A1BrouwerDegrees : Table of Contents

• A1BrouwerDegrees -- package for working with A1-Brouwer degree computations
• addGW -- the direct sum of two Grothendieck-Witt classes
• diagonalizeViaCongruence -- diagonalizes a symmetric matrix via congruence
• getAnisotropicDimension -- returns the anisotropic dimension of a symmetric bilinear form
• getAnisotropicDimensionQQp -- returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers
• getAnisotropicPart -- returns the anisotropic part of a Grothendieck-Witt class
• getBaseField -- the base field of a Grothendieck-Witt class
• getDiagonalClass -- produces a diagonalized form for any Grothendieck-Witt class, with simplified terms on the diagonal
• getDiagonalEntries -- extracts a list of diagonal entries for a GrothendieckWittClass
• getGlobalA1Degree -- computes the global A1-Brouwer degree of a list of n polynomials in n variables over a field k
• getHasseWittInvariant -- computes the Hasse-Witt invariant at a prime p for the quadratic form of the Grothendieck-Witt class
• getHilbertSymbol -- computes the Hilbert symbol of two rational numbers at a prime
• getHilbertSymbolReal -- computes the Hilbert symbol of two rational numbers over the real numbers
• getIntegralDiscriminant -- computes the integral discriminant for a rational symmetric bilinear form
• getLocalA1Degree -- computes a local A1-Brouwer degree of a list of n polynomials in n variables over a field k at a prime ideal in the zero locus
• getLocalAlgebraBasis -- produces a basis for a local finitely generated algebra over a field k
• getMatrix -- the underlying matrix of a Grothendieck-Witt class
• getPadicValuation -- p-adic valuation of a rational number
• getRank -- calculates the rank of a symmetric bilinear form
• getRelevantPrimes -- outputs a list containing all primes p where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial
• getSignature -- computes the signature of a symmetric bilinear form over the real numbers or rational numbers
• getSumDecomposition -- produces a simplified diagonal representative of a Grothendieck-Witt class
• getSumDecompositionString -- produces a simplified diagonal representative of a Grothendieck-Witt class
• getWittIndex -- returns the Witt index of a symmetric bilinear form
• GrothendieckWittClass -- a new type, intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a base field
• isAnisotropic -- determines whether a Grothendieck-Witt class is anisotropic
• isIsomorphicForm -- determines whether two Grothendieck-Witt classes over CC, RR, QQ, or a finite field of characteristic not 2 are isomorphic.
• isIsotropic -- determines whether a Grothendieck-Witt class is isotropic
• makeDiagonalForm -- the Grothendieck-Witt class of a diagonal form
• makeGWClass -- the Grothendieck-Witt class of a symmetric matrix
• makeHyperbolicForm -- the Grothendieck-Witt class of a hyperbolic form
• makePfisterForm -- the Grothendieck-Witt class of a Pfister form
• multiplyGW -- the tensor product of two Grothendieck-Witt classes