A1BrouwerDegrees : Table of Contents

• A1BrouwerDegrees -- for working with A1-Brouwer degree computations
• anisotropicDimension -- returns the anisotropic dimension of a symmetric bilinear form
• anisotropicDimensionQp -- returns the anisotropic dimension of a rational symmetric bilinear form over the p-adics
• anisotropicPart -- returns the anisotropic part of a Grothendieck Witt class
• baseField -- the base field of a Grothendieck Witt class
• congruenceDiagonalize -- diagonalizing a symmetric matrix via congruence
• diagonalClass -- produces a diagonalized form for any Grothendieck-Witt class, with simplified terms on the diagonal
• diagonalEntries -- extracts a list of diagonal entries for a GrothendieckWittClass
• diagonalForm -- the Grothendieck-Witt class of a diagonal form
• globalA1Degree -- computes a global A1-Brouwer degree of a list of n polynomials in n variables over a field k
• GrothendieckWittClass -- a new type, intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a base field
• gwAdd -- the direct sum of two Grothendieck-Witt classes
• gwClass -- the Grothendieck Witt class of a symmetric matrix
• gwIsomorphic -- determines whether two Grothendieck Witt classes are isomorphic over CC, RR, QQ, or a finite field.
• gwMultiply -- the tensor product of two Grothendieck-Witt classes
• HasseWittInvariant -- outputs the Hasse-Witt invariant for a prime p for the quadratic form of the Grothendieck-Witt class
• HilbertSymbol -- computes the Hilbert symbol of two integers or rational numbers at a prime
• HilbertSymbolReal -- computes the Hilbert symbol of two rational numbers over the reals
• hyperbolicForm -- the Grothendieck-Witt class of a hyperbolic form
• integralDiscriminant -- outputs an integral discriminant for a rational symmetric bilinear form
• isAnisotropic -- determines whether a Grothendieck-Witt class is anisotropic
• isIsotropic -- determines whether a Grothendieck-Witt class is isotropic
• localA1Degree -- 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
• localAlgebraBasis -- produces a basis for a local finitely generated algebra over a field k
• padicValuation -- p-adic valuation of a rational number or integer
• PfisterForm -- the Grothendieck-Witt class of a Pfister form
• relevantPrimes -- outputs a list of primes at which the Hasse-Witt invariants of a symmetric bilinear form may be non-trivial
• signature -- outputs the signature of a symmetric bilinear form over the real or rational numbers
• sumDecomposition -- produces a simplified diagonal representative of a Grothendieck Witt class
• sumDecompositionString -- produces a simplified diagonal representative of a Grothendieck Witt class
• WittIndex -- returns the Witt index of a symmetric bilinear form