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Sage Reference Manual

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Multivariate Polynomials and Polynomial Rings

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=============================================

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Sage implements multivariate polynomial rings through several

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backends. The most generic implementation uses the classes

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:class:`sage.rings.polynomial.polydict.PolyDict` and

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:class:`sage.rings.polynomial.polydict.ETuple` to construct a dictionary with

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exponent tuples as keys and coefficients as values.

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Additionally, specialized and optimized implementations over many

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specific coefficient rings are implemented via a shared library interface to

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SINGULAR; and polynomials in the boolean polynomial ring

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.. math::

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    \GF{2}[x_1,...,x_n]/ \langle x_1^2+x_1,...,x_n^2+x_n \rangle.

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are implemented using the PolyBoRi library (cf. :mod:`sage.rings.polynomial.pbori`).

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.. toctree::

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   :maxdepth: 2

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   sage/rings/polynomial/term_order

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   sage/rings/polynomial/multi_polynomial_ring_generic

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   sage/rings/polynomial/multi_polynomial

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   sage/rings/polynomial/multi_polynomial_ring

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   sage/rings/polynomial/multi_polynomial_element

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   sage/rings/polynomial/multi_polynomial_ideal

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   sage/rings/polynomial/multi_polynomial_sequence

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   sage/rings/polynomial/multi_polynomial_libsingular

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   sage/rings/polynomial/multi_polynomial_ideal_libsingular

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   sage/rings/polynomial/polydict

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