The material below was presented in the "Semantic Representation of Mathematical Knowledge Workshop", February 3-5, 2016 at the Fields Institute, University of Toronto. It does not contain "new material". It however presents the digitizing of mathematical information organized in a way that makes sense for areas of mathematics suitable for constructing databases while, at the same time, suitable for using algorithmic approaches - not databases - when tackling related problems - so that these areas are under constant development.The material also focuses on a cherry-picked collection of Maple functionality, that I think is beautiful, not well know, and seldom focused inter-related as here. The amount of information is big, the subsections are there "closed" (if open, it results in a 50 pages document). To open the subsections to actually see the contents you can either use the corresponding mw worksheet, or preview the corresponding pdf file, both linked at the end.<Text-field style="Heading 1" layout="Heading 1"></Text-field>Digitizing of special functions,differential equations,and solutions to Einstein\342\200\231s equations within a computer algebra systemEdgardo S. Cheb-TerrabPhysics, Differential Equations and Mathematical Functions, MaplesoftEditor, Computer Physics Communications
<Text-field style="Heading 1" layout="Heading 1"></Text-field>Digitizing (old paradigm)
Big amounts of knowledge available to everybody in local machines or through the internet
Take advantage of basic computer functionality, like searching and editing
<Text-field style="Heading 1" layout="Heading 1"></Text-field>Digitizing (new paradigm)
By digitizing mathematical knowledge inside appropriate computational contexts that understand about the topics, one can
a) do an articulated, creative and useful use of this knowledge
b) use the digitized knowledge to generate more and higher level knowledge
<Text-field style="Heading 1" layout="Heading 1"></Text-field>Challenges
1) how to identify, test and organize the key blocks of information, 2) how to access it: the interface, 3) how to mathematically process it to obtain "derived information"<Text-field style="Heading 1" layout="Heading 1"></Text-field>Three examples<Text-field style="Heading 2" layout="Heading 2"><Font size="18" bold="true">Mathematical Functions</Font></Text-field>"Mathematical functions, are defined by algebraic expressions. So consider algebraic expressions in general ..."<Text-field style="Heading 3" layout="Heading 3"><Font bold="true">The FunctionAdvisor (basic)</Font></Text-field>"Supporting information on definitions, identities, possible simplifications, integral forms, different types of series expansions, and mathematical properties in general"<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field>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Summarize about a functionLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEwRnVuY3Rpb25BZHZpc29yRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEmR0FNTUFGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRicvJStleGVjdXRhYmxlR0Y+Rj9GP0ZBRj8=<Text-field style="Heading 1" layout="Heading 1"><Font size="18" style="Text" bold="true">GAMMA</Font></Text-field><Text-field style="Heading 3" layout="Heading 3"><Font style="Text" bold="true" family="DejaVu Sans">describe</Font></Text-field>
More complicated relationships between mathematical functions, computed using Maple internal database and algorithms.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 information returned by the FunctionAdvisor command can be used for further computations: verify the 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The relation between all elementary functions and the pFq hypergeometric function: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 the 'specializations' of the arcsin 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<Text-field bookmark="info" style="Heading 2" layout="Heading 2">General description</Text-field>The FunctionAdvisor command provides information on the following topics.
Like the conversion facility for mathematical functions, the FunctionAdvisor command also works with the concept of function classes and considers assumptions on the function parameters, if any. The FunctionAdvisor command provides information on the following function classes.
The FunctionAdvisor command can be considered to be between a help and a computational special function facility. Due to the wide range of information this command can handle and in order to facilitate its use, it includes two distinctive features:If you call the FunctionAdvisor command without arguments, it returns information that you can follow until the appropriate information displays.If you call the FunctionAdvisor command with a topic or function misspelled, but a match exists, it returns the information with a warning message.You do not have to remember the exact Maple name of each mathematical function or the FunctionAdvisor topic. However, to avoid these messages and all FunctionAdvisor verbosity, specify the optional argument quiet when calling the FunctionAdvisor command from another routine.<Text-field bookmark="bkmrk2" style="Heading 3" layout="Heading 3">References</Text-field>- Cheb-Terrab, E.S. "The function advisor project: A Computer Algebra Handbook of Special Functions", Proceedings of the Maple Summer Workshop, University of Waterloo, Ontario, Canada, 2002.<Text-field style="Heading 3" layout="Heading 3"><Font bold="true">Differential equation representation for generic nonlinear algebraic expressions - their use</Font></Text-field>"Compute differential polynomial forms for a given system of non-polynomial, possibly differential, equations - their use"<Text-field style="Heading 3" layout="Heading 3">The Differential Equations representing arbitrary algebraic expresssions</Text-field>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 ease of reading, these functions are declared to be displayed in a compact way. Also, derivatives are displayed as indexed objects.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Consider the following non-polynomial expression.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 differential polynomial system (DPS) is given by: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The dpolyform routine can handle systems of equations containing arbitrary compositions of most functions known to Maple, including fractional or abstract powers. <Text-field style="Heading 3" layout="Heading 3">Deriving knowledge: ODE solving methods</Text-field>
A useful side effect of this is that, by asking for the DP form of a special function for some very generic arguments, one receives the polynomial differential equation it satisfies. For example,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So, if we can recast a given equation in the form above as to tell the values of 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, we directly know its answer:
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The same for the more general 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<Text-field style="Heading 3" layout="Heading 3">Extending the mathematical language to include the inverse functions</Text-field>The dpolyform command can handle expressions involving more abstract representations as DESol, RootOf or @@. For example, consider the inverse of the dawson function.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 differential polynomial representation of this object is an Abel equation of the 2nd kind which happens to admit symmetries separable by product.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<Text-field style="Heading 3" layout="Heading 3">Solving non-polynomial differential equations by solving polynomial differential equations</Text-field>Finally, it is possible to use dpolyform to solve algebraic (nondifferential) systems as well. As an example of this, consider the following non-polynomial, nondifferential system of equations for the unknowns 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.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Due to the non-trivial non-polynomial expressions involved, the Maple solve command in previous releases failed to solve this problem for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYmUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDY+UTAmQXBwbHlGdW5jdGlvbjtGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRicvJSVib2xkR0Y5L0Y1RjkvJSp1bmRlcmxpbmVHRjkvJSpzdWJzY3JpcHRHRjkvJSxzdXBlcnNjcmlwdEdGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y5RjcvJSlyZWFkb25seUdGOS8lKWNvbXBvc2VkR0Y5LyUqY29udmVydGVkR0Y5LyUraW1zZWxlY3RlZEdGOS8lLHBsYWNlaG9sZGVyR0Y5LyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0Y5L0Y7USdub3JtYWxGJy8lJmZlbmNlR0Y5LyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmBwLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRjRGN0Y6RjdGXm9GN0Zeb0Y3Rl5vRitGN0Zebw== and 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. By using dpolyform you can solve LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEkc3lzRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGMi9GNlEnbm9ybWFsRic= as follows. First compute a differential polynomial form for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEkc3lzRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGMi9GNlEnbm9ybWFsRic=.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, solve LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnRFBfc3lzRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGMi9GNlEnbm9ybWFsRic= using 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This solution to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnRFBfc3lzRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGMi9GNlEnbm9ybWFsRic= includes the solution to sys for some particular values of the integration constants 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 involved. To determine 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, substitute the above into sys.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The next step is to solve LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEmc3lzX0NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyL0Y2USdub3JtYWxGJw== for 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. We must expand LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEmc3lzX0NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyL0Y2USdub3JtYWxGJw== in a series. It is sufficient to find a few terms from which you can get a solution. For computational reasons, use three intermediate steps.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Now solve for 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:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUTFfRW52QWxsU29sdXRpb25zRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJkFzc2lnbjtGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1GLDYlRjZGNEY3Rj5GKy8lK2V4ZWN1dGFibGVHRkJGPg==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where, by convention, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlElX1oxfGlyRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGMi9GNlEnbm9ybWFsRic= is an integer (see solve). Finally, the solution above leads to the solution for the nondifferential LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEkc3lzRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGMi9GNlEnbm9ybWFsRic=, by evaluating sol_DP_sys at these values of the integration constants. To see this, take for instance the solution containing the imaginary 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This solution can be verified by substituting into LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEkc3lzRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGMi9GNlEnbm9ybWFsRic=.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field bookmark="bkmrk1" style="Heading 3" layout="Heading 3">References</Text-field>- Cheb-Terrab, E.S. "Special functions in Computer Algebra, " Special Functions in the Digital Age (IMA 2002) Minneapolis, USA.- Cheb-Terrab, E.S. "ODEs, PDEs and Special Functions", presentation, University of Cantabria, Spain, June 2013.<Text-field style="Heading 3" layout="Heading 3"><Font bold="true">Branch Cuts of algebraic expressions</Font></Text-field>"Algebraically compute, and visualize, the branch cuts of a given arbitrary mathematical expression"<Text-field bookmark="examples" style="Heading 3" layout="Heading 3">Examples</Text-field>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 about the cuts of an algebraic expression?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A classic example in the theory of branch cut calculation is that of Kahan's teardrop: 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field bookmark="bkmrk1" style="Heading 3" layout="Heading 3">References</Text-field>- Cheb-Terrab, E.S., England M., Bradford R., Davenport J.H., Wilson, D. "Branch cuts of algebraic expressions", ACM Communications in Computer Algebra 48:1 pp. 24-27, ACM, 2014.- Cheb-Terrab, E.S. "The function wizard project: A Computer Algebra Handbook of Special Functions". Proceedings of the Maple Summer Workshop, University of Waterloo, Ontario, Canada, 2002.<Text-field style="Heading 2" layout="Heading 2"><Font bold="true">Algebraic expresssions in terms of specified functions</Font></Text-field>"A conversion network for mathematical expressions, allowing to rewrite algebraic expressions in terms of different functions in flexible ways"<Text-field bookmark="examples" style="Heading 3" layout="Heading 3">Examples</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk=Start with the error 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5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special functions satisfy identities relating contiguous values of their parameters. These identities can also be computed as "conversions", for instance,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 "rule conversions" can be requested at once and performed in a specified order; for instance, consider the following expression: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 converting it to 'KummerU' and applying rules for normalizing the first and second indices, here respectively called a and b, and then mixing them, you obtain varied representations for the same expression.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A further manipulation actually shows the expression was always equal to zero :)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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field bookmark="info" style="Heading 3" layout="Heading 3">General description</Text-field>The functions to which you can convert - the second argument could be one of these - are:
When a function class name is given as second argument the routines attempt to express expr using any of the functions of that class. The function classes understood by convert are:
* (note spaces between words are filled with _ )Despite the large number of function classes, most of the functions of mathematical physics belong to one of the three hypergeometric classes: 2F1, 1F1, and 0F1 where these three classes also include as particular cases all the elementary functions (trig, hyperbolic trig, their arcs, exp, and ln).<Text-field bookmark="bkmrk1" style="Heading 4" layout="Heading 4">The Optional Arguments</Text-field>The conversion routines accept an optional extra argument indicating a rule; it could be one rule or a sequence of them:
"raise a","lower a","normalize a","raise b","lower b","normalize b","raise c","lower c","normalize c","mix a and b","1F1 to 0F1","0F1 to 1F1""quadratic 1","quadratic 2","quadratic 3""quadratic 4","quadratic 5","quadratic 6""2a2b","raise 1/2","lower 1/2"
<Text-field bookmark="bkmrk2" style="Heading 3" layout="Heading 3">References</Text-field>- Cheb-Terrab, E.S. "The function advisor project: A Computer Algebra Handbook of Special Functions", Proceedings of the Maple Summer Workshop, University of Waterloo, Ontario, Canada, 2002.<Text-field style="Heading 2" layout="Heading 2"><Font bold="true">Symbolic differentiation of algebraic expressions</Font></Text-field>"Perform symbolic differentiation by combining different algebraic techniques, including functions of symbolic sequences and Fa\303\240 di Bruno's formula"<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field>A power where the exponent is linear in the differentiation variable, a relatively easy problem, can be in a databaseLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk=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More complicated, consider the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEjdGhGJ0YyRjVGOEYyRjVGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGNS9GOVEnbm9ybWFsRic= power of a generic function; the corresponding symbolic derivative can be mapped into a sum of symbolic derivatives of powers of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEiekYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= with lower 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For LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1GOTYuUSI9RidGMkY8Rj5GQEZCRkRGRkZIRkovRk1RLDAuMjc3Nzc3OGVtRicvRlBGVUY4LUYsNiZRI2xuRicvRjBGNEYyRjxGMkY8 this result can be expressed using Stirling numbers of the first 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The case of the MeijerG function of an arbitrary number of 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Not only the mathematics of this result is correct: the object returned is actually computable (for given concrete values of n, p, m and q)Finally, the "holy grail" of this problem: the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEjdGhGJ0YyRjVGOEYyRjVGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGNS9GOVEnbm9ybWFsRic= derivative of a composite function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEiZ0YnRi9GMkY1LUY5NiUtRiM2Ji1GLDYmUSJ6RidGL0YyRjVGMi8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvRjZRJ25vcm1hbEYnRjJGSkYyRkdGSkYyRkpGMkZHRko= - this always-unreachable implementation of Faa di Bruno formula. Building on top of the basic blocks of knowledge, it Faa di Bruno is now a new, higher level, basic block: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Note the symbolic sequence of symbolic order derivatives of lower degree, both of of f and g, also within the arguments of the IncompleteBellB function. This is a very abstract formula ... To see this at work, consider, for instance, a case where the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEjdGhGJ0YyRjVGOEYyRjVGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGNS9GOVEnbm9ybWFsRic= derivatives of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEiekYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1GLDYjUSFGJ0YyRkA= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEiekYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= can both be computed, say 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Take for instance LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjNGJ0YyRjxGMkY8LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElZXZhbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYqLUYsNiNRIUYnLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNRZ2JtLy1JJiVkaWZmRzYiNiQtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYqJkkmYWxwaGFHNiIiIiJJInpHNiIiIiIiIiJJJWJldGFHNiIiIiItSSIkRyUqcHJvdGVjdGVkRzYkSSJ6RzYiSSJuRzYiLUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiZJJmFscGhhRzYiIiIiSSJ6RzYiIiIiIiIiSSViZXRhRzYiIiIiIiIiKigjIiIiIiIjIiIiSSRfazJHNiIiIiJJI1BpRyUqcHJvdGVjdGVkRyIiIiIiIiIiIi1JMEluY29tcGxldGVCZWxsQkdJKF9zeXNsaWJHNiI2JUkibkc2IkkkX2syRzYiLUkiJEclKnByb3RlY3RlZEc2JComLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsKComSSZhbHBoYUc2IiIiIkkiekc2IiIiIiIiIkklYmV0YUc2IiIiIiooIyIiIiIiIyIiIkkkX2oxRzYiIiIiSSNQaUclKnByb3RlY3RlZEciIiIiIiIiIiIpSSZhbHBoYUc2IkkkX2oxRzYiIiIiL0kkX2oxRzYiOyIiIiwoSSJuRzYiIiIiSSRfazJHNiIhIiIiIiIiIiIiIiIvSSRfazJHNiI7IiIhSSJuRzYiRicvJSthY3Rpb250eXBlR1E7bWFwbGVzb2Z0LmNvbTpsYWJlbChMMjY1NylGJy8lJXZpZXdHUSZsYWJlbEYnLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZSLyUqc3ltbWV0cmljR0ZSLyUobGFyZ2VvcEdGUi8lLm1vdmFibGVsaW1pdHNHRlIvJSdhY2NlbnRHRlIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJuRidGL0YyLUZLNi1RIj1GJ0ZORlAvRlRGUkZVRldGWUZlbkZnbi9Gam5RLDAuMjc3Nzc3OGVtRicvRl1vRmdvLUkjbW5HRiQ2JFEiM0YnRk4vJStleGVjdXRhYmxlR0ZSRk5GTkZdcEZOLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmdmFsdWVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUVthbS8tSSYlZGlmZkc2IjYmLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiZJJmFscGhhRzYiIiIiSSJ6RzYiIiIiIiIiSSViZXRhRzYiIiIiSSJ6RzYiSSJ6RzYiSSJ6RzYiLUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiZJJmFscGhhRzYiIiIiSSJ6RzYiIiIiIiIiSSViZXRhRzYiIiIiIiIiKigjIiIiIiIjIiIiSSRfazJHNiIiIiJJI1BpRyUqcHJvdGVjdGVkRyIiIiIiIiIiIi1JMEluY29tcGxldGVCZWxsQkdJKF9zeXNsaWJHNiI2JSIiJEkkX2syRzYiLUkiJEclKnByb3RlY3RlZEc2JComLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsKComSSZhbHBoYUc2IiIiIkkiekc2IiIiIiIiIkklYmV0YUc2IiIiIiooIyIiIiIiIyIiIkkkX2oxRzYiIiIiSSNQaUclKnByb3RlY3RlZEciIiIiIiIiIiIpSSZhbHBoYUc2IkkkX2oxRzYiIiIiL0kkX2oxRzYiOyIiIiwmIiIlIiIiSSRfazJHNiIhIiIiIiIvSSRfazJHNiI7IiIhIiIkRicvJSthY3Rpb250eXBlR1E7bWFwbGVzb2Z0LmNvbTpsYWJlbChMMjY1OClGJy8lJXZpZXdHUSZsYWJlbEYnRjovJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGTUZKRk0=The two sides of this equation are 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<Text-field bookmark="bkmrk2" style="Heading 3" layout="Heading 3">References</Text-field>- Cheb-Terrab, E.S. "The function advisor project: A Computer Algebra Handbook of Special Functions", Proceedings of the Maple Summer Workshop, University of Waterloo, Ontario, Canada, 2002.- Cheb-Terrab, E.S.; von B\303\274low, Katherina; "Nth order derivatives and Faa di Bruno formula", Mapleprimes blog, August 2015.<Text-field style="Heading 1" layout="Heading 1">Ordinary Differential Equations</Text-field>"Beyond the concept of a database, classify an arbitrary ODE and suggest solution methods for it"<Text-field bookmark="info" style="Heading 3" layout="Heading 3">General description</Text-field>Given an ODE, the odeadvisor command's main goal is to classify it according to standard text books (see dsolve,references), and to display a help page including related information for solving it .
First order ODEs
The following links point to help pages containing details of the implementation of specific ODE solving algorithms:
First order Abel ODEsFirst order symmetry patternsAlgorithms for first order ODEsAlgorithms for Linear ODEsFactorization of Linear ODEsIntegrating Factors for Linear ODEsAlgorithm for fully exact Linear ODEsIntegrating Factors for 2nd order Non-Linear ODEsAlgorithms for exact solutions for ODEs of all ordersdsolve in EducationHypergeometric solutions to second order linear ODEs
<Text-field bookmark="examples" style="Heading 3" layout="Heading 3">Examples</Text-field>Kamke's ODE 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field bookmark="bkmrk1" style="Heading 3" layout="Heading 3">References</Text-field>- Kamke, E. Differentialgleichungen: Losungsmethoden und Losungen. New York: Chelsea Publishing Company, 1959.- Zwillinger, D. Handbook of Differential Equations. 2d ed. Orlando, Florida: Academic Press, 1992.- Cheb-Terrab, E.S.; Duarte, L.G.S.; and da Mota, L.A.C.P. "Computer Algebra Solving of First Order ODEs Using Symmetry Methods." Computer Physics Communications. Vol. 101. (1997): 254.<Text-field style="Heading 1" layout="Heading 1">Exact Solutions to Einstein's equations</Text-field>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"The authors of "Exact solutions toEinstein's equations" reviewed more than 4,000 papers containing solutions to Einstein\342\200\231s equations in the general relativity literature, organized the whole material into chapters according to the physical properties of these solutions. These solutions are key in the area of general relativity and are now all digitized"
The ability to search the database according to the physical properties of the solutions, their classification, or just by parts of keywords (old paradigm) changes the game. More important, within a computer algebra system this knowledge becomes alive (new paradigm).
The solutions are turned active by a simple call to one commend, called the g_ spacetime metric.Everything else gets automatically derived and set on the fly (Christoffel symbols , Ricci and Riemann tensors orthonormal and null tetrads, etc.)Almost all of the mathematical operations one can perform on these solutions are implemented as commands in the Physics and DifferentialGeometry packages.All the mathematics within the Maple library are instantly ready to work with these solutions and derived mathematical objects. Finally, in the Maple PDEtools package, we have all the mathematical tools to tackle the equivalence problem around these solutions. <Text-field style="Heading 3" layout="Heading 3">Examples</Text-field>Load Physics, set the metric to be LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEuU2Nod2FyenNjaGlsZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiJ0YnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictRiw2JlEic0YnRi9GMkY1Ri9GMkY1 solution (and everything else automatically) in one 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And that is all we do. All of the tensor components of the general relativity tensors related to this solution got derived automatically, on the fly. For instance this is the definition (in terms of Christoffel symbols) of the Riemann tensor followed by its 16 invariants using the formulas by Carminati and McLenaghanLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoUmllbWFubkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRK2RlZmluaXRpb25GJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoUmllbWFubkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRK2ludmFyaWFudHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=The related Weyl scalars in the context of the Newman-Penrose formalismLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSVXZXlsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNiQtRiw2JVEyc2NhbGFyc2RlZmluaXRpb25GJ0Y0RjcvRjhRJ25vcm1hbEYnRkIvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGQkYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGQg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElV2V5bEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRKHNjYWxhcnNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9RkA=The four Killing vectors defining transformations that leave the spacetime metric solution 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 are the 2x2 matrix components of the Christoffel symbols of the second kind (that describe, in coordinates, the effects of parallel transport in curved surfaces), when the first of its three indices is equal to 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This is the tetrad related to the book's metric with number 12.16.1LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKFRldHJhZHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjpGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVkY9RkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZV9GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj1GQA==One can check these things directly; for instance this is the definition of the tetrad, where the right-hand side is the tetrad metricLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZV9GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUStkZWZpbml0aW9uRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZAThis shows that, for the components given by , the definition 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 where are Einstein's equations?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 expression on the left represents the curvature of spacetime as determined by the metric; the expression on the right represents the matter/energy content of spacetime. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpRWluc3RlaW5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUStkZWZpbml0aW9uRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZASubstituting in 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And 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the components:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiNRIUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZAOne could query the database, directly from the spacetime metrics command (g_), about the solutions (metrics) to Einstein's equations related to Levi-Civita, the Italian mathematicianLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZ19GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUSVjaXZpRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUZAThese solutions can be set in one go from the metrics command, just by indicating the number with which it appears in the "Exact Solutions to Einstein's Equations" book.The ability to query rapidly, set things in one go, change everything again etc. are at this point fantastic. The search can also be done visually, by properties.
Example: Search for solutions in the database that are of Pure Radiation type, with Petrov Type "D", Plebanski-Petrov Type "O" and that have Isometry Dimension equal to 1: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Set the solution and everything related in one 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100% of the solutions collected in Exact Solutions to Einstein's Field Equations were digitizedThe Physics package has 76 computational commands to work with these spacetime metric solutions, plus a programming language for Physics with 175 commandsThe DifferentialGeometry package has 289 commands to work with these solutionsThe PDEtools package has other 56 commands to tackle diverse aspects of the equivalence problem for these solutions
Concluding remark, how many solutions are in the 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bookmark="bkmrk1" style="Heading 3" layout="Heading 3">References</Text-field>- Landau, L.D., and Lifshitz, E.M. The Classical Theory of Fields, Course of Theoretical Physics Volume 2, fourth revised English edition. Elsevier, 1975.- Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C. Herlt, E. Exact Solutions of Einstein's Field Equations, Cambridge Monographs on Mathematical Physics, second edition. Cambridge University Press, 2003.- Cheb-Terrab, E.S. "Exact solutions to Einstein's equations", Mapleprimes blog, October 2015.- Cheb-Terrab, E.S. "The Physics project at Maplesoft", Mapleprimes blog, July 2013.TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc4MzEwMTg3MzEwWCwlKWFueXRoaW5nRzYjJSpzeW1tZXRyaWNHNiJbZ2whIiYhISEjKyIlIiUqJiUickciIiIsJkYpISIiJSJtRyIiI0YsIiIhLCQqJEYpRi5GLEYvRi8sJComRilGLi1JJHNpbkc2JCUqcHJvdGVjdGVkRyUoX3N5c2xpYkc2IyUmdGhldGFHRi5GLEYvRi9GLyomLCZGKUYqRi0hIiNGKkYpRiw2Ig==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc4MzEwMTg3NDYyWCwlKWFueXRoaW5nRzYjJSpzeW1tZXRyaWNHNiJbZ2whIiYhISEjKyIlIiUqKCwqKiQtJSJtRzYjJSJ1RyIiJCIiIyooRitGMCUkZXRhRyIiIiUickdGMyEiJyooRjRGMHonNiQlImJHRjJdW1tbW1tbW1tbc0Y1W1tbW1tdW1tbW29GM0YzRitGMyEiIiomRjRGL3opNiVGOSUiZEdGMl5bW1tbW1tbW1tbW24hIiNcW1tbW1tbW1xbW1ttRjNbW1tbXFtbW1tbW1tsRjNGM0YzRjNGNEY6RitGPywkKiZGNEYwRitGOkY6KiZGNEYwRjxGOkY6IiIhRkNGQ0ZDRkMqJkY0RjBGPEYzNiI=