NModuleBasis n

qetaqmev.spad line 187

• n: NonNegativeInteger

NModuleBasis(n) represents the generators of an N-submodule of N^n.

empty: () -> %

empty() represents the empty module basis.

insert: (Vector Integer , %) -> %

insert(v, x) returns a new basis z such that z=x if v is already a N-linear combination of the elements of x. Otherwise, z is the union of v with all elements from x that are not an N-multiple of v. assert(v.i>0 for i in 1..n)

members: % -> List Vector Integer

members(x) returns a basis of the (sub-)module such that no element is a N-linear combination of the other elements.

reduce: (Vector Integer , %) -> Vector Integer

reduce(v, x) returns a vector z such that reducible?(z,x) is false and v-z is a N-linear combination of elements from x.

reducible?: (Vector Integer , %) -> Boolean

reducible?(v, x) returns true if the vector v is N-linear combination of elements in x where N is the ring of natural numbers.

sup: % -> Vector Integer

sup(x) returns a minimal (w.r.t reducibility) element that is reducible by every element of x. If x is empty, it returns the zero vector. sup(x) is the supremum (w.r.t. reducibility) of all elements in x.

supSum: % -> Integer

supSum(x) returns the sum of the entries of sup(x).