Core Algorithms

New and Improved Core Algorithms

Mathematica 8 adds a number of dramatic improvements to its core algorithms, with a new generation of methods for globally solving equations and inequalities, either symbolically or numerically. New symbolic-numeric methods allow you to numerically integrate a wide class of highly oscillatory functions automatically. Mathematica 8 reaches a new high-water mark in exact linear algebra performance, and also includes a number of additions to the world's largest collection of special functions.

  • Solve can solve equations and inequalities over complexes, reals, and integers. »
  • NSolve can solve equations and inequalities over complexes and reals. »
  • Solve and NSolve have new advanced methods for solving transcendental equations.
  • Solve and NSolve have new advanced methods for finding real solutions to high-degree polynomials.
  • New conditionally valid expressions for representing partial functions. »
  • New generation of fast, exact linear algebra. »
  • New hybrid symbolic-numeric method for integrating highly oscillatory functions. »
  • New special functions for probability and statistics. »
Compute with Conditionally Valid Solutions »Find Parametrized Real Solutions of Systems of Equations »Solve Transcendental Equations Numerically »
Solve High-Degree Real Polynomial Equations Numerically »Conditionally Valid Expressions »Fast Determinant Computation for Integer Matrices »
Fast Inverse Computation for Integer Matrices »Fast Solving of Systems of Linear Equations with Integer Coefficients »Fast Null Space Computation for Integer Matrices »
Solve a Numerical Integration Challenge Problem »Integrate Sums, Products, and Compositions of Oscillatory Functions »Integrate Multidimensional Highly Oscillatory Functions »
Compute Binormal Probability over a Polygon »Sublevel Sets for RankedMin »Eigenfunctions of the Laplace Equation »
Compute Values of High-Order Derivatives Directly »Perform Numerical Hankel Transform »

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