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CMakeLists.txt

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@@ -4,7 +4,7 @@ set(CMAKE_LEGACY_CYGWIN_WIN32 0)
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project(Cadabra)
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set(CADABRA_VERSION_MAJOR 2)
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set(CADABRA_VERSION_MINOR 1)
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set(CADABRA_VERSION_PATCH 4)
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set(CADABRA_VERSION_PATCH 5)
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set(COPYRIGHT_YEARS "2001-2017")
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execute_process(COMMAND git rev-parse --short HEAD OUTPUT_VARIABLE GIT_SHORT_SHA OUTPUT_STRIP_TRAILING_WHITESPACE)
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execute_process(COMMAND git rev-list --count HEAD OUTPUT_VARIABLE GIT_COMMIT_SERIAL OUTPUT_STRIP_TRAILING_WHITESPACE)

core/algorithms/evaluate.cc

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@@ -281,7 +281,9 @@ Ex::iterator evaluate::handle_factor(sibling_iterator sib, const index_map_t& fu
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if(!has_acted) {
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// There was not a single rule which matched for this tensor. That's means
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// that the user wants to keep the entire tensor (all components).
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#ifdef DEBUG
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std::cerr << "No single rule matched " << Ex(sib) << std::endl;
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#endif
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sib=dense_factor(sib, ind_free, ind_dummy);
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}
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else {

examples/schwarzschild.cnb

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@@ -60,7 +60,7 @@
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{
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"cell_origin" : "server",
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"cell_type" : "latex_view",
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"source" : "\\begin{dmath*}{}\\left[g_{t t} = -1+\\frac{2M}{r},~\\discretionary{}{}{} g_{r r} = \\frac{1}{1 - \\frac{2M}{r}},~\\discretionary{}{}{} g_{\\theta \\theta} = r^{2},~\\discretionary{}{}{} g_{\\phi \\phi} = r^{2} \\sin{\\theta}^{2},~\\discretionary{}{}{} g^{t t} = \\frac{r}{2M-r},~\\discretionary{}{}{} g^{r r} = \\frac{-2M+r}{r},~\\discretionary{}{}{} g^{\\phi \\phi} = \\frac{1}{r^{2} \\sin{\\theta}^{2}},~\\discretionary{}{}{} g^{\\theta \\theta} = r^{-2}\\right]\\end{dmath*}"
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"source" : "\\begin{dmath*}{}\\left[g_{t t} = -1+\\frac{2M}{r},~\\discretionary{}{}{} g_{r r} = \\frac{1}{1 - \\frac{2M}{r}},~\\discretionary{}{}{} g_{\\theta \\theta} = {r}^{2},~\\discretionary{}{}{} g_{\\phi \\phi} = {r}^{2} {\\left(\\sin{\\theta}\\right)}^{2},~\\discretionary{}{}{} g^{t t} = \\frac{r}{2M-r},~\\discretionary{}{}{} g^{r r} = \\frac{-2M+r}{r},~\\discretionary{}{}{} g^{\\phi \\phi} = \\frac{1}{{r}^{2} {\\left(\\sin{\\theta}\\right)}^{2}},~\\discretionary{}{}{} g^{\\theta \\theta} = {r}^{-2}\\right]\\end{dmath*}"
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}
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],
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"source" : "ss:= { g_{t t} = -(1-2 M/r), \n g_{r r} = 1/(1-2 M/r), \n g_{\\theta\\theta} = r**2, \n g_{\\phi\\phi}=r**2 \\sin(\\theta)**2\n }.\n\ncomplete(ss, $g^{\\mu\\nu}$);"
@@ -92,7 +92,7 @@
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{
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"cell_origin" : "server",
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"cell_type" : "latex_view",
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"source" : "\\begin{dmath*}{}\\Gamma^{\\mu}\\,_{\\nu \\rho} = \\left\\{\\begin{aligned}\\square{}_{\\phi}{}_{r}{}^{\\phi}= & \\frac{1}{r}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\theta}{}^{\\phi}= & \\frac{1}{\\tan{\\theta}}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{r}{}^{\\theta}= & \\frac{1}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{r}{}^{r}= & \\frac{M}{r \\left(2M-r\\right)}\\\\[-.5ex]\n\\square{}_{t}{}_{r}{}^{t}= & \\frac{M}{r \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{r}{}_{\\phi}{}^{\\phi}= & \\frac{1}{r}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\phi}{}^{\\phi}= & \\frac{1}{\\tan{\\theta}}\\\\[-.5ex]\n\\square{}_{r}{}_{\\theta}{}^{\\theta}= & \\frac{1}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{t}{}^{t}= & \\frac{M}{r \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{r}= & \\left(2M-r\\right) \\sin{\\theta}^{2}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{\\theta}= & - \\frac{1}{2}\\sin{2\\theta}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\theta}{}^{r}= & 2M-r\\\\[-.5ex]\n\\square{}_{t}{}_{t}{}^{r}= & M \\frac{-2M+r}{r^{3}}\\\\[-.5ex]\n\\end{aligned}\\right.\n\\end{dmath*}"
95+
"source" : "\\begin{dmath*}{}\\Gamma^{\\mu}\\,_{\\nu \\rho} = \\square{}_{\\nu}{}_{\\rho}{}^{\\mu}\\left\\{\\begin{aligned}\\square{}_{\\phi}{}_{r}{}^{\\phi}= & \\frac{1}{r}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\theta}{}^{\\phi}= & \\frac{1}{\\tan{\\theta}}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{r}{}^{\\theta}= & \\frac{1}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{r}{}^{r}= & \\frac{M}{r \\left(2M-r\\right)}\\\\[-.5ex]\n\\square{}_{t}{}_{r}{}^{t}= & \\frac{M}{r \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{r}{}_{\\phi}{}^{\\phi}= & \\frac{1}{r}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\phi}{}^{\\phi}= & \\frac{1}{\\tan{\\theta}}\\\\[-.5ex]\n\\square{}_{r}{}_{\\theta}{}^{\\theta}= & \\frac{1}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{t}{}^{t}= & \\frac{M}{r \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{r}= & \\left(2M-r\\right) {\\left(\\sin{\\theta}\\right)}^{2}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{\\theta}= & - \\frac{1}{2}\\sin{2\\theta}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\theta}{}^{r}= & 2M-r\\\\[-.5ex]\n\\square{}_{t}{}_{t}{}^{r}= & M \\frac{-2M+r}{{r}^{3}}\\\\[-.5ex]\n\\end{aligned}\\right.\n\\end{dmath*}"
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}
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],
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"source" : "ch:= \\Gamma^{\\mu}_{\\nu\\rho} = 1/2 g^{\\mu\\sigma} ( \n \\partial_{\\rho}{g_{\\nu\\sigma}} \n +\\partial_{\\nu}{g_{\\rho\\sigma}}\n -\\partial_{\\sigma}{g_{\\nu\\rho}} ):\n \nevaluate(ch, ss, rhsonly=True);"
@@ -132,7 +132,7 @@
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{
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"cell_origin" : "server",
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"cell_type" : "latex_view",
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"source" : "\\begin{dmath*}{}R^{\\rho}\\,_{\\sigma \\mu \\nu} = \\left\\{\\begin{aligned}\\square{}_{t}{}_{t}{}^{r}{}_{r}= & 2M \\frac{2M-r}{r^{4}}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\theta}{}^{r}{}_{r}= & - \\frac{M}{r}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{\\theta}{}_{\\theta}= & 2M \\frac{\\sin{\\theta}^{2}}{r}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{r}{}_{r}= & -M \\frac{\\sin{\\theta}^{2}}{r}\\\\[-.5ex]\n\\square{}_{t}{}_{r}{}^{t}{}_{r}= & \\frac{2M}{r^{2} \\left(2M-r\\right)}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\theta}{}^{\\phi}{}_{\\theta}= & - \\frac{2M}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{t}{}^{r}{}_{t}= & 2M \\frac{-2M+r}{r^{4}}\\\\[-.5ex]\n\\square{}_{r}{}_{\\theta}{}^{r}{}_{\\theta}= & \\frac{M}{r}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\phi}{}^{\\theta}{}_{\\phi}= & -2M \\frac{\\sin{\\theta}^{2}}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{\\phi}{}^{r}{}_{\\phi}= & M \\frac{\\sin{\\theta}^{2}}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{r}{}^{t}{}_{t}= & \\frac{2M}{r^{2} \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{r}{}_{r}{}^{\\theta}{}_{\\theta}= & \\frac{M}{r^{2} \\left(2M-r\\right)}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\theta}{}^{\\phi}{}_{\\phi}= & \\frac{2M}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{r}{}^{\\phi}{}_{\\phi}= & \\frac{M}{r^{2} \\left(2M-r\\right)}\\\\[-.5ex]\n\\square{}_{t}{}_{t}{}^{\\phi}{}_{\\phi}= & M \\frac{-2M+r}{r^{4}}\\\\[-.5ex]\n\\square{}_{t}{}_{t}{}^{\\theta}{}_{\\theta}= & M \\frac{-2M+r}{r^{4}}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{t}{}_{t}= & -M \\frac{\\sin{\\theta}^{2}}{r}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\theta}{}^{t}{}_{t}= & - \\frac{M}{r}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{r}{}^{\\phi}{}_{r}= & \\frac{M}{r^{2} \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{t}{}^{\\phi}{}_{t}= & M \\frac{2M-r}{r^{4}}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{r}{}^{\\theta}{}_{r}= & \\frac{M}{r^{2} \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{t}{}^{\\theta}{}_{t}= & M \\frac{2M-r}{r^{4}}\\\\[-.5ex]\n\\square{}_{t}{}_{\\phi}{}^{t}{}_{\\phi}= & M \\frac{\\sin{\\theta}^{2}}{r}\\\\[-.5ex]\n\\square{}_{t}{}_{\\theta}{}^{t}{}_{\\theta}= & \\frac{M}{r}\\\\[-.5ex]\n\\end{aligned}\\right.\n\\end{dmath*}"
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"source" : "\\begin{dmath*}{}R^{\\rho}\\,_{\\sigma \\mu \\nu} = \\square{}_{\\nu}{}_{\\sigma}{}^{\\rho}{}_{\\mu}\\left\\{\\begin{aligned}\\square{}_{t}{}_{t}{}^{r}{}_{r}= & 2M \\frac{2M-r}{{r}^{4}}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\theta}{}^{r}{}_{r}= & - \\frac{M}{r}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{\\theta}{}_{\\theta}= & 2M \\frac{{\\left(\\sin{\\theta}\\right)}^{2}}{r}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{r}{}_{r}= & -M \\frac{{\\left(\\sin{\\theta}\\right)}^{2}}{r}\\\\[-.5ex]\n\\square{}_{t}{}_{r}{}^{t}{}_{r}= & \\frac{2M}{{r}^{2} \\left(2M-r\\right)}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\theta}{}^{\\phi}{}_{\\theta}= & - \\frac{2M}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{t}{}^{r}{}_{t}= & 2M \\frac{-2M+r}{{r}^{4}}\\\\[-.5ex]\n\\square{}_{r}{}_{\\theta}{}^{r}{}_{\\theta}= & \\frac{M}{r}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\phi}{}^{\\theta}{}_{\\phi}= & -2M \\frac{{\\left(\\sin{\\theta}\\right)}^{2}}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{\\phi}{}^{r}{}_{\\phi}= & M \\frac{{\\left(\\sin{\\theta}\\right)}^{2}}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{r}{}^{t}{}_{t}= & \\frac{2M}{{r}^{2} \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{r}{}_{r}{}^{\\theta}{}_{\\theta}= & \\frac{M}{{r}^{2} \\left(2M-r\\right)}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\theta}{}^{\\phi}{}_{\\phi}= & \\frac{2M}{r}\\\\[-.5ex]\n\\square{}_{r}{}_{r}{}^{\\phi}{}_{\\phi}= & \\frac{M}{{r}^{2} \\left(2M-r\\right)}\\\\[-.5ex]\n\\square{}_{t}{}_{t}{}^{\\phi}{}_{\\phi}= & M \\frac{-2M+r}{{r}^{4}}\\\\[-.5ex]\n\\square{}_{t}{}_{t}{}^{\\theta}{}_{\\theta}= & M \\frac{-2M+r}{{r}^{4}}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{\\phi}{}^{t}{}_{t}= & -M \\frac{{\\left(\\sin{\\theta}\\right)}^{2}}{r}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{\\theta}{}^{t}{}_{t}= & - \\frac{M}{r}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{r}{}^{\\phi}{}_{r}= & \\frac{M}{{r}^{2} \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{\\phi}{}_{t}{}^{\\phi}{}_{t}= & M \\frac{2M-r}{{r}^{4}}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{r}{}^{\\theta}{}_{r}= & \\frac{M}{{r}^{2} \\left(-2M+r\\right)}\\\\[-.5ex]\n\\square{}_{\\theta}{}_{t}{}^{\\theta}{}_{t}= & M \\frac{2M-r}{{r}^{4}}\\\\[-.5ex]\n\\square{}_{t}{}_{\\phi}{}^{t}{}_{\\phi}= & M \\frac{{\\left(\\sin{\\theta}\\right)}^{2}}{r}\\\\[-.5ex]\n\\square{}_{t}{}_{\\theta}{}^{t}{}_{\\theta}= & \\frac{M}{r}\\\\[-.5ex]\n\\end{aligned}\\right.\n\\end{dmath*}"
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}
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],
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"source" : "substitute(rm, ch)\nevaluate(rm, ss, rhsonly=True);"
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{
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"cell_origin" : "server",
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"cell_type" : "latex_view",
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"source" : "\\begin{dmath*}{}K = \\frac{48M^{2}}{r^{6}}\\end{dmath*}"
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"source" : "\\begin{dmath*}{}K = \\frac{48{M}^{2}}{{r}^{6}}\\end{dmath*}"
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}
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],
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"source" : "substitute(K, rm)\nevaluate(K, ss, rhsonly=True);"
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{
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"cell_origin" : "server",
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"cell_type" : "latex_view",
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"source" : "\\begin{dmath*}{}K = \\frac{48M^{2}}{r^{6}}\\end{dmath*}"
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"source" : "\\begin{dmath*}{}K = \\frac{48{M}^{2}}{{r}^{6}}\\end{dmath*}"
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}
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],
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"source" : "substitute(K, rm)\nevaluate(K, ss);"

web2/cadabra2/source/layout.html

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<link rel="shortcut icon" type="image/png" href="/static/cadabra.png">
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<script type="text/javascript"
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src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></script>
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src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></script>
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</script>
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<link href='https://fonts.googleapis.com/css?family=Inconsolata' rel='stylesheet' type='text/css'>
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<link href='https://fonts.googleapis.com/css?family=Lato:300,:400' rel='stylesheet' type='text/css'>
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<link href="http://fonts.googleapis.com/css?family=Bree+Serif" rel="stylesheet" type="text/css">
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<link href="https://fonts.googleapis.com/css?family=Bree+Serif" rel="stylesheet" type="text/css">
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<link rel="stylesheet" href="/static/fonts/Bright/cmun-bright.css">
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<script>
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MathJax.Hub.Config({

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