A Linear Space Algorithm for Computing the Hermite Normal Form Daniele Micciancio Bogdan Warinschi University of California, San Diego 9500 Gilman Drive, Mail Code 0114 La Jolla, California 92093 University of California, San Diego 9500 Gilman Drive, Mail Code 0114 La Jolla, California 92093 [email protected] [email protected] =R8-1 *43381eM;2/3Z-*$5 / 38-4J2/-R8O/; :27;27 -2 LN33S-2/w?3 52/-8- <;a3-w:-BV9!f03c r438 eM;2D2/:-27 =R93=?8-946U=R8-=R$q^2/wMd:-M4?;? -2 a$[OL¢?R=Re33:4,;? -2-V£$q/ J 3;,K¤ 46-27 r8-/? !h3: 29J=wMS2/6/_`33=.r2/8-S8-:O0 t;,K]2/a_ + a!¥8=k462/=R+ l=2/3;)=R8- b2/3Z-1$ 438e:;2-K¤ e:;:-d 3:v,8--2/2nARl Sf! 8- d. 3:3b/ 38-.OG8=n460? /-3;S2/J8-f8-2/_ 3KQ=>,33?JR-R25$-M4?;? -2c$[ <;8-Fw3-2r$ 2/-8- t;dO =V ABSTRACT "!#$%'&)(*&+, - . /012/3 546-27 98/-, 93: 2 <;38=33;1->?-2 @AB&DCDFEHGI2/J8:KMLNO%EP32Q46:JR5:S T-, /3-2U$J 3 Q /0WVYX% ::63;:J3 %3 Q2/3Z-5A[LN38O 32@AB&]\D3:TE^G/GOK 32N2/J8-943=LF_`a8=a=2/;b46-8-cS2/_ 32"2/2/F3d8 38-FLN-5LTe?3943f3, -" /38--2-V g 326QLT-2/-, F9Lh i$[T8-: 3f bF!jLN38dk2/-2S;+@AB& \ 3:TE^Gc2/J8- ABBV :V3KY-2/2/? ;l 229 3 c2/3Z-=GOVnmo-l3_ ? -Rk2/3p27 dJRdRo3: 2n$qb, -JRk /0 r 3338= 3]KQ:3: s2S b2n 38-30?_ t;p$% b27; 38=3;'$B27 -27 1AB4 2/8-n3u8-3-, OGS_ 2-Vpmv32/v2/-, *-27 383:3 s$[! 8d3-wM22/427 d, ]2/6-=RaLN-aa:adJR:; -Od =R3 N. /38--2-V 1. 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