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 INPUT for all procedures: n by n matrix, whose columns for a frame of vector-fields on \342\204\235^n with coordinates (u[1],...,u[n]) OUTPUT of each procedure: Gamma: tables of structure coefficients for the given frame and Christoffel symbols for the standard connection relative to this frame DiffEq : set of differential equations appearing in the \316\273-system (uses Gamma) AlgRel: set of differential equations appearing in the \316\273-system (uses Gamma) Lambda: solution of the \316\273-system (calls for DiffEq and AlgRel to construct the \316\273-system and attempts to solve it using the standard command pdsolve) Nmatrix: the matrix of algebraic relations and its rank (uses Gamma)
<Text-field style="Heading 1" layout="Heading 1">Procedures:</Text-field> 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 Gamma computes Christoffel symbols and structure coefficients 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 DiffEq computes the differential part of the \316\273-system 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 AlgRel computes the algebraic part of the \316\273-system 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 Lambda uses pdsolve to solve algebro-differential \316\273-system 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 Nmatrix computes the matrix N of algebraic relations and its rank: 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
<Text-field style="Heading 1" layout="Heading 1">Examples:</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Example 1 (with comments)</Text-field> Input must be a matrix. One can list vectors and arrange them in a matrix: 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PiUjUjNHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGKTYkLUkjbW9HRiY2LVEoJm1pbnVzO0YpLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGKS8lJmZlbmNlR1EmZmFsc2VGKS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYpLyUncnNwYWNlR0ZFLUYlNiMtSSVtc3ViR0YmNiUtSSptdmVyYmF0aW1HRiY2I1ElJSJlR0YpLUZONiNRJSUiekdGKS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYp 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 or, equivalently, make a matrix by listing its columns: 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 Procedure Lambda uses "pdsolve" to solve algebro-differential \316\273-system: 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 PCUvLSZJJ2xhbWJkYUc2IjYjIiIkNiUmSSJ1R0YnNiMiIiImRiw2IyIiIyZGLEYoLUkkX0YxR0YnNiMsJkYyRi4qJkYrRi5GL0YuISIiLy0mRiZGLUYqSSRfQzFHRicvLSZGJkYwRipGPA== To see the equations it solves call this procedure with "show" argument 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 LyZJI0VxRzYiNiQiIiIiIiMvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiU2I0YnJkY1RjImRjU2IyIiJEY0RicqJkY3RictRiw2JEYvRjhGJ0YnIiIh LyZJI0VxRzYiNiQiIiIiIiQvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiU2I0YnJkY1NiMiIiMmRjVGMkY0RicqJkY3RictRiw2JEYvRjpGJ0YnIiIh LyZJI0VxRzYiNiQiIiMiIiIvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiVGMiZGNTYjRicmRjU2IyIiJEY2RigqJkY0RigtRiw2JEYvRjhGKEYoIiIh LyZJI0VxRzYiNiQiIiMiIiQvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiU2IyIiIiZGNTYjRicmRjVGMkY4RjcqJkY0RjctRiw2JEYvRjpGN0Y3IiIh LyZJI0VxRzYiNiQiIiQiIiIvLCQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiVGMiZGNTYjIiIjJkY1NiNGJ0Y5ISIiIiIh LyZJI0VxRzYiNiQiIiQiIiMvLCQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiU2IyIiIiZGNUYyJkY1NiNGJ0Y5ISIiIiIh LyZJJ0FsZ1JlbEc2IjYlIiIiIiIjIiIkLCYtJkknbGFtYmRhR0YlNiNGKDYlJkkidUdGJTYjRicmRjFGLiZGMTYjRikhIiItJkYtRjJGL0Yn PCUvLSZJJ2xhbWJkYUc2IjYjIiIjNiUmSSJ1R0YnNiMiIiImRixGKCZGLDYjIiIkSSRfQzFHRicvLSZGJkYxRiotSSRfRjFHRic2IywmRjBGLiomRi9GLkYrRi4hIiIvLSZGJkYtRipGMw== One can also run all intermediate procedures: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY6LUkjbWlHRiQ2JVEmR2FtbWFGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEiUkYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnRjJGMi1JI21vR0YkNi5RIn5GJ0Y9Rj8vJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZVLUYsNiVRKWNvbXB1dGVzRidGPUY/RkEtRiw2JVEsQ2hyaXN0b2ZmZWxGJ0Y9Rj8tRkI2LUZERjJGRUZHRklGS0ZNRk9GUUZTRlYtRiw2JVEoc3ltYm9sc0YnRj1GP0Zobi1GLDYlRi5GPUY/LUZCNi5RIidGJ0Y9Rj9GRUZHRklGS0ZNRk9GUS9GVFEsMC4xMTExMTExZW1GJ0ZWLUYsNiVRInNGJ0Y9Rj9GQS1GQjYvUSRhbmRGJy8lJWJvbGRHRjFGPUY/RkVGR0ZJRktGTUZPRlFGU0ZWRkEtRiw2JVEqc3RydWN0dXJlRidGPUY/RkEtRiw2JVEtY29lZmZpY2llbnRzRidGPUY/RmhuLUYsNiVRImNGJ0Y9Rj8tRkI2LUZhb0YyRkVGR0ZJRktGTUZPRlFGYm9GVkZobkZkb0Yy (only non-zero values are printed). LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmR2FtbWFGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiUkYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGMUYyRjItSSNtb0dGJDYtUSI7RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYnRkFGMg== LyZJJkdhbW1hRzYiNiUiIiIiIiMiIiQhIiI= LyZJJkdhbW1hRzYiNiUiIiMiIiIiIiQhIiI= SSZnYW1tYUc2Ig== DiffEq(R) produces the differential part of the \316\273-system LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnRGlmZkVxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiUkYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiO0YnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y9RkA= LyZJI0VxRzYiNiQiIiIiIiMvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiU2I0YnJkY1RjImRjU2IyIiJEY0RicqJkY3RictRiw2JEYvRjhGJ0YnIiIh LyZJI0VxRzYiNiQiIiIiIiQvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiU2I0YnJkY1NiMiIiMmRjVGMkY0RicqJkY3RictRiw2JEYvRjpGJ0YnIiIh LyZJI0VxRzYiNiQiIiMiIiIvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiVGMiZGNTYjRicmRjU2IyIiJEY2RigqJkY0RigtRiw2JEYvRjhGKEYoIiIh LyZJI0VxRzYiNiQiIiMiIiQvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiU2IyIiIiZGNTYjRicmRjVGMkY4RjcqJkY0RjctRiw2JEYvRjpGN0Y3IiIh LyZJI0VxRzYiNiQiIiQiIiIvLCQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiVGMiZGNTYjIiIjJkY1NiNGJ0Y5ISIiIiIh LyZJI0VxRzYiNiQiIiQiIiMvLCQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUdGJTYjRig2JSZJInVHRiU2IyIiIiZGNUYyJkY1NiNGJ0Y5ISIiIiIh PCgvLCQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJJ2xhbWJkYUc2IjYjIiIiNiUmSSJ1R0YsRi0mRjE2IyIiIyZGMTYjIiIkRjUhIiIiIiEvLCQtRiY2JC0mRitGM0YvRjVGOEY5LywmLUYmNiRGPkYwRi4qJkYyRi5GPEYuRi5GOS8sJi1GJjYkLSZGK0Y2Ri9GMkYuKiZGMEYuLUYmNiRGSUY1Ri5GLkY5LywmLUYmNiRGSUYwRi4qJkYyRi5GTEYuRi5GOS8sJi1GJjYkRilGMkYuKiZGMEYuRiVGLkYuRjk= AlgRel produces the algebraic part of the \316\273-system LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnQWxnUmVsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiUkYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiO0YnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y9RkA= L0knQWxnUmVsRzYiPCMvLCYtJkknbGFtYmRhR0YkNiMiIiI2JSZJInVHRiRGKyZGLzYjIiIjJkYvNiMiIiRGLC0mRipGMUYtISIiIiIh PCMvLCYtJkknbGFtYmRhRzYiNiMiIiI2JSZJInVHNiI2IyIiIiZJInVHNiI2IyIiIyZJInVHNiI2IyIiJCIiIi0mSSdsYW1iZGFHNiI2IyIiIzYlJkkidUc2IjYjIiIiJkkidUc2IjYjIiIjJkkidUc2IjYjIiIkISIiIiIh Nmatrix computes the matrix N and its rank (the first output are rows of the matrix, then follows the matrix, after this its rank. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoTm1hdHJpeEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRIlJGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGPUZA 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
<Text-field style="Heading 2" layout="Heading 2">Gas dynamics</Text-field> u[1]- specific volume (volume per unit mass), u[2]- velocity, u[3] - specific entropy. P(u[1],u[3]) is a given pressure as function of volume and entropy. General case (type IIa non-trivial solution): 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See the article for a general solution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnTGFtYmRhRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRIlJGJ0YvRjIvJStleGVjdXRhYmxlR0YxRjJGMkY9RjI= Error, (in PDEtools/eval/2) numeric exception: division by zero LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Additional examples with non-rich frames</Text-field>
<Text-field style="Heading 3" layout="Heading 3">n=3, a single algebraic relation of type IIa and only trivial solutions</Text-field> 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<Text-field style="Heading 3" layout="Heading 3">n=3, a single algebraic relation of type IIb and non trivial solutions</Text-field> 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnTGFtYmRhRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRIlJGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHRjFGMkYyLUkjbW9HRiQ2LVEiO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0ZBRjI= PCUvLSZJJ2xhbWJkYUc2IjYjIiIiNiUmSSJ1R0YnRigmRiw2IyIiIyZGLDYjIiIkLUkkX0YxR0YnNiMsJiomRi9GKUYtRikhIiIqJClGMEYvRilGKS8tJkYmRi5GKkkkX0MxR0YnLy0mRiZGMUYqRj4= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnQWxnUmVsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiUkYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiOkYnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWRj1GQA== LyZJJ0FsZ1JlbEc2IjYlIiIiIiIkIiIjLCYtJkknbGFtYmRhR0YlNiNGKDYlJkkidUdGJTYjRicmRjE2I0YpJkYxRi5GJy0mRi1GNEYvISIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmR2FtbWFGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiUkYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGMUYyRjItSSNtb0dGJDYtUSI7RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYnRkFGMg== LyZJJkdhbW1hRzYiNiUiIiRGJyIiIkYo LyZJJkdhbW1hRzYiNiUiIiIiIiQiIiNGJw== LyZJJkdhbW1hRzYiNiUiIiRGJyIiIyZJInVHRiU2I0Yn LyZJImNHNiI2JSIiJCIiIiIiIyEiIg== SSZnYW1tYUc2Ig==
<Text-field style="Heading 3" layout="Heading 3">n=3, a single algebraic relation of type IIb and only trivial solutions</Text-field> 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<Text-field style="Heading 3" layout="Heading 3">n=4, three independent algebraic relations, (maximal rank) and hence only trivial solutions</Text-field> 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<Text-field style="Heading 2" layout="Heading 2">Additional examples with rich frames</Text-field>
<Text-field style="Heading 3" layout="Heading 3">n=2 system (eigencurves are hyperbolas and straight lines) </Text-field> 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<Text-field style="Heading 3" layout="Heading 3">n=3 rich orthogonal frame (spherical coordinates) </Text-field> 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<Text-field style="Heading 3" layout="Heading 3">n=3 rich with an algebraic relation (rank N=1) non-trivial solution</Text-field> 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<Text-field style="Heading 3" layout="Heading 3">n=3 rich with two algebraic relations (rank N=2) and hence only trivial solution (eigencurves are lines, circles and spirals)</Text-field> 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