# GcdBasis R¶

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 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)
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)