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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\342\200\234</Font><Hyperlink linktarget="http://www.cambridge.org/ne/academic/subjects/physics/theoretical-physics-and-mathematical-physics/exact-solutions-einsteins-field-equations-2nd-edition?format=AR" hyperlink="true"><Font style="Text" underline="true" encoding="UTF-8" foreground="[18,93,153]">Exact solutions to Einstein\342\200\231s equations</Font></Hyperlink><Font encoding="UTF-8">\342\200\235 is one of those books that are difficult even to imagine: the authors reviewed more than <Font bold="true">4,000 papers containing solutions to Einstein\342\200\231s equations</Font></Font> in the general relativity literature, collecting, classifying, discarding repetitions in disguise, and organizing the whole material into chapters according to the physical properties of these solutions. The book is already in its second edition and it is a monumental piece of work.</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">As good as it is, however, the project resulted only in printed material, a textbook constituted of paper and ink. In 2006, when the DifferentialGeometry package was rewritten to enter the Maple library, one of the first things that passed through our minds was to bring the whole of \342\200\234Exact solutions to Einstein\342\200\231s equations\342\200\235 into Maple. </Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">It took some time to start but in 2010, for Maple 14, we featured the first 26 solutions from this book. In Maple 15 this number jumped to 61. For Maple 17 we decided to emphasize the general relativity functionality of the DifferentialGeometry package, and Maple 18 added 50 more, featuring in total 225 of these solutions - great! but still far from the whole thing \342\200\246</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">And this is when we decided to \342\200\234step on the gas\342\200\235 - go for it, the whole book. One year later, </Font>working in collaboration with Denitsa Staicova from Bulgarian Academy of Sciences,<Font encoding="UTF-8"> Maple 2015 appeared with 330 solutions to Einstein\342\200\231s equations. Today we have already implemented 492 solutions, and for the first time we can see the end of the tunnel: we are targeting </Font><Font italic="true">finishing the whole book by the end of this year</Font>.</Text-field>
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<Text-field style="Text" layout="Normal">Wow<Font superscript="true">2</Font><Font encoding="UTF-8">! This is a terrific result. First, because these solutions are key in the area of general relativity, and at this point what we have in Maple is already the most thorough digitized database of solutions to Einstein\342\200\231s equations in the world. Second, and not any less important, because within Maple </Font><Font italic="true">this knowledge comes alive</Font>. The solutions are fully searcheable and are set by a simple call to the <Hyperlink linktarget="Help:Physics,g_" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Physics:-g_</Font></Hyperlink> spacetime metric command, and that automatically sets the related coordinates, <Hyperlink linktarget="Help:Physics,Christoffel" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Christoffel symbols</Font></Hyperlink>, <Hyperlink linktarget="Help:Physics,Ricci" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Ricci</Font></Hyperlink> and <Hyperlink linktarget="Help:Physics,Riemann" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Riemann</Font></Hyperlink> tensors, <Hyperlink linktarget="Help:Physics,Tetrads" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">orthonormal and null tetrads</Font></Hyperlink>, etc. All of this happens on the fly, and all the mathematics within the Maple library are ready to work with these solutions. Having everything come alive completely changes the game. The ability to search the database according to the physical properties of the solutions, their classification, or just by parts of keywords also makes the whole book concretely more useful. </Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">And, not only are these solutions to Einstein\342\200\231s equations brought to life in a full-featured way through the </Font><Hyperlink linktarget="Help:Physics" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Physics</Font></Hyperlink> package: they can also be reached through the <Hyperlink linktarget="Help:DifferentialGeometry:-Library:-MetricSearch" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">DifferentialGeometry:-Library:-MetricSearch</Font></Hyperlink> applet. Almost all of the mathematical operations one can perform on them are also implemented as commands in <Hyperlink linktarget="Help:DifferentialGeometry" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">DifferentialGeometry</Font></Hyperlink>.</Text-field>
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<Text-field style="Text" layout="Normal">Finally, in the Maple <Hyperlink linktarget="Help:PDEtools" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">PDEtools package</Font></Hyperlink>, we already have all the mathematical tools to start resolving <Font italic="true">the equivalence problem around these solutions</Font>. That is: to answer whether a new solution is or not new, or whether it can be obtained from an existing solution by transformations of coordinates of different kinds. And we are going for it.</Text-field>
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<Text-field style="Text" layout="Normal">What follows is a basic illustration of what has already been implemented. As usual, in order to reproduce these results, you need to update your Physics library from the <Hyperlink linktarget="http://www.maplesoft.com/products/maple/features/physicsresearch.aspx" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Maplesoft R&amp;D Physics webpage</Font></Hyperlink>.</Text-field>
<Text-field style="Text" size="8" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Load <Hyperlink linktarget="Help:Physics" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Physics</Font></Hyperlink>, set the metric to <Equation executable="false" style="2D Math" input-equation="" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEuU2Nod2FyenNjaGlsZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEuU2Nod2FyenNjaGlsZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==</Equation> (and everything else automatically) in one go</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKFBoeXNpY3NGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjpGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVkY9RkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKFBoeXNpY3NGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjpGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVkY9RkA=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZ19GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUSNzY0YnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj1GQA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZ19GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUSNzY0YnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj1GQA==</Equation></Text-field>
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<Output>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVFJVGhlflNjaHdhcnpzY2hpbGR+bWV0cmljfmlufmNvb3JkaW5hdGVzfkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYjUSFGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYsLUYsNiVRInJGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkgvJSpzeW1tZXRyaWNHRkgvJShsYXJnZW9wR0ZILyUubW92YWJsZWxpbWl0c0dGSC8lJ2FjY2VudEdGSC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRKCZ0aGV0YTtGJy9GMEZIRkRGQC1GLDYlUSYmcGhpO0YnRmhuRkRGQC1GLDYlUSJ0RidGL0YyLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0ZIRkRGRC8lJW9wZW5HUScmbHNxYjtGJy8lJmNsb3NlR1EnJnJzcWI7RidGRA==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEtUGFyYW1ldGVyczp+RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiNRIUYnLUkobWZlbmNlZEdGJDYmLUYsNiVRIm1GJ0YvRjIvRjNRJ25vcm1hbEYnLyUlb3BlbkdRJyZsc3FiO0YnLyUmY2xvc2VHUScmcnNxYjtGJ0Y+">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEtUGFyYW1ldGVyczp+RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiNRIUYnLUkobWZlbmNlZEdGJDYmLUYsNiVRIm1GJ0YvRjIvRjNRJ25vcm1hbEYnLyUlb3BlbkdRJyZsc3FiO0YnLyUmY2xvc2VHUScmcnNxYjtGJ0Y+</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" 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<Text-field style="Text" layout="Normal">And that is all we do :) Although the strength in <Hyperlink linktarget="Help:Physics" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Physics</Font></Hyperlink> is to compute with tensors using indicial notation, all of the tensor components and related properties of this metric are also derived on the fly (and no, they are not in any database). For instance these are the definition in terms of <Hyperlink linktarget="Help:Physics,Christoffel" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Christoffel symbols</Font></Hyperlink>, and the covariant components of the <Hyperlink linktarget="Help:Physics,Ricci" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Ricci tensor</Font></Hyperlink></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmUmljY2lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUStkZWZpbml0aW9uRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmUmljY2lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUStkZWZpbml0aW9uRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmUmljY2lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj1GQA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmUmljY2lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj1GQA==</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvJkkmUmljY2lHNiZGJi9JK21vZHVsZW5hbWVHRihJKFBoeXNpY3NHRiUvSTFoaWRlbW9kdWxlcHJlZml4R0YoSSV0cnVlR0YmRic2JEkjbXVHRihJI251R0YoLUknUlRBQkxFR0YoNiUiNXE7KCl6InlTdVklPS1JJ01BVFJJWEdGKDYjNyY3JiIiIUZCRkJGQkZBRkFGQUknTWF0cml4R0YlNyMvRi0tRkM2Iy9JJCVpZEdGKEY8</Equation></Text-field>
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<Text-field style="Text" layout="Normal">These are the <Hyperlink linktarget="Help:Physics,Riemann" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">16 Riemann invariants</Font></Hyperlink> for Schwarzschild solution, using the formulas by <Hyperlink linktarget="https://en.wikipedia.org/wiki/Carminati\342\200\223McLenaghan_invariants" hyperlink="true" encoding="UTF-8"><Font style="Text" underline="true" foreground="[18,93,153]">Carminati and McLenaghan</Font></Hyperlink></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoUmllbWFubkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRK2ludmFyaWFudHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoUmllbWFubkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRK2ludmFyaWFudHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ni0vJkkickc2Iy9JJ19sb2NhbEclKnByb3RlY3RlZEdJLV9uNDQ5NDk2MzUyMEc2IjYjIiIhRi0vJkYlNiMiIiJGLS8mRiU2IyIiI0YtLyZGJTYjIiIkRi0vJkkid0c2Iy9GKEktX240NDk0OTYzNTUyR0YrRjAsJCooIiInRjEpSSJtR0YrRjVGMSlGJUZCISIiRjEvJkY8RjQsJCooRkJGMSlGREY5RjEpRiUiIipGRkYxLyZGREYwRi0vJkZERjRGLS8mRkRGOEYtLyZGRDYjIiIlRi0vJkZENiMiIiZGLQ==</Equation></Text-field>
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<Text-field style="Text" layout="Normal">The related <Hyperlink linktarget="Help:Physics,Weyl" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Weyl scalars</Font></Hyperlink> in the context of the <Hyperlink linktarget="https://en.wikipedia.org/wiki/Newman\342\200\223Penrose_formalism" hyperlink="true" encoding="UTF-8"><Font style="Text" underline="true" foreground="[18,93,153]">Newman-Penrose formalism</Font></Hyperlink></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElV2V5bEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRKHNjYWxhcnNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElV2V5bEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRKHNjYWxhcnNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NicvSSdwc2lfXzBHNiMvSSdfbG9jYWxHJSpwcm90ZWN0ZWRHSS1fbjQ0ODcyNjMyNjRHNiIiIiEvSSdwc2lfXzFHNiMvRidJLV9uNDQ4NzI2MzIzMkdGKkYrL0kncHNpX18yRzYjL0YnSS1fbjQ0ODcyNjMyMDBHRiosJComKUkickdGKiIiJCEiIkkibUdGKiIiIkY7L0kncHNpX18zRzYjL0YnSS1fbjQ0ODcyNjMxNjhHRipGKy9JJ3BzaV9fNEc2Iy9GJ0ktX240NDg3MjYzMTM2R0YqRis=</Equation></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Group labelreference="L64" drawlabel="true" applyint="true" applyrational="true">
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<Text-field style="Text" layout="Normal">These are the 2x2 matrix components of the <Hyperlink linktarget="https://en.wikipedia.org/wiki/Christoffel_symbols" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Christoffel symbols of the second kind</Font></Hyperlink> (that describe, in coordinates, the effects of parallel transport in curved surfaces), when the first of its three indices is equal to 1</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">In Physics, the Christoffel symbols of the first kind are represented by the same object (not two commands) just by taking the first index covariant, as we do when computing with paper and pencil</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSxDaHJpc3RvZmZlbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYqLUkjbW5HRiQ2JFEiMUYnL0Y4USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZDLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRJmFscGhhRicvRjVGS0ZDRkUtRiw2JVElYmV0YUYnRltvRkNGRS1GLDYlUSdtYXRyaXhGJ0Y0RjdGQ0ZDLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRkNGKy8lK2V4ZWN1dGFibGVHRktGQw==">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">One could query the database, directly from the spacetime metrics, about the solutions (metrics) to Einstein's equations related to Levi-Civita, the Italian mathematician</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZ19GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUSVjaXZpRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZ19GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUSVjaXZpRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LzclIiM3IiM7IiIiNyUvUShBdXRob3JzNiI3JlEwQmVydG90dGl+KDE5NTkpRipRLktyYW1lcn4oMTk3OClGKlEzTGV2aS1DaXZpdGF+KDE5MTcpRipRMFJvYmluc29ufigxOTU5KUYqL1EzUHJpbWFyeURlc2NyaXB0aW9uRipRMEVpbnN0ZWluTWF4d2VsbEYqL1E1U2Vjb25kYXJ5RGVzY3JpcHRpb25GKjcjUSxIb21vZ2VuZW91c0Yq</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVFnbl9fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SWduX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fRzYi</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">These solutions can be set in one go from the metrics command, just by indicating the number with which it appears in &quot;Exact Solutions to Einstein's Equations&quot;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">Automatically, everything gets set accordingly; these are the contravariant components of the related Ricci tensor</Text-field>
</Input>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmUmljY2lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1JI21vR0YkNi1RInxpckYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZRLyUrZXhlY3V0YWJsZUdGQkY+Rj4vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGVEY+">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmUmljY2lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1JI21vR0YkNi1RInxpckYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZRLyUrZXhlY3V0YWJsZUdGQkY+Rj4vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGVEY+</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvJkkmUmljY2lHNiZGJi9JK21vZHVsZW5hbWVHRihJKFBoeXNpY3NHRiUvSTFoaWRlbW9kdWxlcHJlZml4R0YoSSV0cnVlR0YmRic2JEkkfGlybXVHRihJJHxpcm51R0YoLUknUlRBQkxFR0YoNiUiNV0ocCl6InlTdVklPS1JJ01BVFJJWEdGKDYjNyY3JiomKUkia0dGKCIiJSEiIiktSSVzaW5oR0YlNiNJInhHRigiIiNGRiIiIUZNRk03JkZNLCQqJEZDRkZGRkZNRk03JkZNRk1GUEZNNyZGTUZNRk0qJkZDRkYpLUkkc2luR0YlNiNJJnRoZXRhR0YoRkxGRkknTWF0cml4R0YlNyMvRi0tRlk2Iy9JJCVpZEdGKEY8</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">One works with the Newman-Penrose formalism frequently using tetrads (local system of references); the Physics subpackage for this is <Hyperlink linktarget="Help:Physics,Tetrads" hyperlink="true"><Font style="Text" underline="true" foreground="[18,93,153]">Tetrads</Font></Hyperlink></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKFRldHJhZHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1GLDYjUSFGJ0Y9RkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKFRldHJhZHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1GLDYjUSFGJ0Y9RkA=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVFmblNldHRpbmd+bG93ZXJjYXNlbGF0aW5+bGV0dGVyc350b35yZXByZXNlbnR+dGV0cmFkfmluZGljZXN+RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn">SWZuU2V0dGluZ35sb3dlcmNhc2VsYXRpbn5sZXR0ZXJzfnRvfnJlcHJlc2VudH50ZXRyYWR+aW5kaWNlc35HNiI=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NictSSVtcm93RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHNiRGJkkoX3N5c2xpYkdGKTYlLUkjbWlHRiU2I1E9YERlZmluZWR+YXN+dGV0cmFkfnRlbnNvcnN+YEYpLUkjbW9HRiVGKS1JKG1mZW5jZWRHRiU2Iy1GLzYjUTdgc2Vlfj9QaHlzaWNzLHRldHJhZHNgRikmSSNlX0c2JkYmL0YoSShUZXRyYWRzRzYlRiYvRihJKFBoeXNpY3NHRisvSTFoaWRlbW9kdWxlcHJlZml4R0YpSSV0cnVlR0YmRkJGLDYkSSJhR0YpSSNtdUdGKSZJJWV0YV9HRjw2JEZGSSJiR0YpJkknZ2FtbWFfR0Y8NiVGRkZLSSJjR0YpJkkobGFtYmRhX0dGPEZO</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NictSSVtcm93RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHNiRGJkkoX3N5c2xpYkdGKTYlLUkjbWlHRiU2I1FjcGBEZWZpbmVkfmFzfnNwYWNldGltZX50ZW5zb3JzfnJlcHJlc2VudGluZ350aGV+TlB+bnVsbH52ZWN0b3Jzfm9mfnRoZX50ZXRyYWR+Zm9ybWFsaXNtfmBGKS1JI21vR0YlRiktSShtZmVuY2VkR0YlNiMtRi82I1E3YHNlZX4/UGh5c2ljcyx0ZXRyYWRzYEYpJkkjbF9HNiZGJi9GKEkoVGV0cmFkc0c2JUYmL0YoSShQaHlzaWNzR0YrL0kxaGlkZW1vZHVsZXByZWZpeEdGKUkldHJ1ZUdGJkZCRiw2I0kjbXVHRikmSSNuX0dGPEZFJkkjbV9HRjxGRSZJJG1iX0dGPEZF</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ny9JKUlzVGV0cmFkRzYiSStOdWxsVGV0cmFkR0YkSTJPcnRob25vcm1hbFRldHJhZEdGJEkvU2ltcGxpZnlUZXRyYWRHRiRJMFRyYW5zZm9ybVRldHJhZEdGJEkjZV9HRiRJJWV0YV9HRiRJJ2dhbW1hX0dGJEkjbF9HRiRJKGxhbWJkYV9HRiRJI21fR0YkSSRtYl9HRiRJI25fR0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L69" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field style="Text" layout="Normal">This is the tetrad related to the book's metric with number 12.16.1</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZV9GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj1GQA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZV9GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj1GQA==</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field style="Text" layout="Normal">One can check these directly; for instance this is the definition of the tetrad, where the right-hand side is the tetrad metric</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZV9GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUStkZWZpbml0aW9uRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZV9GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUStkZWZpbml0aW9uRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LyomJkkjZV9HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShUZXRyYWRzRzYlRicvRilJKFBoeXNpY3NHNiRGJ0koX3N5c2xpYkdGKi9JMWhpZGVtb2R1bGVwcmVmaXhHRipJJXRydWVHRidGMUYwNiRJImFHRipJI211R0YqIiIiJkYlNiRJImJHRipJJHxpcm11R0YqRjcmSSVldGFfR0YmNiRGNUY6</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field style="Text" layout="Normal">This shows that, for the components given by <Label label="L28" view="label" executable="false"></Label>, the definition holds</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" display="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">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</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1QTlTJj55U3VZJT0tSSdNQVRSSVhHRig2IzcmNyYvIiIiRjYvIiIhRjhGN0Y3NyZGNy8hIiJGO0Y3Rjc3JkY3RjdGOkY3NyZGN0Y3RjdGOkknTWF0cml4R0YlNyMtRj42Iy9JJCVpZEdGKEYv</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">One frequently works with a different signature and null tetrads; set that, and everything gets automatically recomputed for the metric 12.16.1 accordingly</Text-field>
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<Group labelreference="L31" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyQvSSpzaWduYXR1cmVHSShfc3lzbGliRzYiSSgrfi1+LX4tR0YmL0ktdGV0cmFkbWV0cmljR0YmPCQvNiQiIiIiIiNGLS82JCIiJCIiJSEiIg==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElZXRhX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiNRIUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElZXRhX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiNRIUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA</Equation></Text-field>
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<Output>
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<Input>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1IVI+OD55U3VZJT0tSSdNQVRSSVhHRig2IzcmNyYvIiIhRjYvIiIiRjhGNUY1NyZGN0Y1RjVGNTcmRjVGNUY1LyEiIkY8NyZGNUY1RjtGNUknTWF0cml4R0YlNyMtRj42Iy9JJCVpZEdGKEYv</Equation></Text-field>
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<Text-field style="Text" layout="Normal">The related 16 Riemann invariant</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoUmllbWFubkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRK2ludmFyaWFudHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoUmllbWFubkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRK2ludmFyaWFudHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ni0vJkkickc2Iy9JJ19sb2NhbEclKnByb3RlY3RlZEdJLV9uNDQ5NTMzNTIwMEc2IjYjIiIhRi0vJkYlNiMiIiIqJClJImtHRisiIiUhIiIvJkYlNiMiIiNGLS8mRiU2IyIiJCwkKiYjRjFGNUYxKUY0IiIpRjZGMS8mSSJ3RzYjL0YoSS1fbjQ0OTUzMzUyMzJHRitGMEYtLyZGRkY5Ri0vJkkibUc2Iy9GKEktX240NDk1MzM1MjY0R0YrRjBGLS8mRk5GOUYtLyZGTkY9Ri0vJkZONiNGNUYtLyZGTjYjIiImRi0=</Equation></Text-field>
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<Text-field style="Text" layout="Normal">The ability to query rapidly, set things in one go, change everything again etc. are at this point fantastic. For instance, these are the metrics by Kaigorodov; next are those published in 1962</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZ19GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUStLYWlnb3JvZG92RidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZ19GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUStLYWlnb3JvZG92RidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZA</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVFnbl9fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SWduX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fRzYi</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LzclIiM3IiNNIiIiNyYvUShBdXRob3JzNiI3JlEyS2FpZ29yb2Rvdn4oMTk2MilGKlEtQ2FoZW5+KDE5NjQpRipRLlNpa2xvc34oMTk4MSlGKlEvT3pzdmF0aH4oMTk4NylGKi9RM1ByaW1hcnlEZXNjcmlwdGlvbkYqUSlFaW5zdGVpbkYqL1E1U2Vjb25kYXJ5RGVzY3JpcHRpb25GKjcjUSxIb21vZ2VuZW91c0YqL1EpQ29tbWVudHNGKjcjUVxyQWxsfm1ldHJpY3N+d2l0aH5fZXBzaWxvbn48Pn4wfmFyZX5lcXVpdmFsZW50fnRvfnRoZX5jYXNlc35fZXBzaWxvbn49fisxLH4tMSx+X2Vwc2lsb25+PX4wfmlzfmFudGktZGVTaXR0ZXJ+c3BhY2VGKg==</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVFnbl9fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SWduX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fRzYi</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYmLUYjNiotSSNtbkdGJDYkUSMxMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYxNiRRIzM1RidGNEY3LUYxNiRRIjFGJ0Y0LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9RjRGNC8lJW9wZW5HUScmbHNxYjtGJy8lJmNsb3NlR1EnJnJzcWI7RictRjg2LVEpJmVxdWFscztGJ0Y0RjsvRj9GPUZBRkNGRUZHRkkvRkxRLDAuMjc3Nzc3OGVtRicvRk9GYW8tRiw2Ji1GIzYqLUYjNiYtSSNtc0dGJDYjUShBdXRob3JzRidGXG8tRiw2Ji1GIzYsLUZqbzYjUTJLYWlnb3JvZG92figxOTYyKUYnRjctRmpvNiNRLUNhaGVufigxOTY0KUYnRjctRmpvNiNRLlNpa2xvc34oMTk4MSlGJ0Y3LUZqbzYjUS9PenN2YXRofigxOTg3KUYnRldGWkY0RjRGZm5GaW5GNEY3LUYjNiYtRmpvNiNRM1ByaW1hcnlEZXNjcmlwdGlvbkYnRlxvLUZqbzYjUSlFaW5zdGVpbkYnRjRGNy1GIzYmLUZqbzYjUTVTZWNvbmRhcnlEZXNjcmlwdGlvbkYnRlxvLUYsNiYtRiM2KC1Gam82I1EsSG9tb2dlbmVvdXNGJ0Y3LUZqbzYjUTFTaW1wbGVUcmFuc2l0aXZlRidGV0ZaRjRGNEZmbkZpbkY0RldGWkY0RjRGZm5GaW5GNA==">LzclIiM3IiNOIiIiNyUvUShBdXRob3JzNiI3JlEyS2FpZ29yb2Rvdn4oMTk2MilGKlEtQ2FoZW5+KDE5NjQpRipRLlNpa2xvc34oMTk4MSlGKlEvT3pzdmF0aH4oMTk4NylGKi9RM1ByaW1hcnlEZXNjcmlwdGlvbkYqUSlFaW5zdGVpbkYqL1E1U2Vjb25kYXJ5RGVzY3JpcHRpb25GKjckUSxIb21vZ2VuZW91c0YqUTFTaW1wbGVUcmFuc2l0aXZlRio=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNnX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYkLUYsNiVRJ2AxOTYyYEYnRjRGNy9GOFEnbm9ybWFsRidGQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZCRisvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0ZC">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNnX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYkLUYsNiVRJ2AxOTYyYEYnRjRGNy9GOFEnbm9ybWFsRidGQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZCRisvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0ZC</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVFnbl9fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SWduX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fRzYi</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" 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<Text-field style="Text" layout="Normal"></Text-field>
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<Group labelreference="L37" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field style="Text" layout="Normal">The related Riemann invariants:</Text-field>
</Input>
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<Group labelreference="L36" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoUmllbWFubkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRK2ludmFyaWFudHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoUmllbWFubkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRK2ludmFyaWFudHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ni0vJkkickc2Iy9JJ19sb2NhbEclKnByb3RlY3RlZEdJLV9uNDUwMDM2ODU3Nkc2IjYjIiIhRi0vJkYlNiMiIiJGLS8mRiU2IyIiI0YtLyZGJTYjIiIkRi0vJkkid0c2Iy9GKEktX240NTAwMzY4NjA4R0YrRjAsJCooIiInRjEpLUkibUdGKzYjSSJ1R0YrRjVGMSlGJUZCISIiRjEvJkY8RjQsJCooRkJGMSlGREY5RjEpRiUiIipGSUZJLyZGRUYwRi0vJkZFRjRGLS8mRkVGOEYtLyZGRTYjIiIlRi0vJkZFNiMiIiZGLQ==</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">To conclude, how many solutions from the book have we already implemented?</Text-field>
</Input>
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<Group labelreference="L79" drawlabel="true" applyint="true" applyrational="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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