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 Real Numbers
  • QQtoRR
  • RRtoRR
  • RealField()
  • RealField_class
  • RealLiteral
  • RealNumber
  • ZZtoRR
  • create_RealField()
  • create_RealNumber()
  • double_toRR
  • int_toRR
  • is_RealField()
  • is_RealNumber()
  • mpfr_get_exp_max()
  • mpfr_get_exp_max_max()
  • mpfr_get_exp_min()
  • mpfr_get_exp_min_min()
  • mpfr_prec_max()
  • mpfr_prec_min()
  • mpfr_set_exp_max()
  • mpfr_set_exp_min()
• Arbitrary Precision Floating Point Complex Numbers
  • ComplexField()
  • ComplexField_class
  • ComplexNumber
  • RRtoCC
  • cmp_abs()
  • create_ComplexNumber()
  • is_ComplexField()
  • is_ComplexNumber()
  • late_import()
  • make_ComplexNumber0()
  • set_global_complex_round_mode()
• Arbitrary Precision Complex Numbers using GNU MPC
  • CCtoMPC
  • INTEGERtoMPC
  • MPComplexField()
  • MPComplexField_class
  • MPComplexNumber
  • MPCtoMPC
  • MPFRtoMPC
  • late_import()
  • split_complex_string()
• Double Precision Real Numbers
  • RealDoubleElement
  • RealDoubleField()
  • RealDoubleField_class
  • ToRDF
  • is_RealDoubleElement()
  • is_RealDoubleField()
• Double Precision Complex Numbers
  • ComplexDoubleElement
  • ComplexDoubleField()
  • ComplexDoubleField_class
  • ComplexToCDF
  • FloatToCDF
  • is_ComplexDoubleElement()
  • is_ComplexDoubleField()

Interval Arithmetic

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

• Arbitrary Precision Real Intervals
  • RealInterval()
  • RealIntervalField()
  • RealIntervalFieldElement
  • RealIntervalField_class
  • is_RealIntervalField()
  • is_RealIntervalFieldElement()
• Real intervals with a fixed absolute precision
  • Factory
  • MpfrOp
  • RealIntervalAbsoluteElement
  • RealIntervalAbsoluteField()
  • RealIntervalAbsoluteField_class
  • shift_ceil()
  • shift_floor()
• Field of Arbitrary Precision Complex Intervals
  • ComplexIntervalField()
  • ComplexIntervalField_class
  • is_ComplexIntervalField()
• Arbitrary Precision Complex Intervals
  • ComplexIntervalFieldElement
  • create_ComplexIntervalFieldElement()
  • is_ComplexIntervalFieldElement()
  • make_ComplexIntervalFieldElement0()
• Arbitrary precision real balls using Arb
  • Data Structure
  • Comparison
  • Classes and Methods
• Arbitrary precision complex balls using Arb
  • Data Structure
  • Comparison
  • Coercion
  • Classes and Methods

Exact Real Arithmetic

• Lazy real and complex numbers
  • ComplexLazyField()
  • ComplexLazyField_class
  • LazyAlgebraic
  • LazyBinop
  • LazyConstant
  • LazyField
  • LazyFieldElement
  • LazyNamedUnop
  • LazyUnop
  • LazyWrapper
  • LazyWrapperMorphism
  • RealLazyField()
  • RealLazyField_class
  • make_element()

Indices and Tables

• Index

• Module Index

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