How substitute ToNumberField by LatticeReduce

• To: mathgroup at smc.vnet.net
• Subject: [mg119891] How substitute ToNumberField by LatticeReduce
• From: Artur <grafix at csl.pl>
• Date: Tue, 28 Jun 2011 07:56:10 -0400 (EDT)

```Dear Mathemtica Gurus,
How to substitute ToNumberField (which reduce Lattice dimension 120) to
procedure LatticeReduce to reduce size of reduced Lattice only to
dimension of 24 if is know that rational non zero coefficients can
occured only in powers divisable by 5.
Best wishes
Artur

ToNumberField[Root[#1^5 - #1 - 1 &, 1],
Root[9094947017729282379150390625 -
80789832281880080699920654296875000 #1^5 -
237192506515554850921034812927246093750 #1^10 +
705139879836163417436182498931884765625 #1^15 -
459824984328944450385570526123046875000 #1^20 +
10487457513893135823309421539306640625 #1^25 -
13478302141651816107332706451416015625 #1^30 +
1217709585276403392553329467773437500 #1^35 +
96420138101358171461105346679687500 #1^40 -
20220763484193313419818878173828125 #1^45 +
1336349922106355488300323486328125 #1^50 -
53762394424955668354034423828125 #1^55 +
1516376166478566884155273437500 #1^60 -
32266834412110710144042968750 #1^65 +
471313578630447387695312500 #1^70 -
4120317118819763183593750 #1^75 + 19549724707421728515625 #1^80 -
66036048919677734375 #1^85 + 470517877197265625 #1^90 -
2778681728515625 #1^95 + 8651930171875 #1^100 -
14638671875 #1^105 + 13671875 #1^110 - 6250 #1^115 + #1^120 &, 1]]

```

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