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) undocumented

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

factorList(k, n, m, j) 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.