PoslavskySV Rings Versions Save

Bugfix for #66

Bugfix for #65

Bugfix for #63

Fixed bug (#a668655) in Newton polygon method which caused wrong irreducibility test for bivariate polynomials.

Bug fixes and small improvements:

• added possibility to cache all modular inverses for small finite fields (#59)
• switched to libdivide4j v1.2
• compatibility fixes with Java 12
• fix #60

Bugfix release:

• bugfixes in rational functions #45 #46 #49
• fix performance dip of multivariate gcd for equal polynomials https://github.com/PoslavskySV/rings/commit/1e6936aea691f96e39a3d644b11dc4a34cb7e942
• fix some bad cases for univariate factorization over Z #47 (todo: implement LLL based van Hoeij's algorithm in future)
• fix #48

Bugfix release:

• minor bugfix in LeinartDecomposition
• minor bugfix in bivariate MultivariateFactorization
• better Scala API for GroebnerMethods
• other small fixes & improvements
• added -V option to rings.repl (specify Rings version)

This version introduces rigorous support of algebraic number fields and general field extensions (#43):

• Implementation of algebraic number fields (AlgebraicNumberField) via simple (SimpleFieldExtension) and multiple (MultipleFieldExtension) field extensions
• Fully support polynomial GCD, resultants and factorization over algebraic number fields
• Methods for constructing splitting fields (SplittingField(poly))

Various methods from theory of resultants:

• Implementation of different univariate polynomial remainder sequences, subresultant sequences, resultants and discriminants over arbitrary fields (UnivariateResultants)
• Efficient multivariate resultants and discriminants over arbitrary fields by adapting Brown's and Zippel's algorithms for GCD (MultivariateResultants)

Methods related to Groebner bases (GroebnerMethods):

• Special elimination methods GroebnerMethods.eliminate(polys, variable)
• Methods for testing algebraic dependence of polynomials and computing algebraic relations (annihilators) GroebnerMethods.algebraicRelations(polys)
• Computation of Nullstellensatz certificates GroebnerMethods.NullstellensatzCertificate(polys)
• Leinart's partial fraction decomposition of multivariate fractions (GroebnerMethods.LeinartDecomposition(fraction))

Two major improvements:

• improved mathematical expressions IO (#38)
• vastly improved implementation of rationals, including rational function arithmetic (#39)
• minor fixes and improvements

Important bug fix that caused fail of sparse Hensel lifting in many cases.