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Re: Algebraic Integers
*To*: mathgroup at smc.vnet.net
*Subject*: [mg28516] Re: Algebraic Integers
*From*: Konstantin L Kouptsov <klk206 at nyu.edu>
*Date*: Tue, 24 Apr 2001 01:48:51 -0400 (EDT)
*Organization*: New York University
*References*: <9bvvjt$3sq@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Thanks to all who replied.
Considering that P can be more complex that I mentioned
(for example 23-sqrt(17)), the solution should not use
N[] in the first place. Here is what I came up with:
P /: N[P, n_:6] := N[23 - Sqrt[17], n];
Unprotect[Less];
Less[a_. + b_. P, c_. + d_. P] :=
LessZero[(a - c) + P (b - d)];
Less[a_, b_. + c_. P] := LessZero[(a - b) - c P];
Less[a_. + b_. P, c_] := LessZero[(a - c) + b P];
Protect[Less];
(* This can be simply N[] or something less trivial *)
LessZero[x_] := N[x, 200] < 0
Unprotect[Min, Max];
Min[x_List] := First[Sort[x, Less]];
Max[x_List] := Last[Sort[x, Less]];
Protect[Min, Max];
Konstantin.
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