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SumTools[IndefiniteSum][HomotopySum] - compute closed forms of indefinite sums of expressions containing unspecified functions
Calling Sequence
HomotopySum(E, k)
Parameters
E
-
any algebraic expression
k
name, specifies the summation index
Description
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 .
HomotopySum uses discrete homotopy methods to find an anti-difference of the given expression - see the reeferences at the end.
Notes
This command is based on code written by Bernard Deconinck, Michael A. Nivala, and Matthew S. Patterson.
Examples
If no anti-difference is found, HomotopySum minimizes the number of terms remaining unsummed, as well as the order of their summation indices.
The input expression may contain combinations of specified and unspecified functions of the summation index.
See Also
SumTools, SumTools[IndefiniteSum]
References
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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