SumTools[IndefiniteSum][HomotopySum] - compute closed forms of indefinite sums of expressions containing unspecified functions
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Calling Sequence
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HomotopySum(E, k)
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Parameters
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E
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any algebraic expression
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k
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name, specifies the summation index
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Description
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The HomotopySum command allows for the symbolic summation of expressions containing unspecified functions of a discrete variable. A typical example is HomotopySum(u[k+1]-u[k], k), which returns .
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HomotopySum uses discrete homotopy methods to find an anti-difference of the given expression - see the reeferences at the end.
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Notes
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This command is based on code written by Bernard Deconinck, Michael A. Nivala, and Matthew S. Patterson.
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Examples
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If no anti-difference is found, HomotopySum minimizes the number of terms remaining unsummed, as well as the order of their summation indices.
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The input expression may contain combinations of specified and unspecified functions of the summation index.
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References
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Hereman, W.; Colagrosso, M.; Sayers, R.; Ringler, A.; Deconinck, B.; Nivala, M.; and Hickman, M. "Continuous and Discrete Homotopy Operators with Applications in Integrability Testing." In Differential Equations with Symbolic computation, pp. 255-290. Edited by D. Wang and Z. Zheng. Birkhauser, 2005.
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