[Axiom-mail] Lexicographic order

[Jens Axel Søgaard]

Hi all,

Is there a smarter way than the following to write lexorder?(p,q) ?

lexorder?(p,q) ==
  if empty?(variables(p))
  then return ~empty(variables(q))
  else
    vars := members(difference( set(variables( secret1*p + secret2*q)),
                                set([secret1, secret2])))
    a := members(degree( p::DMP(vars,?) ))
    b := members(degree( q::DMP(vars,?) ))
    return negative?( first(a) - first(b) )


My first attempt used:

  vars := sort(members(union(set(variables(p), variables(q)))))

but was surprised to see

 > sort([x,y,z])
 [z,y,x]

 > sort([x,z,y])
 [y,z,x]

and thus made up the secret-trick in order to avoid sort.

--
Jens Axel Søgaard