^{xz} B^{xyz} + A^{x} B^{xy} + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{xy} - A^{xy} B^{xyz} - A^{xz} B^{x} + A^{x} B^{xz} - A^{yz} B^{y} + A^{y} B^{yz}\\right ) \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{z} + A^{xz} B^{yz} - A^{x} B^{y} - A^{yz} B^{xz} + A^{y} B^{x} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{xyz} B^{y} - A^{xy} B^{yz} - A^{x} B^{z} + A^{yz} B^{xy} - A^{y} B^{xyz} + A^{z} B^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{xyz} B^{x} + A^{xy} B^{xz} - A^{xz} B^{xy} + A^{x} B^{xyz} - A^{y} B^{z} + A^{z} B^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( - A^{xy} B^{z} + A^{xz} B^{y} - A^{x} B^{yz} - A^{yz} B^{x} + A^{y} B^{xz} - A^{z} B^{xy}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}"
461+
"\\left ( A B + 2 A^{x} B^{x} - 2 A^{xy} B^{xy} - 2 A^{xyz} B^{xyz} - 2 A^{xz} B^{xz} + 2 A^{y} B^{y} - 2 A^{yz} B^{yz} + 2 A^{z} B^{z}\\right ) + \\left ( A^{xy} B^{y} - A^{xyz} B^{yz} + A^{xz} B^{z} - A^{y} B^{xy} - A^{yz} B^{xyz} - A^{z} B^{xz}\\right ) \\boldsymbol{e}_{x} + \\left ( A^{x} B^{xy} - A^{xy} B^{x} + A^{xyz} B^{xz} + A^{xz} B^{xyz} + A^{yz} B^{z} - A^{z} B^{yz}\\right ) \\boldsymbol{e}_{y} + \\left ( A^{x} B^{xz} - A^{xy} B^{xyz} - A^{xyz} B^{xy} - A^{xz} B^{x} + A^{y} B^{yz} - A^{yz} B^{y}\\right ) \\boldsymbol{e}_{z} + \\left ( - A^{x} B^{y} + A^{xyz} B^{z} + A^{xz} B^{yz} + A^{y} B^{x} - A^{yz} B^{xz} + A^{z} B^{xyz}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + \\left ( - A^{x} B^{z} - A^{xy} B^{yz} - A^{xyz} B^{y} - A^{y} B^{xyz} + A^{yz} B^{xy} + A^{z} B^{x}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + \\left ( A^{x} B^{xyz} + A^{xy} B^{xz} + A^{xyz} B^{x} - A^{xz} B^{xy} - A^{y} B^{z} + A^{z} B^{y}\\right ) \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} + \\left ( - A^{x} B^{yz} - A^{xy} B^{z} + A^{xz} B^{y} + A^{y} B^{xz} - A^{yz} B^{x} - A^{z} B^{xy}\\right ) \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}"
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]
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},
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"execution_count": 21,
@@ -494,7 +494,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.2"
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"version": "3.8.0"
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}
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},
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"nbformat": 4,

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