`lex_hensel', `lex_tl', `tolex', `tolex_d', `tolex_tl'
------------------------------------------------------

lex_hensel(PLIST,VLIST1,ORDER,VLIST2,HOMO)
lex_tl(PLIST,VLIST1,ORDER,VLIST2,HOMO)
     :: Ѵˤ뼭񼰽֥ʴη׻

tolex(PLIST,VLIST1,ORDER,VLIST2)
tolex_d(PLIST,VLIST1,ORDER,VLIST2,PROCS)
tolex_tl(PLIST,VLIST1,ORDER,VLIST2,HOMO)
     :: ֥ʴϤȤ,
     Ѵˤ뼭񼰽֥ʴη׻

RETURN
     ꥹ

PLIST, VLIST1, VLIST2, PROCS
     ꥹ

ORDER
     , ꥹȤޤϹ

HOMO
     ե饰

   * ɸ饤֥ `gr' Ƥ.

   * `lex_hensel()', `lex_tl()' , ¿༰ꥹ PLIST , ѿ
     VLIST1,  ORDER ˴ؤ륰֥ʴ, ,
     ѿ VLIST2 μ񼰽֥ʴѴ.

   * `tolex()', `tolex_tl()' , ѿ VLIST1,  ORDER
     ˴ؤ륰֥ʴǤ ¿༰ꥹ PLIST ѿ VLIST2
     μ񼰽֥ Ѵ.  `tolex_d()' , `tolex()'
     ˤ, ƴη׻, ҥץ ꥹ PROCS
     γƥץʬ׻.

   * `lex_hensel()', `lex_tl()' ˤƤ, 񼰽֥ʴ
     ׻ϼΤ褦˹Ԥ. (`[Noro,Yokoyama]' .)
       1. VLIST1, ORDER ˴ؤ륰֥ʴ G0 ׻.
          (`lex_hensel()' Τ. )

       2. G0 γƸ VLIST2 ˴ؤ뼭񼰽ˤƬʤ
          褦ǿ P , GF(P) Ǥμ񼰽֥ʴ GP
          ׻.

       3. GP ˸뤹٤Ƥι, G0 ˴ؤ NF ׻.

       4. GP γƸ F ˤĤ, F η̤그, F γƹб
          NF θ֤, ƹη 0 ֤,
          ̤그˴ؤ LF .

       5. LF , ˡ P ǰղĤȤѤ LF β ˡ Pβ򤫤
          Hensel ˤ.

       6. ٤Ƥ GP θˤĤ򤱤餽βΤ
          񼰽ǤΥ֥ʴ.
          ⤷ɤ줫ε˼Ԥ, P
          ȤľƤľ.

   * `lex_tl()', `tolex_tl()' ˤƤ, 񼰽֥ʴ
     ׻ϼΤ褦˹Ԥ.

       1. VLIST1, ORDER ˴ؤ륰֥ʴ G0 ׻.
          (`lex_hensel()' Τ. )

       2. G0  0 ƥǤʤȤ, G0 ϤȤ, G0 γƸ
          VLIST2 ˴ؤ뼭񼰽ˤƬʤ 褦ǿ
          P , P Ѥ trace-lifting ˤ꼭
          Υ֥ʴ,
          ⤷ޤäʤåʤˤ줬
          ֥ʴȤʤ. ⤷Ԥ, P ȤľƤľ.

       3. G0  0 ƥΤȤ, G0 ϤȤ, ޤ, VLIST2
          κǸѿʳõõˤ ֥ʴ G1
          ׻, 줫鼭񼰽Υ֥ʴ ׻.
          κ, ƥƥåפǤ, ϤγƸ, ˤ
          ƬʤǿѤ trace-lifting
          ǥ֥ʴ,
          ⤷ޤäåʤˤ줬νǤΥ֥ʴȤʤ.

   * ͭη׻, `lex_tl()', `tolex_tl()' Τ߼դ.

   * `homo'  0 Ǥʤ, ǵư Buchberger 르ꥺ
     , ƼԤ.

   * `tolex_d()' ɽ֤, ȡ¹ԤƤץ
     ƹԤ줿׻бƤ,
     ҥץˤ֤ϴޤޤʤ.

     [78] K=katsura(5)$
     30msec + gc : 20msec
     [79] V=[u5,u4,u3,u2,u1,u0]$
     0msec
     [80] G0=hgr(K,V,2)$
     91.558sec + gc : 15.583sec
     [81] G1=lex_hensel(K,V,0,V,0)$
     49.049sec + gc : 9.961sec
     [82] G2=lex_tl(K,V,0,V,1)$
     31.186sec + gc : 3.500sec
     [83] gb_comp(G0,G1);
     1
     10msec
     [84] gb_comp(G0,G2);
     1


     *Note `dp_gr_main dp_gr_mod_main': dp_gr_main dp_gr_mod_main,
     *Note `dp_ord': dp_ord, *Note `ʬ׻': ʬ׻

