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Update gr_metrics.ipynb for SymPy 1.11
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utensil committed Mar 28, 2024
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14 changes: 7 additions & 7 deletions examples/ipython/gr_metrics.ipynb
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"\\begin{equation*}\\left[\\begin{array}{}\\left[\\begin{array}{}0 & 0 & 0 & 0\\\\0 & - \\frac{u e^{4 z}}{2} & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & - \\frac{u}{2}\\end{array}\\right] & \\left[\\begin{array}{}0 & \\frac{u e^{4 z}}{2} & 0 & 0\\\\\\frac{u e^{4 z}}{2} & 0 & 0 & u^{2} e^{4 z}\\\\0 & 0 & 0 & 0\\\\0 & u^{2} e^{4 z} & 0 & 0\\end{array}\\right] & \\left[\\begin{array}{}0 & 0 & 0 & e^{- z}\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & - 12 e^{- 2 z}\\\\e^{- z} & 0 & - 12 e^{- 2 z} & - u e^{- z}\\end{array}\\right] & \\left[\\begin{array}{}0 & 0 & 0 & \\frac{u}{2}\\\\0 & - u^{2} e^{4 z} & 0 & 0\\\\0 & 0 & 12 e^{- 2 z} & 0\\\\\\frac{u}{2} & 0 & 0 & 0\\end{array}\\right]\\end{array}\\right]\\end{equation*}"
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"\\begin{equation*}\\left[\\begin{array}\\left[\\begin{array}0 & 0 & 0 & 0\\\\0 & 3 u e^{4 z} & 0 & 0\\\\0 & 0 & \\frac{24 e^{- 2 z}}{u} & 12 e^{- z}\\\\0 & 0 & 12 e^{- z} & 6 u\\end{array}\\right] & \\left[\\begin{array}0 & \\frac{1}{u} & 0 & 0\\\\\\frac{1}{u} & 0 & 0 & 2\\\\0 & 0 & 0 & 0\\\\0 & 2 & 0 & 0\\end{array}\\right] & \\left[\\begin{array}0 & 0 & 0 & 0\\\\0 & \\frac{u e^{5 z}}{2} & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{u e^{z}}{2}\\end{array}\\right] & \\left[\\begin{array}0 & 0 & 0 & \\frac{1}{u}\\\\0 & - 3 e^{4 z} & 0 & 0\\\\0 & 0 & \\frac{24 e^{- 2 z}}{u^{2}} & 0\\\\\\frac{1}{u} & 0 & 0 & -1\\end{array}\\right]\\end{array}\\right]\\end{equation*}"
"\\begin{equation*}\\left[\\begin{array}{}\\left[\\begin{array}{}0 & 0 & 0 & 0\\\\0 & 3 u e^{4 z} & 0 & 0\\\\0 & 0 & \\frac{24 e^{- 2 z}}{u} & 12 e^{- z}\\\\0 & 0 & 12 e^{- z} & 6 u\\end{array}\\right] & \\left[\\begin{array}{}0 & \\frac{1}{u} & 0 & 0\\\\\\frac{1}{u} & 0 & 0 & 2\\\\0 & 0 & 0 & 0\\\\0 & 2 & 0 & 0\\end{array}\\right] & \\left[\\begin{array}{}0 & 0 & 0 & 0\\\\0 & \\frac{u e^{5 z}}{2} & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{u e^{z}}{2}\\end{array}\\right] & \\left[\\begin{array}{}0 & 0 & 0 & \\frac{1}{u}\\\\0 & - 3 e^{4 z} & 0 & 0\\\\0 & 0 & \\frac{24 e^{- 2 z}}{u^{2}} & 0\\\\\\frac{1}{u} & 0 & 0 & -1\\end{array}\\right]\\end{array}\\right]\\end{equation*}"
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"\\begin{equation*}\\left[\\begin{array}{}\\left[\\begin{array}{}0 & \\frac{G M}{c^{2} r^{2}} & 0 & 0\\\\\\frac{G M}{c^{2} r^{2}} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{array}\\right] & \\left[\\begin{array}{}- \\frac{G M}{c^{2} r^{2}} & 0 & 0 & 0\\\\0 & \\frac{G M c^{2}}{4 G^{2} M^{2} + c^{2} r \\left(- 4 G M + c^{2} r\\right)} & 0 & 0\\\\0 & 0 & r & 0\\\\0 & 0 & 0 & r {\\sin{\\left (\\theta \\right )}}^{2}\\end{array}\\right] & \\left[\\begin{array}{}0 & 0 & 0 & 0\\\\0 & 0 & - r & 0\\\\0 & - r & 0 & 0\\\\0 & 0 & 0 & \\frac{r^{2} \\sin{\\left (2 \\theta \\right )}}{2}\\end{array}\\right] & \\left[\\begin{array}{}0 & 0 & 0 & 0\\\\0 & 0 & 0 & - r {\\sin{\\left (\\theta \\right )}}^{2}\\\\0 & 0 & 0 & - \\frac{r^{2} \\sin{\\left (2 \\theta \\right )}}{2}\\\\0 & - r {\\sin{\\left (\\theta \\right )}}^{2} & - \\frac{r^{2} \\sin{\\left (2 \\theta \\right )}}{2} & 0\\end{array}\\right]\\end{array}\\right]\\end{equation*}"
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"\\begin{equation*}\\left[\\begin{array}{}\\left[\\begin{array}{}0 & \\frac{G M}{r \\left(- 2 G M + c^{2} r\\right)} & 0 & 0\\\\\\frac{G M}{r \\left(- 2 G M + c^{2} r\\right)} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{array}\\right] & \\left[\\begin{array}{}\\frac{G M \\left(- 2 G M + c^{2} r\\right)}{c^{4} r^{3}} & 0 & 0 & 0\\\\0 & \\frac{G M}{r \\left(2 G M - c^{2} r\\right)} & 0 & 0\\\\0 & 0 & \\frac{2 G M}{c^{2}} - r & 0\\\\0 & 0 & 0 & \\frac{\\left(2 G M - c^{2} r\\right) {\\sin{\\left (\\theta \\right )}}^{2}}{c^{2}}\\end{array}\\right] & \\left[\\begin{array}{}0 & 0 & 0 & 0\\\\0 & 0 & \\frac{1}{r} & 0\\\\0 & \\frac{1}{r} & 0 & 0\\\\0 & 0 & 0 & - \\frac{\\sin{\\left (2 \\theta \\right )}}{2}\\end{array}\\right] & \\left[\\begin{array}{}0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{1}{r}\\\\0 & 0 & 0 & \\frac{1}{\\tan{\\left (\\theta \\right )}}\\\\0 & \\frac{1}{r} & \\frac{1}{\\tan{\\left (\\theta \\right )}} & 0\\end{array}\\right]\\end{array}\\right]\\end{equation*}"
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"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.0"
"version": "3.11.8"
}
},
"nbformat": 4,
"nbformat_minor": 2
"nbformat_minor": 4
}

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