Symbolic Calculus

Calculus is done using symbolic expressions which consist of symbols and numeric objects linked by operators (functions).

Note

While polynomial manipulation can be done with expressions, it is more efficient to use polynomial ring elements

Using calculus

• Symbolic Computation

• Examples

  • Calculus examples

  • Calculus Tests and Examples

  • Further examples from Wester’s paper

• More about symbolic variables and functions

• Main operations on symbolic expressions

• Assumptions about symbols and functions

• Symbolic Equations and Inequalities

• Symbolic Integration

• Solving ordinary differential equations

• Solving ODE numerically by GSL

• Numerical Integration

• Real Interpolation using GSL

• Transforms

  • Discrete Wavelet Transform

  • Discrete Fourier Transforms

  • Fast Fourier Transforms Using GSL

• Vector Calculus

• Riemann Mapping

• Other calculus functionality

• Complexity Measures

• Units of measurement

Internal functionality supporting calculus

• The symbolic ring

• Subrings of the Symbolic Ring

• Operators

• Classes for symbolic functions

• Functional notation support for common calculus methods

• Factory for symbolic functions

• Internals of Callable Symbolic Expressions

• Conversion of symbolic expressions to other types

• Substitution Maps

• Benchmarks

• Randomized tests of GiNaC / PyNaC

• Access to Maxima methods

• External integrators

• External interpolators

Indices and Tables

• Index

• Module Index

• Search Page