The SAGE Manual
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5.2.2.1 FreeAbelianMonoidElement Objects
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The SAGE Manual
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6.1 Infinity
6. Rings and Fields
Subsections
6.1 Infinity
6.1.1
rings.infinity
-
6.1.1.1 Infinity Objects
6.2 The Integer Ring
6.2.1
rings.integer_ring
- The Integer Ring
6.2.1.1 IntegerRing Objects
6.2.2
rings.integer
- Integers
6.2.2.1 Integer Objects
6.3 The Integers Modulo
6.3.1
rings.integer_mod_ring
- Ring of integers modulo n.
6.3.1.1 IntegerModRing_field Objects
6.3.1.2 IntegerModRing_generic Objects
6.3.2
rings.integer_mod
- Element of integers modulo n.
6.3.2.1 IntegerMod Objects
6.4 The Rational Field
6.4.1
rings.rational_field
- The field of rational numbers.
6.4.1.1 RationalField Objects
6.4.2
rings.rational
-
6.4.2.1 Rational Objects
6.5 The Real Numbers
6.5.1
rings.real_field
-
6.5.1.1 RealField Objects
6.5.2
rings.real_field_element
-
6.5.2.1 RealNumber Objects
6.6 The Complex Numbers
6.6.1
rings.complex_field
- Complex numbers
6.6.1.1 ComplexField Objects
6.6.2
rings.complex_number
- A complex number
6.6.2.1 ComplexNumber Objects
6.7 Finite Fields
6.7.1
rings.finite_field
- A finite field
6.7.1.1 FiniteField_ext_pari Objects
6.7.1.2 FiniteField_generic Objects
6.7.1.3 FiniteField_prime_modn Objects
6.7.1.4 RingElement Objects
6.7.2
rings.finite_field_element
- Element of finite field.
6.7.2.1 FiniteFieldElement Objects
6.8 Number Fields
6.8.1
rings.number_field
- Number fields
6.8.1.1 FractionalIdeal Objects
6.8.1.2 NumberField_cyclotomic Objects
6.8.1.3 NumberField_generic Objects
6.8.1.4 NumberField_quadratic Objects
6.8.2
rings.number_field_element
- Number field element
6.8.2.1 NumberFieldElement Objects
6.9 Local Fields
6.9.1
rings.padic_field
- Field Q_p of p-adic numbers.
6.9.1.1 pAdicField_generic Objects
6.9.2
rings.padic
- p-adic numbers
6.9.2.1 pAdic Objects
6.10 Fraction Fields
6.10.1
rings.fraction_field
- Fraction field of any integral domain.
6.10.1.1 FractionField_generic Objects
6.10.2
rings.fraction_field_element
- Fraction field element.
6.10.2.1 FractionFieldElement Objects
6.11 Univariate Polynomial Rings
6.11.1
rings.polynomial_ring
- Univariate Polynomial Rings
6.11.1.1 PolynomialRing_dense_mod_n Objects
6.11.1.2 PolynomialRing_dense_mod_p Objects
6.11.1.3 PolynomialRing_field Objects
6.11.1.4 PolynomialRing_generic Objects
6.11.1.5 PolynomialRing_integral_domain Objects
6.11.2
rings.polynomial_element
- Univariate Polynomial
6.11.2.1 Polynomial Objects
6.11.2.2 Polynomial_dense_mod_n Objects
6.11.2.3 Polynomial_dense_mod_p Objects
6.11.2.4 Polynomial_generic_dense Objects
6.11.2.5 Polynomial_generic_dense_field Objects
6.11.2.6 Polynomial_generic_field Objects
6.11.2.7 Polynomial_generic_sparse Objects
6.11.2.8 Polynomial_generic_sparse_field Objects
6.11.2.9 Polynomial_integer_dense Objects
6.11.2.10 Polynomial_rational_dense Objects
6.12 Quotients of Univariate Polynomial Rings
6.12.1
rings.polynomial_quotient_ring
- Quotients of univariate polynomial rings
6.12.1.1 PolynomialQuotientRing_domain Objects
6.12.1.2 PolynomialQuotientRing_field Objects
6.12.1.3 PolynomialQuotientRing_generic Objects
6.12.2
rings.polynomial_quotient_ring_element
- Elements of quotients of univariate polynomial rings
6.12.2.1 PolynomialQuotientRingElement Objects
6.13 Multivariate Polynomial Rings
6.13.1
rings.multi_polynomial_ring
- Multivariate Polynomials
6.13.1.1 MPolynomialRing_generic Objects
6.13.1.2 MPolynomialRing_polydict Objects
6.13.1.3 MPolynomialRing_polydict_domain Objects
6.13.1.4 MPolynomialRing_polylist Objects
6.13.1.5 MPolynomialRing_polylist_domain Objects
6.13.2
rings.multi_polynomial
- Multivariate polynomial element
6.13.2.1 MPolynomial Objects
6.13.2.2 MPolynomial_polydict Objects
6.13.2.3 MPolynomial_polylist Objects
6.14 Power Series Rings
6.14.1
rings.power_series_ring
- Univariate Power Series Rings
6.14.1.1 PowerSeriesRing_domain Objects
6.14.1.2 PowerSeriesRing_generic Objects
6.14.1.3 PowerSeriesRing_over_field Objects
6.14.2
rings.power_series
- Element of a power series
6.14.2.1 PowerSeries Objects
6.14.2.2 PowerSeries_generic_dense Objects
6.15 Laurent Series Rings
6.15.1
rings.laurent_series_ring
- Laurent series ring
6.15.1.1 LaurentSeriesRing_domain Objects
6.15.1.2 LaurentSeriesRing_field Objects
6.15.1.3 LaurentSeriesRing_generic Objects
6.15.2
rings.laurent_series
- Element of Laurent series ring
6.15.2.1 LaurentSeries Objects
6.16 Ideals of Rings
6.16.1
rings.ideal
- Ideals
6.16.1.1 Ideal_fractional Objects
6.16.1.2 Ideal_generic Objects
6.16.1.3 Ideal_pid Objects
6.16.1.4 Ideal_principal Objects
The SAGE Manual
Previous:
5.2.2.1 FreeAbelianMonoidElement Objects
Up:
The SAGE Manual
Next:
6.1 Infinity
Release 0.8.2, documentation updated on October 22, 2005.
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