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## [Axiom-math] Re: [Axiom-mail] Lexicographic order

 From: Martin Rubey Subject: [Axiom-math] Re: [Axiom-mail] Lexicographic order Date: Mon, 29 Aug 2005 10:28:13 +0200

```Dear Jens,

Although I'm not 100% sure what lexorder? ought to do exactly, you might want
to notice the following:

the first matching type the interpreter finds for [x,y,z] is

(13) -> [x,y,z]

(13)  [x,y,z]
Type: List OrderedVariableList [x,y,z]

which means that in sort([x,z,y]) you are using the order imposed by
OrderedVariableList [x,y,z], which is z < y < x.

So, although

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

is surprising, it shouldn't be ;-) (<- please note the smiley !)

If you say

sort([x,z,y]::List Symbol), you will get the expected output.

I'm not totally sure how you can find out what ordering a domain uses. But very
likely, if its name doesn't contain something like "Ordered", it is the usual
lexicographic order.

Hope this helps,

Martin

Jens Axel Søgaard writes:
> 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
>
>
>
> _______________________________________________
> Axiom-mail mailing list
> address@hidden
> http://lists.nongnu.org/mailman/listinfo/axiom-mail
>

```

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