inttovec - Maple Help

combinat

 vectoint
 index of vector in canonical ordering
 inttovec
 vector referenced by integer in canonical ordering

 Calling Sequence vectoint(l) inttovec(m, n)

Parameters

 l - list of non-negative integers m - non-negative integer n - non-negative integer

Description

 • These two functions provide a one-to-one correspondence between the non-negative integers and all vectors composed of n non-negative integers.
 • The one-to-one correspondence is defined as follows.  View all vectors of n non-negative integers as exponent vectors on n variables. Therefore, for each vector, there is a corresponding monomial.  Collect all such monomials and order them by increasing total degree.  Resolve ties by ordering monomials of the same degree in lexicographic order. This gives a canonical ordering.
 • Given a vector l of n non-negative integers, the corresponding integer m is its index in this canonical ordering.  The function vectoint(l) computes and returns this integer m.
 • Given a non-negative integer m, the corresponding vector l is the m^th vector in this canonical ordering of vectors of length n.  The function inttovec(m, n) computes and returns this vector l.
 • Here is a sample canonical ordering where n is 3:

 Vector Number Monomial [0,0,0] 0 1 [1,0,0] 1 x [0,1,0] 2 y [0,0,1] 3 z [2,0,0] 4 x^2 [1,1,0] 5 x*y [1,0,1] 6 x*z [0,2,0] 7 y^2 ... ... ...

 • The command with(combinat,vectoint) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{combinat}\right):$
 > $\mathrm{vectoint}\left(\left[1,0,1\right]\right)$
 ${6}$ (1)
 > $\mathrm{inttovec}\left(6,3\right)$
 $\left[{1}{,}{0}{,}{1}\right]$ (2)