Artifact 57c9da71236086d701e1ce4986345b04ff808c4d633efe59d03ea2966e4fc460:
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r37/packages/redlog/redlog.rlg
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2011-09-02 18:13:33
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Thu Apr 15 22:02:44 MET DST 1999 REDUCE 3.7, 15-Apr-1999 ... 1: 1: 2: 2: 2: 2: 2: 2: 2: 2: 2: 3: 3: % ---------------------------------------------------------------------- % $Id: redlog.tst,v 1.5 1999/04/13 21:53:26 sturm Exp $ % ---------------------------------------------------------------------- % Copyright (c) 1995-1997 % Andreas Dolzmann and Thomas Sturm, Universitaet Passau % ---------------------------------------------------------------------- % $Log: redlog.tst,v $ % Revision 1.5 1999/04/13 21:53:26 sturm % Removed "on echo". % % Revision 1.4 1999/04/05 12:25:29 dolzmann % Fixed a bug. % % Revision 1.3 1999/04/05 12:15:43 dolzmann % Added code for testing the contexts acfsf and dvfsf. % % Revision 1.2 1997/08/20 16:22:07 sturm % Do not use "on time". % % Revision 1.1 1997/08/18 15:59:01 sturm % Renamed "rl.red" to "redlog.red", and thus "rl.tst" to this file % "redlog.tst." % % ---------------------------------------------------------------------- % Revision 1.3 1996/10/14 16:18:39 sturm % Added sc50b for testing the optimizer. % % Revision 1.2 1996/10/03 16:09:39 sturm % Added new QE example for testing rlatl, ..., rlifacml, rlstruct, % rlifstruct. % % Revision 1.1 1996/09/30 17:07:52 sturm % Initial check-in. % % ---------------------------------------------------------------------- on rlverbose; % Ordered fields standard form: rlset ofsf; {} rlset(); {ofsf} % Chains -3/5<x>y>z<=a<>b>c<5/3; - 5*x - 3 < 0 and x - y > 0 and y - z > 0 and - a + z <= 0 and a - b <> 0 and b - c > 0 and 3*c - 5 < 0 % For loop actions. g := for i:=1:6 mkor for j := 1:6 mkand mkid(a,i) <= mkid(a,j); g := false or (true and 0 <= 0 and a1 - a2 <= 0 and a1 - a3 <= 0 and a1 - a4 <= 0 and a1 - a5 <= 0 and a1 - a6 <= 0) or (true and - a1 + a2 <= 0 and 0 <= 0 and a2 - a3 <= 0 and a2 - a4 <= 0 and a2 - a5 <= 0 and a2 - a6 <= 0) or (true and - a1 + a3 <= 0 and - a2 + a3 <= 0 and 0 <= 0 and a3 - a4 <= 0 and a3 - a5 <= 0 and a3 - a6 <= 0) or (true and - a1 + a4 <= 0 and - a2 + a4 <= 0 and - a3 + a4 <= 0 and 0 <= 0 and a4 - a5 <= 0 and a4 - a6 <= 0) or (true and - a1 + a5 <= 0 and - a2 + a5 <= 0 and - a3 + a5 <= 0 and - a4 + a5 <= 0 and 0 <= 0 and a5 - a6 <= 0) or (true and - a1 + a6 <= 0 and - a2 + a6 <= 0 and - a3 + a6 <= 0 and - a4 + a6 <= 0 and - a5 + a6 <= 0 and 0 <= 0) % Quantifier elimination and variants h := rlsimpl rlall g; h := all a1 all a2 all a3 all a4 all a5 all a6 ((a1 - a2 <= 0 and a1 - a3 <= 0 and a1 - a4 <= 0 and a1 - a5 <= 0 and a1 - a6 <= 0) or (a1 - a2 >= 0 and a2 - a3 <= 0 and a2 - a4 <= 0 and a2 - a5 <= 0 and a2 - a6 <= 0) or ( a1 - a3 >= 0 and a2 - a3 >= 0 and a3 - a4 <= 0 and a3 - a5 <= 0 and a3 - a6 <= 0 ) or (a1 - a4 >= 0 and a2 - a4 >= 0 and a3 - a4 >= 0 and a4 - a5 <= 0 and a4 - a6 <= 0) or (a1 - a5 >= 0 and a2 - a5 >= 0 and a3 - a5 >= 0 and a4 - a5 >= 0 and a5 - a6 <= 0) or (a1 - a6 >= 0 and a2 - a6 >= 0 and a3 - a6 >= 0 and a4 - a6 >= 0 and a5 - a6 >= 0)) rlmatrix h; (a1 - a2 <= 0 and a1 - a3 <= 0 and a1 - a4 <= 0 and a1 - a5 <= 0 and a1 - a6 <= 0) or (a1 - a2 >= 0 and a2 - a3 <= 0 and a2 - a4 <= 0 and a2 - a5 <= 0 and a2 - a6 <= 0) or (a1 - a3 >= 0 and a2 - a3 >= 0 and a3 - a4 <= 0 and a3 - a5 <= 0 and a3 - a6 <= 0) or (a1 - a4 >= 0 and a2 - a4 >= 0 and a3 - a4 >= 0 and a4 - a5 <= 0 and a4 - a6 <= 0) or ( a1 - a5 >= 0 and a2 - a5 >= 0 and a3 - a5 >= 0 and a4 - a5 >= 0 and a5 - a6 <= 0 ) or (a1 - a6 >= 0 and a2 - a6 >= 0 and a3 - a6 >= 0 and a4 - a6 >= 0 and a5 - a6 >= 0) on rlrealtime; rlqe h; ---- (all a1 a2 a3 a4 a5 a6) [DFS: depth 6, watching 5] [0e] [1e] [2e] [3e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [3e] [1e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [3e] [1e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [1e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [1e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [1e] [2e] [3e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [2e] [3e] [3e] [3e] [3e] [DEL:25/116] Realtime: 2 s true off rlrealtime; h := rlsimpl rlall(g,{a2}); h := all a1 all a3 all a4 all a5 all a6 ((a1 - a2 <= 0 and a1 - a3 <= 0 and a1 - a4 <= 0 and a1 - a5 <= 0 and a1 - a6 <= 0) or (a1 - a2 >= 0 and a2 - a3 <= 0 and a2 - a4 <= 0 and a2 - a5 <= 0 and a2 - a6 <= 0) or ( a1 - a3 >= 0 and a2 - a3 >= 0 and a3 - a4 <= 0 and a3 - a5 <= 0 and a3 - a6 <= 0 ) or (a1 - a4 >= 0 and a2 - a4 >= 0 and a3 - a4 >= 0 and a4 - a5 <= 0 and a4 - a6 <= 0) or (a1 - a5 >= 0 and a2 - a5 >= 0 and a3 - a5 >= 0 and a4 - a5 >= 0 and a5 - a6 <= 0) or (a1 - a6 >= 0 and a2 - a6 >= 0 and a3 - a6 >= 0 and a4 - a6 >= 0 and a5 - a6 >= 0)) rlqe h; ---- (all a1 a3 a4 a5 a6) [BFS: depth 5] -- left: 5 [1e] -- left: 4 [6e] [5e] [4e] [3e] [2e] [1e] -- left: 3 [17e] [16e] [15e] [14e] [13e] [12e] [11e] [10e] [9e] [8e] [7e] [6e] [5e] [4e] [3 e] [2e] [1e] -- left: 2 [16e] [15e] [14e] [13e] [12e] [11e] [10e] [9e] [8e] [7e] [6e] [5e] [4e] [3e] [2e ] [1e] [DEL:65/40] true off rlqeheu,rlqedfs; rlqe ex(x,a*x**2+b*x+c>0); ---- (ex x) [BFS: depth 1] -- left: 1 [1e] [DEL:0/1] 3 a > 0 or (2*a*b*c - b > 0 and a = 0 and b <> 0) 2 or (a = 0 and (b > 0 or (b = 0 and c > 0))) or (4*a*c - b < 0 and a < 0) on rlqedfs; rlqe ex(x,a*x**2+b*x+c>0); ---- (ex x) [DFS: depth 1, watching 1] [0e] [DEL:0/1] 3 a > 0 or (2*a*b*c - b > 0 and a = 0 and b <> 0) 2 or (a = 0 and (b > 0 or (b = 0 and c > 0))) or (4*a*c - b < 0 and a < 0) on rlqeheu; rlqe(ex(x,a*x**2+b*x+c>0),{a<0}); ---- (ex x) [BFS: depth 1] -- left: 1 [1e] [DEL:0/1] 2 4*a*c - b < 0 rlgqe ex(x,a*x**2+b*x+c>0); ---- (ex x) [BFS: depth 1] -- left: 1 [1e!] [DEL:0/1] {{a <> 0}, 2 4*a*c - b < 0 or a >= 0} rlthsimpl ({a*b*c=0,b<>0}); {a*c = 0,b <> 0} rlqe ex({x,y},(for i:=1:5 product mkid(a,i)*x**10-mkid(b,i)*y**2)<=0); ---- (ex x y) [BFS: depth 2] -- left: 2 [1(y^2)(x^10)(SVF).e] -- left: 1 [6e] [5e] [4e] [3e] [2e] [1e] [DEL:0/7] true sol := rlqe ex(x,a*x**2+b*x+c>0); ---- (ex x) [BFS: depth 1] -- left: 1 [1e] [DEL:0/1] 3 sol := a > 0 or (2*a*b*c - b > 0 and a = 0 and b <> 0) 2 or (a = 0 and (b > 0 or (b = 0 and c > 0))) or (4*a*c - b < 0 and a < 0) rlatnum sol; 10 rlatl sol; 3 {2*a*b*c - b > 0, 2 4*a*c - b < 0, a = 0, a < 0, a > 0, b = 0, b <> 0, b > 0, c > 0} rlatml sol; 3 {{2*a*b*c - b > 0,1}, 2 {4*a*c - b < 0,1}, {a = 0,2}, {a < 0,1}, {a > 0,1}, {b = 0,1}, {b <> 0,1}, {b > 0,1}, {c > 0,1}} rlterml sol; 2 {b*(2*a*c - b ), 2 4*a*c - b , a, b, c} rltermml sol; 2 {{b*(2*a*c - b ),1}, 2 {4*a*c - b ,1}, {a,4}, {b,3}, {c,1}} rlifacl sol; 2 {4*a*c - b , 2 2*a*c - b , a, b, c} rlifacml sol; 2 {{4*a*c - b ,1}, 2 {2*a*c - b ,1}, {a,4}, {b,4}, {c,1}} rlstruct(sol,v); {v3 > 0 or (v1 > 0 and v3 = 0 and v4 <> 0) or (v3 = 0 and (v4 > 0 or (v4 = 0 and v5 > 0))) or (v2 < 0 and v3 < 0), 3 {v1 = 2*a*b*c - b , 2 v2 = 4*a*c - b , v3 = a, v4 = b, v5 = c}} rlifstruct(sol,v); {v3 > 0 or (v2*v4 > 0 and v3 = 0 and v4 <> 0) or (v3 = 0 and (v4 > 0 or (v4 = 0 and v5 > 0))) or (v1 < 0 and v3 < 0), 2 {v1 = 4*a*c - b , 2 v2 = 2*a*c - b , v3 = a, v4 = b, v5 = c}} rlitab sol; 10 = 100% [9: 18] [8: 15] [7: 15] [6: 15] [5: 9] [4: 9] [3: 9] [2: 16] [1: 20] Success: 10 -> 9 0 = 100% No success, returning the original formula 5 = 100% [5: 7] [4: 5] [3: 5] [2: 5] [1: 9] No success, returning the original formula 1 = 100% [1: 1] No success, returning the original formula a > 0 3 or (a = 0 and (b > 0 or (b = 0 and c > 0) or (2*a*b*c - b > 0 and b < 0))) 2 or (4*a*c - b < 0 and a < 0) rlatnum ws; 9 rlgsn sol; [DNF] global: 1; impl: 1; no neq: 3; glob-prod-al: 0. [GP] [1] [3] [2] [1] 3 a > 0 or (a = 0 and b = 0 and c > 0) or (2*a*b*c - b > 0 and a = 0 and b <> 0) 2 or (a = 0 and b > 0) or (4*a*c - b < 0 and a < 0) rlatnum ws; 11 off rlverbose; rlqea ex(x,m*x+b=0); {{b = 0 and m = 0,{x = infinity1}}, - b {m <> 0,{x = ------}}} m % from Marc van Dongen. Finding the first feasible solution for the % solution of systems of linear diophantine inequalities. dong := { 3*X259+4*X261+3*X262+2*X263+X269+2*X270+3*X271+4*X272+5*X273+X229=2, 7*X259+11*X261+8*X262+5*X263+3*X269+6*X270+9*X271+12*X272+15*X273+X229=4, 2*X259+5*X261+4*X262+3*X263+3*X268+4*X269+5*X270+6*X271+7*X272+8*X273=1, X262+2*X263+5*X268+4*X269+3*X270+2*X271+X272+2*X229=1, X259+X262+2*X263+4*X268+3*X269+2*X270+X271-X273+3*X229=2, X259+2*X261+2*X262+2*X263+3*X268+3*X269+3*X270+3*X271+3*X272+3*X273+X229=1, X259+X261+X262+X263+X268+X269+X270+X271+X272+X273+X229=1}; dong := {x229 + 3*x259 + 4*x261 + 3*x262 + 2*x263 + x269 + 2*x270 + 3*x271 + 4*x272 + 5*x273 = 2, x229 + 7*x259 + 11*x261 + 8*x262 + 5*x263 + 3*x269 + 6*x270 + 9*x271 + 12*x272 + 15*x273 = 4, 2*x259 + 5*x261 + 4*x262 + 3*x263 + 3*x268 + 4*x269 + 5*x270 + 6*x271 + 7*x272 + 8*x273 = 1, 2*x229 + x262 + 2*x263 + 5*x268 + 4*x269 + 3*x270 + 2*x271 + x272 = 1, 3*x229 + x259 + x262 + 2*x263 + 4*x268 + 3*x269 + 2*x270 + x271 - x273 = 2, x229 + x259 + 2*x261 + 2*x262 + 2*x263 + 3*x268 + 3*x269 + 3*x270 + 3*x271 + 3*x272 + 3*x273 = 1, x229 + x259 + x261 + x262 + x263 + x268 + x269 + x270 + x271 + x272 + x273 = 1} sol := rlopt(dong,0); sol := {0, {{x229 - x262 - 2*x263 - 5*x268 - 4*x269 - 3*x270 - 2*x271 - x272 + 1 = -----------------------------------------------------------------, 2 x259 = (x262 + 2*x263 + 7*x268 + 6*x269 + 5*x270 + 4*x271 + 3*x272 + 2*x273 + 1)/2, x261 = - x262 - x263 - 2*x268 - 2*x269 - 2*x270 - 2*x271 - 2*x272 - 2*x273}}} % Substitution sub(first second sol,for each atf in dong mkand atf); true and 0 = 0 and 0 = 0 and 0 = 0 and 0 = 0 and 0 = 0 and 0 = 0 and 0 = 0 rlsimpl ws; true sub(x=a,x=0 and a=0 and ex(x,x=y) and ex(a,x>a)); a = 0 and a = 0 and ex x (x - y = 0) and ex a0 (a - a0 > 0) f1 := x=0 and b>=0; f1 := x = 0 and b >= 0 f2 := a=0; f2 := a = 0 f := f1 or f2; f := (x = 0 and b >= 0) or a = 0 % Boolean normal forms. rlcnf f; (a = 0 or b >= 0) and (a = 0 or x = 0) rldnf ws; a = 0 or (b >= 0 and x = 0) rlcnf f; (a = 0 or b >= 0) and (a = 0 or x = 0) % Negation normal form and prenex normal form hugo := a=0 and b=0 and y<0 equiv ex(y,y>=a) or a>0; hugo := (a = 0 and b = 0 and y < 0) equiv (ex y ( - a + y >= 0) or a > 0) rlnnf hugo; ((a = 0 and b = 0 and y < 0) and (ex y ( - a + y >= 0) or a > 0)) or ((a <> 0 or b <> 0 or y >= 0) and (all y ( - a + y < 0) and a <= 0)) rlpnf hugo; all y1 ex y0 (((a = 0 and b = 0 and y < 0) and ( - a + y0 >= 0 or a > 0)) or ((a <> 0 or b <> 0 or y >= 0) and ( - a + y1 < 0 and a <= 0))) % Length and Part part(hugo,0); equiv part(hugo,2,1,2); - a + y >= 0 length ws; 2 length hugo; 2 length part(hugo,1); 3 % Tableau mats := all(t,ex({l,u},( (t>=0 and t<=1) impl (l>0 and u<=1 and -t*x1+t*x2+2*t*x1*u+u=l*x1 and -2*t*x2+t*x2*u=l*x2)))); mats := all t ex l ex u ((t >= 0 and t - 1 <= 0) impl (l > 0 and u - 1 <= 0 and - l*x1 + 2*t*u*x1 - t*x1 + t*x2 + u = 0 and - l*x2 + t*u*x2 - 2*t*x2 = 0) ) sol := rlgsn rlqe mats; sol := 3*x1 + 2 <> 0 and 2*x1 + 1 <> 0 and x1 + 1 <> 0 and x2 = 0 2 2 and (2*x1 + x1 < 0 or x1 >= 0) and (3*x1 + 5*x1 + 2 < 0 2 2 2 or 2*x1 + 3*x1 + 1 >= 0 or 2*x1 + x1 < 0 or x1 + x1 > 0) 2 2 2 and (3*x1 + 5*x1 + 2 < 0 or 2*x1 + x1 < 0 or x1 + x1 > 0 or x1 = 0) 2 2 2 and (2*x1 + 3*x1 + 1 >= 0 or 2*x1 + x1 < 0 or x1 + x1 > 0) 2 2 2 and (2*x1 + 3*x1 + 1 >= 0 or 2*x1 + x1 < 0 or x1 + x1 > 0 or x1 = 0) 2 2 and (x1 + x1 < 0 or x1 >= 0) and (3*x1 + 2*x1 < 0 or x1 >= 0) rltab(sol,{x1>0,x1<0,x1=0}); 2 2 (x1 = 0 and (x2 = 0 and (3*x1 + 5*x1 + 2 < 0 or 2*x1 + 3*x1 + 1 >= 0 2 2 or 2*x1 + x1 < 0 or x1 + x1 > 0) 2 2 2 and (2*x1 + 3*x1 + 1 >= 0 or 2*x1 + x1 < 0 or x1 + x1 > 0))) or (x1 < 0 and 2 2 2 (3*x1 + 2*x1 < 0 and 2*x1 + x1 < 0 and x1 + x1 < 0 and 3*x1 + 2 <> 0 and 2*x1 + 1 <> 0 and x1 + 1 <> 0 and x2 = 0)) or (x1 > 0 and (x2 = 0 and ( 2 2 2 2 3*x1 + 5*x1 + 2 < 0 or 2*x1 + 3*x1 + 1 >= 0 or 2*x1 + x1 < 0 or x1 + x1 > 0) 2 2 2 and (3*x1 + 5*x1 + 2 < 0 or 2*x1 + x1 < 0 or x1 + x1 > 0) 2 2 2 and (2*x1 + 3*x1 + 1 >= 0 or 2*x1 + x1 < 0 or x1 + x1 > 0))) % Part on psopfn / cleanupfn part(rlqe ex(x,m*x+b=0),1); b = 0 walter := (x>0 and y>0); walter := x > 0 and y > 0 rlsimpl(true,rlatl walter); true part(rlatl walter,1,1); x % Optimizer sc50b!-t := -1*vCOL00004$ sc50b!-c := { vCOL00001 >= 0,vCOL00002 >= 0,vCOL00003 >= 0,vCOL00004 >= 0,vCOL00005 >= 0, vCOL00006 >= 0,vCOL00007 >= 0,vCOL00008 >= 0,vCOL00009 >= 0,vCOL00010 >= 0, vCOL00011 >= 0,vCOL00012 >= 0,vCOL00013 >= 0,vCOL00014 >= 0,vCOL00015 >= 0, vCOL00016 >= 0,vCOL00017 >= 0,vCOL00018 >= 0,vCOL00019 >= 0,vCOL00020 >= 0, vCOL00021 >= 0,vCOL00022 >= 0,vCOL00023 >= 0,vCOL00024 >= 0,vCOL00025 >= 0, vCOL00026 >= 0,vCOL00027 >= 0,vCOL00028 >= 0,vCOL00029 >= 0,vCOL00030 >= 0, vCOL00031 >= 0,vCOL00032 >= 0,vCOL00033 >= 0,vCOL00034 >= 0,vCOL00035 >= 0, vCOL00036 >= 0,vCOL00037 >= 0,vCOL00038 >= 0,vCOL00039 >= 0,vCOL00040 >= 0, vCOL00041 >= 0,vCOL00042 >= 0,vCOL00043 >= 0,vCOL00044 >= 0,vCOL00045 >= 0, vCOL00046 >= 0,vCOL00047 >= 0,vCOL00048 >= 0, 3*vCOL00001+(3*vCOL00002)+(3*vCOL00003) <= 300, 1*vCOL00004+(-1*vCOL00005) = 0, -1*vCOL00001+(1*vCOL00006) = 0, -1*vCOL00002+(1*vCOL00007) = 0, -1*vCOL00003+(1*vCOL00008) = 0, -1*vCOL00006+(1*vCOL00009) <= 0, -1*vCOL00007+(1*vCOL00010) <= 0, -1*vCOL00008+(1*vCOL00011) <= 0, -1*vCOL00009+(3*vCOL00012)+(3*vCOL00013)+(3*vCOL00014) <= 300, 0.400000*vCOL00005+(-1*vCOL00010) <= 0, 0.600000*vCOL00005+(-1*vCOL00011) <= 0, 1.100000*vCOL00004+(-1*vCOL00015) = 0, 1*vCOL00005+(1*vCOL00015)+(-1*vCOL00016) = 0, -1*vCOL00006+(-1*vCOL00012)+(1*vCOL00017) = 0, -1*vCOL00007+(-1*vCOL00013)+(1*vCOL00018) = 0, -1*vCOL00008+(-1*vCOL00014)+(1*vCOL00019) = 0, -1*vCOL00017+(1*vCOL00020) <= 0, -1*vCOL00018+(1*vCOL00021) <= 0, -1*vCOL00019+(1*vCOL00022) <= 0, -1*vCOL00020+(3*vCOL00023)+(3*vCOL00024)+(3*vCOL00025) <= 300, 0.400000*vCOL00016+(-1*vCOL00021) <= 0, 0.600000*vCOL00016+(-1*vCOL00022) <= 0, 1.100000*vCOL00015+(-1*vCOL00026) = 0, 1*vCOL00016+(1*vCOL00026)+(-1*vCOL00027) = 0, -1*vCOL00017+(-1*vCOL00023)+(1*vCOL00028) = 0, -1*vCOL00018+(-1*vCOL00024)+(1*vCOL00029) = 0, -1*vCOL00019+(-1*vCOL00025)+(1*vCOL00030) = 0, -1*vCOL00028+(1*vCOL00031) <= 0, -1*vCOL00029+(1*vCOL00032) <= 0, -1*vCOL00030+(1*vCOL00033) <= 0, -1*vCOL00031+(3*vCOL00034)+(3*vCOL00035)+(3*vCOL00036) <= 300, 0.400000*vCOL00027+(-1*vCOL00032) <= 0, 0.600000*vCOL00027+(-1*vCOL00033) <= 0, 1.100000*vCOL00026+(-1*vCOL00037) = 0, 1*vCOL00027+(1*vCOL00037)+(-1*vCOL00038) = 0, -1*vCOL00028+(-1*vCOL00034)+(1*vCOL00039) = 0, -1*vCOL00029+(-1*vCOL00035)+(1*vCOL00040) = 0, -1*vCOL00030+(-1*vCOL00036)+(1*vCOL00041) = 0, -1*vCOL00039+(1*vCOL00042) <= 0, -1*vCOL00040+(1*vCOL00043) <= 0, -1*vCOL00041+(1*vCOL00044) <= 0, -1*vCOL00042+(3*vCOL00045)+(3*vCOL00046)+(3*vCOL00047) <= 300, 0.400000*vCOL00038+(-1*vCOL00043) <= 0, 0.600000*vCOL00038+(-1*vCOL00044) <= 0, 1.100000*vCOL00037+(-1*vCOL00048) = 0, -0.700000*vCOL00045+(0.300000*vCOL00046)+(0.300000*vCOL00047) <= 0, -1*vCOL00046+(0.400000*vCOL00048) <= 0, -1*vCOL00047+(0.600000*vCOL00048) <= 0}$ rlopt(sc50b!-c,sc50b!-t); {-70, {{vcol00001 = 30, vcol00002 = 28, vcol00003 = 42, vcol00004 = 70, vcol00005 = 70, vcol00006 = 30, vcol00007 = 28, vcol00008 = 42, vcol00009 = 30, vcol00010 = 28, vcol00011 = 42, vcol00012 = 33, 154 vcol00013 = -----, 5 231 vcol00014 = -----, 5 vcol00015 = 77, vcol00016 = 147, vcol00017 = 63, 294 vcol00018 = -----, 5 441 vcol00019 = -----, 5 vcol00020 = 63, 294 vcol00021 = -----, 5 441 vcol00022 = -----, 5 363 vcol00023 = -----, 10 847 vcol00024 = -----, 25 2541 vcol00025 = ------, 50 847 vcol00026 = -----, 10 2317 vcol00027 = ------, 10 993 vcol00028 = -----, 10 2317 vcol00029 = ------, 25 6951 vcol00030 = ------, 50 993 vcol00031 = -----, 10 2317 vcol00032 = ------, 25 6951 vcol00033 = ------, 50 3993 vcol00034 = ------, 100 9317 vcol00035 = ------, 250 27951 vcol00036 = -------, 500 9317 vcol00037 = ------, 100 32487 vcol00038 = -------, 100 13923 vcol00039 = -------, 100 32487 vcol00040 = -------, 250 97461 vcol00041 = -------, 500 13923 vcol00042 = -------, 100 32487 vcol00043 = -------, 250 97461 vcol00044 = -------, 500 43923 vcol00045 = -------, 1000 102487 vcol00046 = --------, 2500 307461 vcol00047 = --------, 5000 102487 vcol00048 = --------}}} 1000 % Algebraically closed fields standard form: sub(x=a,x=0 and a=0 and ex(x,x=y) and ex(a,x<>a)); a = 0 and a = 0 and ex x (x - y = 0) and ex a0 (a - a0 <> 0) rlset acfsf; {ofsf} rlsimpl(x^2+y^2+1<>0); 2 2 x + y + 1 <> 0 rlqe ex(x,x^2=y); true clear f; h := rlqe ex(x,x^3+a*x^2+b*x+c=0 and x^3+d*x^2+e*x+f=0); 2 2 2 2 3 2 h := (a*b*c - 2*a*b*c*f + a*b*f - a*c *e + 2*a*c*e*f - a*e*f + b *f - b *c*e 2 2 2 3 2 3 2 3 - 2*b *e*f + 2*b*c*e + b*e *f - c + 3*c *f - c*e - 3*c*f + f = 0 or ( 3 2 2 2 2 a*b*c - a*b*f - a*c*e + a*e*f - b + 2*b *e - b*e - c + 2*c*f - f <> 0 and a - d <> 0) or (a*b - a*e - c + f <> 0 and a - d <> 0 and b - e <> 0) or (a - d <> 0 and b - e <> 0)) and (a - d <> 0 or b - e <> 0 or c - f = 0) and 2 2 2 2 (a *e - a*b*d - a*c - a*d*e + a*f + b + b*d - 2*b*e + c*d - d*f + e <> 0 2 2 3 2 or a *f - a*c*d - a*d*f + b*c - b*f + c*d - c*e + e*f = 0) and (a *f 2 2 2 2 2 2 2 - a *b*e*f - 2*a *c*d*f + a *c*e - a *d*f + a*b *d*f - a*b*c*d*e + 3*a*b*c*f 2 2 2 2 2 2 + a*b*d*e*f - 3*a*b*f + a*c *d - 2*a*c *e + 2*a*c*d *f - a*c*d*e + a*c*e*f 2 3 2 2 2 2 2 2 + a*e*f - b *f + b *c*e - b *d *f + 2*b *e*f - b*c *d + b*c*d *e - b*c*d*f 2 2 2 3 2 3 2 2 - 2*b*c*e + 2*b*d*f - b*e *f + c - c *d + 3*c *d*e - 3*c *f - 3*c*d*e*f 3 2 3 + c*e + 3*c*f - f = 0 or a - d = 0) rlstruct h; {(v4 = 0 or (v5 <> 0 and v7 <> 0) or (v6 <> 0 and v7 <> 0 and v8 <> 0) or (v7 <> 0 and v8 <> 0)) and (v7 <> 0 or v8 <> 0 or v9 = 0) and (v2 <> 0 or v3 = 0) and (v1 = 0 or v7 = 0), 3 2 2 2 2 2 2 2 2 {v1 = a *f - a *b*e*f - 2*a *c*d*f + a *c*e - a *d*f + a*b *d*f - a*b*c*d*e 2 2 2 2 2 + 3*a*b*c*f + a*b*d*e*f - 3*a*b*f + a*c *d - 2*a*c *e + 2*a*c*d *f 2 2 3 2 2 2 2 2 - a*c*d*e + a*c*e*f + a*e*f - b *f + b *c*e - b *d *f + 2*b *e*f - b*c *d 2 2 2 2 3 2 3 2 + b*c*d *e - b*c*d*f - 2*b*c*e + 2*b*d*f - b*e *f + c - c *d + 3*c *d*e 2 3 2 3 - 3*c *f - 3*c*d*e*f + c*e + 3*c*f - f , 2 2 2 2 v2 = a *e - a*b*d - a*c - a*d*e + a*f + b + b*d - 2*b*e + c*d - d*f + e , 2 2 v3 = a *f - a*c*d - a*d*f + b*c - b*f + c*d - c*e + e*f, 2 2 2 2 3 2 v4 = a*b*c - 2*a*b*c*f + a*b*f - a*c *e + 2*a*c*e*f - a*e*f + b *f - b *c*e 2 2 2 3 2 3 2 3 - 2*b *e*f + 2*b*c*e + b*e *f - c + 3*c *f - c*e - 3*c*f + f , 3 2 2 2 2 v5 = a*b*c - a*b*f - a*c*e + a*e*f - b + 2*b *e - b*e - c + 2*c*f - f , v6 = a*b - a*e - c + f, v7 = a - d, v8 = b - e, v9 = c - f}} rlqe rlall (h equiv resultant(x^3+a*x^2+b*x+c,x^3+d*x^2+e*x+f,x)=0); true clear h; % Discretely valued fields standard form: rlset dvfsf; *** p is being cleared *** turned off switch rlqeheu *** turned off switch rlqedfs *** turned on switch rlsusi {acfsf} sub(x=a,x=0 and a=0 and ex(x,x=y) and ex(a,x~a)); a = 0 and a = 0 and ex x (x - y = 0) and ex a0 (a ~ a0) % P-adic Balls, taken from Andreas Dolzmann, Thomas Sturm. P-adic % Constraint Solving, Proceedings of the ISSAC '99. rlset dvfsf; *** turned on switch rlqeheu *** turned on switch rlqedfs *** turned off switch rlsusi *** p is being cleared *** turned off switch rlqeheu *** turned off switch rlqedfs *** turned on switch rlsusi {dvfsf} rlqe all(r_1,all(r_2,all(a,all(b, ex(x,r_1||x-a and r_2||x-b and r_1|r_2) impl all(y,r_2||y-b impl r_1||y-a))))); 2 2 (p - 4*p + 3 | 2 or 2 ~ 1) and (p + p - 2 | 3 or 3 ~ 1) and (p + 2 | 2*p or p - 2 || p + 2) rlmkcanonic ws; true rlset(dvfsf,100003); *** turned on switch rlqeheu *** turned on switch rlqedfs *** turned off switch rlsusi *** p is set to 100003 *** turned off switch rlqeheu *** turned off switch rlqedfs *** turned on switch rlsusi {dvfsf} rlqe all(r_1,all(r_2,all(a,all(b, ex(x,r_1||x-a and r_2||x-b and r_1|r_2) impl all(y,r_2||y-b impl r_1||y-a))))); true % Size of the Residue Field, taken from Andreas Dolzmann, Thomas % Sturm. P-adic Constraint Solving. Proceedings of the ISSAC '99. rlset(dvfsf); *** turned on switch rlqeheu *** turned on switch rlqedfs *** turned off switch rlsusi *** p is being cleared *** turned off switch rlqeheu *** turned off switch rlqedfs *** turned on switch rlsusi {dvfsf,100003} rlqe ex(x,x~1 and x-1~1 and x-2~1 and x-3~1 and 2~1 and 3~1); (3 ~ 1 and 2 ~ 1) or (7 ~ 1 and 6 ~ 1 and 5 ~ 1 and 3 ~ 1 and 2 ~ 1) or (5 ~ 1 and 3 ~ 1 and 2 ~ 1) or (11 ~ 1 and 10 ~ 1 and 6 ~ 1 and 3 ~ 1 and 2 ~ 1) or (7 ~ 1 and 6 ~ 1 and 3 ~ 1 and 2 ~ 1) or (6 ~ 1 and 5 ~ 1 and 3 ~ 1 and 2 ~ 1) rlexplats ws; (3 ~ 1 and 2 ~ 1) or (7 ~ 1 and 5 ~ 1 and 3 ~ 1 and 2 ~ 1) or (11 ~ 1 and 5 ~ 1 and 3 ~ 1 and 2 ~ 1) or (7 ~ 1 and 3 ~ 1 and 2 ~ 1) or (5 ~ 1 and 3 ~ 1 and 2 ~ 1) rldnf ws; 3 ~ 1 and 2 ~ 1 % Selecting contexts: rlset ofsf; *** turned on switch rlqeheu *** turned on switch rlqedfs *** turned off switch rlsusi {dvfsf} f:= ex(x,m*x+b=0); f := ex x (b + m*x = 0) rlqe f; b = 0 or m <> 0 rlset dvfsf; *** p is being cleared *** turned off switch rlqeheu *** turned off switch rlqedfs *** turned on switch rlsusi {ofsf} rlqe f; b + m = 0 or m <> 0 rlset acfsf; *** turned on switch rlqeheu *** turned on switch rlqedfs *** turned off switch rlsusi {dvfsf} rlqe f; b = 0 or m <> 0 end; 4: 4: 4: 4: 4: 4: 4: 4: 4: Time for test: 11860 ms, plus GC time: 770 ms 5: 5: Quitting Thu Apr 15 22:03:15 MET DST 1999