Quelle system_solvers.pvs Sprache: PVS

system_solvers : THEORY

  BEGIN

% different versions of algorithms to compute the number of solutions to a system

IMPORTING poly_systems, matrices@query_coeff

  a,r,g : VAR [nat->int]
  p : VAR [nat->[nat->int]]
  relseq: VAR [nat->RealOrder]
  n : VAR [nat->nat]
  d,i,j,k : VAR nat
  m: VAR posnat
  %m : VAR posnat
  x,y,c,b : VAR real
  babove,bbelow,bbelow2,babove2: VAR bool
  RelF6,TQRow: VAR [nat->subrange(0,5)]

%    ORIGINAL ALGORITHM ---- Others should use this signature.
%
%    starm_tarski_solver_slow_basic(k,a,(m|a(m)/=0),p,
%                (n|FORALL (i:upto(k)):p(i)(n(i))/=0),RelF6):
%     {r:real | r = NSol_all(k,a,m,p,n,RelF6) AND rational_pred(r) AND integer_pred(r)} =
%      LET ii = base_n_to_nat(6,RelF6,k) IN
%        dot(row(tensor_power_alt(A63,k+1))(ii),col(TQ_vect3k(k,a,m,p,n))(0))


% sturm_tarski_tail_generic(k,a,(m|a(m)/=0),p,
%                 (n|FORALL (i:upto(k)):p(i)(n(i))/=0),RelF6,
% (F:{ff:[[nat->below(3)]->real]|FORALL (j:below(3^(k+1))): ff(base_n(3,j)) = entry(tensor_power_alt(A63,k+1))(base_n_to_nat(6, RelF6, k),j)}),
% (G:{ff:[[nat->below(3)]->real]|FORALL (j:below(3^(k+1))): ff(base_n(3,j)) = TQ_fam(k,a,m, p ,n,base_n(3, j))})   ):
%      {r:real | r = NSol_all(k,a,m,p,n,RelF6) AND rational_pred(r) AND integer_pred(r)} =
%        dot_tail_sum2(k+1, F, G, 0, 0, base_n(3, 0))

% % testing the generic solver...

% F1(RelF6, k)(f:[nat->below(3)]): real = entry(tensor_power_alt(A63,k+1))(base_n_to_nat(6, RelF6, k),base_n_to_nat(3,f,k))
% G1(k,a,(m|a(m)/=0),p, (n|FORALL (i:upto(k)):p(i)(n(i))/=0))(f:[nat->below(3)]): real = TQ_fam(k,a,m, p ,n,f)

% sturm_tarski_generic_test(k,a,(m|a(m)/=0),p,
%                 (n|FORALL (i:upto(k)):p(i)(n(i))/=0),RelF6):
%      {r:real | r = NSol_all(k,a,m,p,n,RelF6) AND rational_pred(r) AND integer_pred(r)} =
%          sturm_tarski_tail_generic(k,a,m,p,n,RelF6, F1(RelF6, k), G1(k,a,m,p,n))

rows_fun(RelF6, k)(j:upto(k)):  {V: Vector| V = row(A63)(RelF6(j)) AND length(V)=3} = row(A63)( RelF6(j))

entry_fun(k, (RowF:[upto(k)->{V:Vector|length(V) = 3}]))((L:listn[below(3)](k+1))):
         real = product[nat](0, k, LAMBDA(i:nat): IF i<=k THEN nth(RowF(i), nth(L, i)) ELSE 1 ENDIF)

entry_is: LEMMA FORALL (RelF6, k, (i:below(3^(k+1))) ):
       entry_fun(k, rows_fun(RelF6, k))(base_list(3, i, k+1)) =
       entry(tensor_power_alt(A63, k+1))(base_n_to_nat(6, RelF6, k), i)

TQlist_fun(k,a,(m|a(m)/=0),p, (n|FORALL (i:upto(k)):p(i)(n(i))/=0))(L:listn[below(3)](k+1)): real = TQ_fam(k,a,m, p ,n,list2array[below(3)](0)(L))

TQlist_lem: LEMMA FORALL (k,a,(m|a(m)/=0),p, (n|FORALL (i:upto(k)):p(i)(n(i))/=0), j:below(3^(k+1))):
    TQlist_fun(k,a,m,p,n)(base_list(3,j,k+1)) = TQ_fam(k,a,m,p,n,base_n(3, j))

sturm_tarski_faster(k,a,(m|a(m)/=0),p,
                (n|FORALL (i:upto(k)):p(i)(n(i))/=0),RelF6):
     {r:real | r = NSol_all(k,a,m,p,n,RelF6) AND rational_pred(r) AND integer_pred(r)} =
     LET EntFun  = entry_fun(k, rows_fun(RelF6, k)) IN
     IF k=0 THEN   sturm_tarski_solver_slow_basic(k,a,m,p,n,RelF6)
     ELSE dot_tail_sum2plus(k+1, EntFun, TQlist_fun(k,a,m,p,n), 0, 0, base_list(3, 0, k+1))
     ENDIF


T1(n:posnat, i, j:nat): real = entry(tensor_power_alt(A63, n))(i,j)

T2(M:PosFullMatrix, i, j:nat): real = entry(M)(i,j)

Test1(n:posnat, j:nat): RECURSIVE real =
   if j=0 THEN T1(n, j, j)
   ELSE LET ent = T1(n, j, j) in
    Test1(n, j-1)
   ENDIF
   MEASURE j

Test2recurse(M:PosFullMatrix, j:nat): RECURSIVE real=
  IF j=0 THEN T2(M, j, j)
  ELSE LET ent  = T2(M, j, j) IN
       Test2recurse(M, j-1)
  ENDIF
  MEASURE j

Test2(n: posnat,  j:nat): real =
    LET M = (tensor_power_alt(A63, n)) IN
    Test2recurse(M, j)

  END system_solvers

quality88%

¤ Dauer der Verarbeitung: 0.14 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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