ChineseRemainderToolsForIntegralBases(K, R, UP)

padiclib.spad line 88 [edit on github]

• K : FiniteFieldCategory
• R : UnivariatePolynomialCategory(K)
• UP : UnivariatePolynomialCategory(R)

Modular helpers for computing integral bases.

chineseRemainder : (List(UP), List(Record(basis : Matrix(R), basisDen : R, basisInv : Matrix(R))), NonNegativeInteger) -> Record(basis : Matrix(R), basisDen : R, basisInv : Matrix(R))

chineseRemainder(lu, lr, n) is undocumented

factorList : (K, NonNegativeInteger, NonNegativeInteger, NonNegativeInteger) -> List(SparseUnivariatePolynomial(K))

factorList(k, n, m, j) is undocumented

listConjugateBases : (Record(basis : Matrix(R), basisDen : R, basisInv : Matrix(R)), NonNegativeInteger, NonNegativeInteger) -> List(Record(basis : Matrix(R), basisDen : R, basisInv : Matrix(R)))

listConjugateBases(bas, q, n) returns the list [bas, bas^Frob, bas^(Frob^2), ...bas^(Frob^(n-1))], where Frob raises the coefficients of all polynomials appearing in the basis bas to the qth power.