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Building on Mathematica's long-standing strength in special functions, and on a major mathematical and algorithmic breakthrough made at Wolfram Research, Mathematica 7 introduces new kinds of symbolic objects that represent global solutions to differential and difference equations. These objects dramatically generalize traditional special functions and sequences—and for the first time allow symbolic methods to be broadly used in handling solutions to arbitrary differential and difference problems.
- General symbolic representation of solutions to linear differential equations. »
- General symbolic representation of solutions of linear difference equations. »
- General symbolic representation of holonomic functions and sequences.
- Support for algebraic operations on differential and difference roots.
- Efficient numerical evaluation of differential and difference roots.
- Significant extension of closed-form results from equation solvers and calculus operations.
- Systematic reduction of special functions and sequences to differential and difference roots. »
- Integration, differentiation, summation and other operations on differential and difference roots.
- Systematic identity proving for holonomic functions and sequences.