GcdBasis(R)

muldep.spad line 1 [edit on github]

• R : GcdDomain

Gcd basis provides functions to find structure of multiplicative group (and semigroup) generated by elements of Gcd domain.

gcdBasis : Vector(R) -> Vector(R)

gcdBasis(v) returns basis part of gcdDecomposition(v).

gcdDecomposition : Vector(R) -> Record(basis : Vector(R), transform : Matrix(Integer))

gcdDecomposition(v) returns [b, t] such that elements of b are relatively prime and that v(i) = product(b(j)^(t(j, i)), j=1..n)

gcdDecomposition : Vector(Fraction(R)) -> Record(basis : Vector(R), transform : Matrix(Integer))

gcdDecomposition(v) returns [b, t] such that elements of b are relatively prime and that v(i) = product(b(j)^(t(j, i)), j=1..n)