Fixed and Arbitrary Precision Numerical Fields

Floating-Point Arithmetic

Sage supports arbitrary precision real (RealField) and complex fields (ComplexField). Sage also provides two optimized fixed precision fields for numerical computation, the real double (RealDoubleField) and complex double fields (ComplexDoubleField).

Real and complex double elements are optimized implementations that use the GNU Scientific Library for arithmetic and some special functions. Arbitrary precision real and complex numbers are implemented using the MPFR library, which builds on GMP. In many cases, the PARI C-library is used to compute special functions when implementations aren’t otherwise available.

• Arbitrary precision floating point real numbers using GNU MPFR
• Arbitrary precision floating point complex numbers using GNU MPFR
• Arbitrary precision floating point complex numbers using GNU MPC
• Double precision floating point real numbers
• Double precision floating point complex numbers

Interval Arithmetic

Sage implements real and complex interval arithmetic using MPFI (RealIntervalField, ComplexIntervalField) and FLINT (RealBallField, ComplexBallField).

• Arbitrary precision real intervals using MPFI
• Real intervals with a fixed absolute precision
• Arbitrary precision complex intervals (parent class)
• Arbitrary precision complex intervals
• Arbitrary precision real balls
• Arbitrary precision complex balls

Exact Real Arithmetic

• Lazy real and complex numbers

Indices and Tables

• Index

• Module Index

• Search Page