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Transcendental Roots

Building on a mathematical and algorithmic breakthrough made at Wolfram Research, Mathematica 7 introduces full symbolic coverage of roots of transcendental functions. The systematic treatment of traditional algebraic equations based on polynomials was a central achievement of nineteenth century mathematics. Until now, transcendental equations have mostly been treated on a case-by-case basis. Mathematica 7 for the first time allows systematic treatment of transcendental equations, providing exact representations of roots in a symbolic form suitable for general manipulation, and yielding validated global numerical results to any degree of precision.
  • Solutions to arbitrary exp, log equations over the reals.
  • Solutions to arbitrary bounded trigonometric equations.
  • Solutions to bounded equations involving special functions.
  • Solutions to arbitrarily nested transcendental equations.
  • General symbolic representation of transcendental equation roots. »
  • Fully validated root sets for all equations involving elementary functions.
  • Efficient arbitrary-precision numerical evaluation of transcendental roots.
  • General algorithm for solving univariate holomorphic equations over bounded regions.
  • Provable decidability achieved by interval arithmetic and symbolic methods.
  • Full integration with Reduce and other Mathematica functions. »
 
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