share/contrib/sarag/quickSignDetermination.mac

   1 /* files by Mathieu Kohli summer 2014*/
   2
   3
   4 /* New functions where we write I as a decreasing list, therefore reversing the rows in Info and Sigma for example. The first function allows us to reverse the rows of Sigma*/
   5
   6 Reverserows(Sigma):=
   7   if equal(Sigma,[]) then
   8     Sigma
   9   else append([reverse(first(Sigma))],Reverserows(rest(Sigma,1)))
  10 ;
  11
  12 cut_Sigma1(revSigma,temprow):=
  13   block([templ_0,templ_1,templ_s],
  14   if equal(revSigma,[]) then
  15     [[],[],[]]
  16   elseif equal(first(revSigma),[]) then
  17     [[],[],[]]
  18   elseif equal(rest(revSigma,1),[])  then
  19     [[],[],[temprow]]
  20   else
  21     (if equal(rest(first(revSigma)),rest(second(revSigma))) then
  22       ([templ_0,templ_1,templ_s] : cut_Sigma1(rest(revSigma,2),temprow+2),
  23       [append([temprow],templ_0),append([temprow+1],templ_1),templ_s])
  24     else
  25       ([templ_0,templ_1,templ_s] : cut_Sigma1(rest(revSigma,1),temprow+1),
  26       [templ_0,templ_1,append([temprow],templ_s)])
  27     )
  28   );
  29
  30 cut_Sigma(revSigma):=cut_Sigma1(revSigma,1);
  31
  32 extractXiXiprime1(temprevSigma,temprow,templ_0,templ_1,templ_s):=
  33   block([tempXiprime,tempXi],
  34   if equal(temprevSigma,[]) then
  35     [[],[]]
  36   elseif notequal(templ_0,[]) and equal(first(templ_0),temprow) then
  37     ([tempXiprime,tempXi] : extractXiXiprime1(rest(temprevSigma,1),temprow+1,rest(templ_0,1),templ_1,templ_s),
  38     [tempXiprime,append([rest(first(temprevSigma),1)],tempXi)] )
  39   elseif notequal(templ_s,[]) and equal(first(templ_s),temprow) then
  40     ([tempXiprime,tempXi] : extractXiXiprime1(rest(temprevSigma,1),temprow+1,templ_0,templ_1,rest(templ_s,1)),
  41     [tempXiprime,append([rest(first(temprevSigma),1)],tempXi)] )
  42   else
  43     ([tempXiprime,tempXi] : extractXiXiprime1(rest(temprevSigma,1),temprow+1,templ_0,rest(templ_1,1),templ_s),
  44     [append([rest(first(temprevSigma),1)],tempXiprime),tempXi]) )
  45 ;
  46
  47 extractXiXiprime(revSigma,l_0,l_1,l_s):=extractXiXiprime1(revSigma,1,l_0,l_1,l_s);
  48
  49 assembleInfo1(tempInfoXi,tempInfoXiprime,temprow,templ_0,templ_1,templ_s):=
  50   block([],
  51   if notequal(templ_0,[]) and equal(first(templ_0),temprow) then
  52     (append([append([0],first(tempInfoXi))],assembleInfo1(rest(tempInfoXi,1),tempInfoXiprime,temprow+1,rest(templ_0,1),templ_1,templ_s))
  53     )
  54   elseif notequal(templ_s,[]) and equal(first(templ_s),temprow) then
  55     (append([append([s],first(tempInfoXi))],assembleInfo1(rest(tempInfoXi,1),tempInfoXiprime,temprow+1,templ_0,templ_1,rest(templ_s,1)))
  56     )
  57   elseif notequal(templ_1,[]) then
  58     (append([append([1],first(tempInfoXiprime))],assembleInfo1(tempInfoXi,rest(tempInfoXiprime,1),temprow+1,templ_0,rest(templ_1,1),templ_s))
  59     )
  60   else []
  61   );
  62
  63
  64 revInfo(revSigma,I):=
  65   if equal(I,[]) then
  66     revSigma
  67   else
  68     block([l_0,l_1,l_s,Xi,Xiprime],
  69     [l_0,l_1,l_s] : cut_Sigma(revSigma),
  70     [Xiprime,Xi] : extractXiXiprime(revSigma,l_0,l_1,l_s),
  71     assembleInfo1(revInfo(Xi,rest(I,1)),revInfo(Xiprime,rest(I,1)),1,l_0,l_1,l_s)
  72   );
  73
  74 adaptedfamilyrow(rowrevInfo,I):=
  75   if equal(rowrevInfo,[]) then
  76     []
  77   elseif first(rowrevInfo)=0 or first(rowrevInfo)=s then
  78     adaptedfamilyrow(rest(rowrevInfo,1),rest(I,1))
  79   else
  80     append([first(I)],adaptedfamilyrow(rest(rowrevInfo,1),rest(I,1)))
  81   ;
  82
  83 adapted_family(revInfo,I):=
  84   if equal(revInfo,[]) then
  85     []
  86   else append([adaptedfamilyrow(first(revInfo),I)],adapted_family(rest(revInfo,1),I)) ;
  87
  88 scalarproduct(v,w):=
  89   if equal(v,[]) then 0
  90   else first(v)*first(w)+scalarproduct(rest(v,1),rest(w,1));
  91
  92 evaluation(Mat,vect):=
  93   if Mat=[] then []
  94   else append([scalarproduct(first(Mat),vect)],evaluation(rest(Mat,1),vect));
  95
  96 decreasinginsert(a,decreasinglist):=
  97   if equal(decreasinglist,[]) then [a]
  98   elseif a>first(decreasinglist) then
  99     append([a],decreasinglist)
 100   elseif equal(a,first(decreasinglist)) then
 101     decreasinglist
 102   else
 103     append([first(decreasinglist)],decreasinginsert(a,rest(decreasinglist,1))) ;
 104
 105 comp(Ada):=
 106   if equal(Ada,[]) or equal(Ada,[[]]) then []
 107   elseif equal(first(Ada),[]) then
 108     comp(rest(Ada,1))
 109   else decreasinginsert(first(first(Ada)),comp(append([rest(first(Ada),1)],rest(Ada,1)))) ;
 110
 111 rowcompression(row,comp,I):=
 112   if equal(comp,[]) then []
 113   elseif equal(first(comp),first(I)) then
 114     append([first(row)],rowcompression(rest(row,1),rest(comp,1),rest(I,1)))
 115   else
 116     rowcompression(rest(row,1),comp,rest(I,1)) ;
 117
 118 Matrixcomp(Mat,comp,I):=
 119   if equal(Mat,[]) then []
 120   else append([rowcompression(first(Mat),comp,I)],Matrixcomp(rest(Mat,1),comp,I)) ;
 121
 122 power(znzcondition,i,I):=
 123   if equal(i,first(I)) then first(znzcondition)
 124   else power(rest(znzcondition,1),i,rest(I,1)) ;
 125
 126 powerlist(znzcondition,J,I):=
 127   if equal(J,[]) then 1
 128   else power(znzcondition,first(J),I)*powerlist(znzcondition,rest(J,1),I) ;
 129
 130 Sigmatopowerlist(revSigma,J,I):=
 131   if revSigma=[] then []
 132   else
 133     append([powerlist(first(revSigma),J,I)],Sigmatopowerlist(rest(revSigma,1),J,I)) ;
 134
 135 /*the next matrix we are about to define is NOT reversed if we compare it to what is written in the article*/
 136
 137 Mat(A,revSigma,I):=
 138   if equal(A,[]) then []
 139   else
 140     append([Sigmatopowerlist(revSigma,first(A),I)],Mat(rest(A,1),revSigma,I));
 141
 142 /*Let's notice that in the case where A equals Ada, Mat(Ada,revSigma,I)=Mat(Ada,Matrixcomp(revSigma,comp,I),comp), which is quicker to compute*/
 143
 144 extractlines1(Mat,lines,templine):=
 145   block([tempresult,temprest],
 146   if equal(lines,[]) then [[],Mat]
 147   elseif equal(first(lines),templine) then
 148     ([tempresult,temprest] : extractlines1(rest(Mat,1),rest(lines,1),templine+1),
 149     [append([first(Mat)],tempresult),temprest]
 150     )
 151   else
 152     ([tempresult,temprest] : extractlines1(rest(Mat,1),lines,templine+1),
 153     [tempresult,append([first(Mat)],temprest)]
 154     )
 155   );
 156
 157 extractlines(Mat,lines):=extractlines1(Mat,lines,1);
 158
 159 extractcolumns(Mat,columns):=
 160   block([tempresult,temprest,columnsfirstrow,restfirstrow],
 161   if equal(Mat,[]) then [[],[]]
 162   else
 163     ([tempresult,temprest] : extractcolumns(rest(Mat,1),columns),
 164     [columnsfirstrow,restfirstrow] : extractlines(first(Mat),columns),
 165     [append([columnsfirstrow],tempresult),append([restfirstrow],temprest)]
 166     )
 167   );
 168
 169 assemblevector1(partnb1,partnb2,indexpartnb1,tempindex):=
 170   if equal(indexpartnb1,[]) then partnb2
 171   elseif equal(tempindex,first(indexpartnb1)) then
 172     append([first(partnb1)],assemblevector1(rest(partnb1,1),partnb2,rest(indexpartnb1,1),tempindex+1))
 173   else append([first(partnb2)],assemblevector1(partnb1,rest(partnb2,1),indexpartnb1,tempindex+1)) ;
 174
 175 assemblevector(partnb1,partnb2,indexpartnb1):=assemblevector1(partnb1,partnb2,indexpartnb1,1);
 176
 177 extractinfo1(revInfo,tempindex):=
 178   block([l0,l1,ls,l0Uls,InfoXi,InfoXiprime,card0,cards],
 179   if equal(revInfo,[]) or equal(first(revInfo),[]) then [[],[],[],[],[],[],0,0]
 180   elseif first(first(revInfo))=s then
 181     ([l0,l1,ls,l0Uls,InfoXi,InfoXiprime,card0,cards] : extractinfo1(rest(revInfo,1),tempindex+1),
 182     [l0,l1,append([tempindex],ls),append([tempindex],l0Uls),append([rest(first(revInfo),1)],InfoXi),InfoXiprime,card0,cards+1]
 183     )
 184   elseif equal(first(first(revInfo)),0) then
 185     ([l0,l1,ls,l0Uls,InfoXi,InfoXiprime,card0,cards] : extractinfo1(rest(revInfo,1),tempindex+1),
 186     [append([tempindex],l0),l1,ls,append([tempindex],l0Uls),append([rest(first(revInfo),1)],InfoXi),InfoXiprime,card0+1,cards]
 187     )
 188   else
 189     ([l0,l1,ls,l0Uls,InfoXi,InfoXiprime,card0,cards] : extractinfo1(rest(revInfo,1),tempindex+1),
 190     [l0,append([tempindex],l1),ls,l0Uls,InfoXi,append([rest(first(revInfo),1)],InfoXiprime),card0,cards]
 191     )
 192   );
 193
 194 extractinfo(revInfo):=extractinfo1(revInfo,1);
 195
 196 substract(v,w):=
 197   if w=[] then v
 198   else append([first(v)-first(w)],substract(rest(v,1),rest(w,1))) ;
 199
 200 assemble1(cl0,cl1,cls,temprow,templ_0,templ_1,templ_s):=
 201   block([],
 202   if notequal(templ_0,[]) and equal(first(templ_0),temprow) then
 203     (append([first(cl0)],assemble1(rest(cl0,1),cl1,cls,temprow+1,rest(templ_0,1),templ_1,templ_s))
 204     )
 205   elseif notequal(templ_s,[]) and equal(first(templ_s),temprow) then
 206     (append([first(cls)],assemble1(cl0,cl1,rest(cls,1),temprow+1,templ_0,templ_1,rest(templ_s,1)))
 207     )
 208   elseif notequal(templ_1,[]) then
 209     (append([first(cl1)],assemble1(cl0,rest(cl1,1),cls,temprow+1,templ_0,rest(templ_1,1),templ_s))
 210     )
 211   else []
 212   );
 213
 214 assemble(cl0,cl1,cls,templ_0,templ_1,templ_s):=assemble1(cl0,cl1,cls,1,templ_0,templ_1,templ_s);
 215
 216 linear_solving(Mat,I,revInfo,v):=
 217   block([l0,l1,ls,l0Uls,InfoXi,InfoXiprime,card0,cards,A,B,MatXi,M12,M21,MatXiprime,tl,M,w,tl1,cl0,cl1,cls],
 218   if I=[] then v
 219   else
 220     ([l0,l1,ls,l0Uls,InfoXi,InfoXiprime,card0,cards] : extractinfo(revInfo),
 221     [A,B] : extractlines(Mat,l0Uls),
 222     [MatXi,M12] : extractcolumns(A,l0Uls),
 223     [M21,MatXiprime] : extractcolumns(B,l0Uls),
 224     tl : linear_solving(MatXi,rest(I,1),InfoXi,first(extractlines(v,l0Uls))),
 225     if equal(ls,[]) then (tl1 : first(extractlines(v,l1)) )
 226     else
 227       (M : Matrixcomp(M21,ls,l0Uls),
 228       w : evaluation(M,rowcompression(tl,ls,l0Uls)),
 229       tl1 : substract(first(extractlines(v,l1)),w)
 230       ),
 231     cl1 : linear_solving(MatXiprime,rest(I,1),InfoXiprime,tl1),
 232     cl0 : substract(rowcompression(tl,l0,l0Uls),cl1),
 233     cls : rowcompression(tl,ls,l0Uls),
 234     assemble(cl0,cl1,cls,l0,l1,ls)
 235     )
 236   );
 237
 238 /* We are now going to build the inversibility-query */
 239
 240 /* In the next function, we suppose that second(gcdfreepartmethod(p,q)) gives the gcd free part of p with respect to q, as the function gcdFreePart (for example) does */
 241 keepsimpleroots(P,var,gcdfreepartmethod):=second(gcdfreepartmethod(P,diff(P,var,1),var));
 242
 243 gcd1(P,Q,var):=first(gcdFreePart(P,Q,var));
 244
 245 gcdInvertibilityQuery(Q,P,var):=degree(expand(P),var)-degree(gcd1(expand(P),expand(diff(P,var,1)*Q),var),var);
 246
 247 polynomfamilymult(polylist,multiplyindex,I):=
 248   if equal(multiplyindex,[]) then 1
 249   elseif equal(first(multiplyindex),first(I)) then
 250     first(polylist)*polynomfamilymult(rest(polylist,1),rest(multiplyindex,1),rest(I,1))
 251   else
 252     polynomfamilymult(rest(polylist,1),multiplyindex,rest(I,1))
 253   ;
 254
 255 AdaptedQuerylist(Ada,P,usefullpoly,comp,var,Qu):=
 256   if equal(Ada,[]) then []
 257   else
 258     append([Qu(polynomfamilymult(usefullpoly,first(Ada),comp),P,var)],AdaptedQuerylist(rest(Ada,1),P,usefullpoly,comp,var,Qu));
 259
 260 addfirstcolumn(elem,Mat):=
 261   if equal(Mat,[]) then
 262     []
 263   else
 264     append([append([elem],first(Mat))],addfirstcolumn(elem,rest(Mat,1))) ;
 265
 266 add01to(Mat):=
 267   if equal(Mat,[]) then []
 268   else
 269     append([append([0],first(Mat))],append([append([1],first(Mat))],add01to(rest(Mat,1))));
 270
 271 insert0atevenindex(v):=
 272   if equal(v,[]) then []
 273   else
 274     append([first(v)],append([0],insert0atevenindex(rest(v,1))));
 275
 276 double(v):=
 277   if equal(v,[]) then []
 278   else
 279     append([first(v)],append([first(v)],double(rest(v,1))));
 280
 281 createMatAuxSigma(Mat):=
 282   if equal(Mat,[]) then []
 283   else
 284     append([insert0atevenindex(first(Mat))],append([double(first(Mat))],createMatAuxSigma(rest(Mat,1))));
 285
 286 alternateelemfrom(v,w):=
 287   if equal(v,[]) then []
 288   else
 289     append([first(v)],alternateelemfrom(w,rest(v,1)));
 290
 291 computeCiSigmaiLi1(Auxc,AuxSigma,AuxCompSigma,temprow):=
 292   if equal(AuxSigma,[]) then [[],[],[],[],[],[],[]]
 293   else
 294     (block([c,Sigma,CompSigma,l0,l1,ls,l]),
 295     if notequal(first(Auxc),0) and notequal(second(Auxc),0) then
 296       ([c,Sigma,CompSigma,l0,l1,ls,l] : computeCiSigmaiLi1(rest(Auxc,2),rest(AuxSigma,2),rest(AuxCompSigma,2),temprow+2),
 297       [append([first(Auxc)],append([second(Auxc)],c)),append([first(AuxSigma)],append([second(AuxSigma)],Sigma)),append([first(AuxCompSigma)],append([second(AuxCompSigma)],CompSigma)),append([temprow],l0),append([temprow+1],l1),ls,append([temprow],l)]
 298       )
 299     elseif notequal(first(Auxc),0) then
 300       ([c,Sigma,CompSigma,l0,l1,ls,l] : computeCiSigmaiLi1(rest(Auxc,2),rest(AuxSigma,2),rest(AuxCompSigma,2),temprow+1),
 301       [append([first(Auxc)],c),append([first(AuxSigma)],Sigma),append([first(AuxCompSigma)],CompSigma),l0,l1,append([temprow],ls),append([temprow],l)]
 302       )
 303     else
 304       ([c,Sigma,CompSigma,l0,l1,ls,l] : computeCiSigmaiLi1(rest(Auxc,2),rest(AuxSigma,2),rest(AuxCompSigma,2),temprow+1),
 305       [append([second(Auxc)],c),append([second(AuxSigma)],Sigma),append([second(AuxCompSigma)],CompSigma),l0,l1,append([temprow],ls),append([temprow],l)]
 306       )
 307     );
 308
 309 computeCiSigmaiLi(Auxc,AuxSigma,AuxCompSigma,previouscompsigma):=
 310   block([c,Sigma,CompSigma,l0,l1,ls,l],
 311   [c,Sigma,CompSigma,l0,l1,ls,l] : computeCiSigmaiLi1(Auxc,AuxSigma,AuxCompSigma,1),
 312   if notequal(l0,[]) then
 313     [c,Sigma,CompSigma,l0,l1,ls,l]
 314   else [c,Sigma,previouscompsigma,l0,l1,ls,l]
 315   );
 316
 317 deletefirstcolumn(Mat):=
 318   if equal(Mat,[]) then []
 319   else append([rest(first(Mat),1)],deletefirstcolumn(rest(Mat,1)));
 320
 321 assembleAda_i1(previousAda,AdaXiprime_i,i,temprow,l0,l1,ls):=
 322   if notequal(l0,[]) and equal(first(l0),temprow) then
 323     append([first(previousAda)],assembleAda_i1(rest(previousAda,1),AdaXiprime_i,i,temprow+1,rest(l0,1),l1,ls))
 324   elseif notequal(ls,[]) and equal(first(ls),temprow) then
 325     append([first(previousAda)],assembleAda_i1(rest(previousAda,1),AdaXiprime_i,i,temprow+1,l0,l1,rest(ls,1)))
 326   elseif notequal(l1,[]) and equal(first(l1),temprow) then
 327     append([append([i],first(AdaXiprime_i))],assembleAda_i1(previousAda,rest(AdaXiprime_i,1),i,temprow+1,l0,rest(l1,1),ls))
 328   else [] ;
 329
 330 assembleAda_i(previousAda,AdaXiprime_i,i,l0,l1,ls):=assembleAda_i1(previousAda,AdaXiprime_i,i,1,l0,l1,ls);
 331
 332 assembleQulist(AdaQulist,AdaQuPrime,l1,temprow):=
 333   if equal(l1,[]) then AdaQulist
 334   elseif equal(first(l1),temprow) then
 335     append([first(AdaQuPrime)],assembleQulist(AdaQulist,rest(AdaQuPrime,1),rest(l1,1),temprow+1))
 336   else
 337     append([first(AdaQulist)],assembleQulist(rest(AdaQulist,1),AdaQuPrime,l1,temprow+1)) ;
 338
 339 listunion(l1,ls):=
 340   if equal(l1,[]) then ls
 341   elseif equal(ls,[]) then l1
 342   elseif first(l1)<first(ls) then append([first(l1)],listunion(rest(l1,1),ls))
 343   else append([first(ls)],listunion(l1,rest(ls))) ;
 344
 345 put0atposition(row,l0,tempposition):=
 346   if equal(l0,[]) then row
 347   elseif equal(first(l0),tempposition) then
 348     append([0],put0atposition(row,rest(l0,1),tempposition+1))
 349   else
 350     append([first(row)],put0atposition(rest(row,1),l0,tempposition+1)) ;
 351
 352 put0atcolumn(Mat,l0):=
 353   if equal(Mat,[]) then []
 354   else append([put0atposition(first(Mat),l0,1)],put0atcolumn(rest(Mat,1),l0)) ;
 355
 356 extendrow(row,l0,ls):=
 357   if equal(l0,[]) then row
 358   elseif equal(ls,[]) then double(row)
 359   elseif first(l0)<first(ls) then append([first(row),first(row)],extendrow(rest(row,1),rest(l0,1),ls))
 360   else append([first(row)],extendrow(rest(row,1),l0,rest(ls,1))) ;
 361
 362 extendMat(Mat,l0,ls):=
 363   if equal(Mat,[]) then []
 364   else append([extendrow(first(Mat),l0,ls)],extendMat(rest(Mat,1),l0,ls));
 365
 366
 367 quickZerononzeroDeterminationwithcardinals(polylist,P,Qu,var):=
 368   block([r,Sigma_i,CompressedSigma_i,c_i,comp_i,Info_i,Ada_i,Mat_i,AdaQulist,i,temppolylist,usefullpoly,InvQu,cPidiffzero,vprime,AuxSigma,AuxSigma2,InfoAux,AuxMat,v,c,Xiprime_i,InfoXiprime_i,AdaXiprime_i,CompletedAdaXiprime_i,AdaQuPrime,M,N,R,Mat_i],
 369   r : Qu(1,P,var),
 370   if equal(r,0) then [[],[]]
 371   else
 372     (Sigma_i : [[]],
 373     CompressedSigma_i : [[]],
 374     c_i : [r],
 375     comp_i : [],
 376     Info_i : [[]],
 377     Ada_i : [[]],
 378     Mat_i : [[1]],
 379     AdaQulist : [r],
 380     i : 0,
 381     temppolylist : polylist,
 382     usefullpoly : [],
 383     while notequal(temppolylist,[]) do
 384       (i : i+1,
 385       InvQu : Qu(first(temppolylist),P,var),
 386       cPidiffzero : InvQu,
 387       cPiequalzero : r-InvQu,
 388       if equal(cPiequalzero,0) then
 389         (Sigma_i : addfirstcolumn(1,Sigma_i)
 390         )
 391       elseif equal(cPidiffzero,0) then
 392         (Sigma_i : addfirstcolumn(0,Sigma_i)
 393         )
 394       else
 395         (vprime : AdaptedQuerylist(addfirstcolumn(i,Ada_i),P,append([first(temppolylist)],usefullpoly),append([i],comp_i),var,Qu),
 396         AuxSigma : add01to(CompressedSigma_i),
 397         AuxSigma2 : add01to(Sigma_i),
 398         InfoAux : add01to(Info_i),
 399         AuxMat : createMatAuxSigma(Mat_i),
 400         v : alternateelemfrom(AdaQulist,vprime),
 401         c : linear_solving(AuxMat,append([i],comp_i),InfoAux,v),
 402         [c_i,Sigma_i,CompressedSigma_i,l0,l1,ls,l] : computeCiSigmaiLi(c,AuxSigma2,AuxSigma,CompressedSigma_i),
 403         if equal(l0,[]) then (1=1)
 404         else
 405           (comp_i : append([i],comp_i),
 406           usefullpoly : append([first(temppolylist)],usefullpoly),
 407           Xiprime_i : first(extractlines(deletefirstcolumn(CompressedSigma_i),l1)),
 408           InfoXiprime_i : revInfo(Xiprime_i,rest(comp_i)),
 409           AdaXiprime_i : adapted_family(InfoXiprime_i,rest(comp_i)),
 410           CompletedAdaXiprime_i : addfirstcolumn(i,AdaXiprime_i),
 411           AdaQuPrime : AdaptedQuerylist(CompletedAdaXiprime_i,P,usefullpoly,comp_i,var,Qu),
 412           AdaQulist : assembleQulist(AdaQulist,AdaQuPrime,l1,1),
 413           Info_i : assembleInfo1(Info_i,InfoXiprime_i,1,l0,l1,ls),
 414           Ada_i : assembleAda_i(Ada_i,AdaXiprime_i,i,l0,l1,ls),
 415           M : Mat(CompletedAdaXiprime_i,first(extractlines(CompressedSigma_i,listunion(l1,ls))),comp_i),
 416           N : put0atcolumn(M,l0),
 417           R : extendMat(Mat_i,l0,ls),
 418           Mat_i : assembleQulist(R,N,l1,1)
 419           )
 420         ),
 421       temppolylist : rest(temppolylist,1)
 422       )
 423     ),
 424   [c_i,Reverserows(Sigma_i)]
 425   );
 426
 427 quickZerononzeroDetermination(polylist,P,Qu,var):=
 428   second(quickZerononzeroDeterminationwithcardinals(polylist,P,Qu,var));
 429
 430 /* __________________________________________________________________________*/
 431
 432 deletefirstcolumn(Mat):=
 433   if equal(Mat,[]) then []
 434   else append([rest(first(Mat),1)],deletefirstcolumn(rest(Mat,1)));
 435
 436 extractfirstcolumn(Mat):=
 437   if equal(Mat,[]) then []
 438   else append([[first(first(Mat))]],extractfirstcolumn(rest(Mt,1)));
 439
 440 extractfirstcolumn2(Mat):=
 441   if equal(Mat,[]) then [[],[]]
 442   else
 443     block([result,left],
 444     [result,left] : extractfirstcolumn2(rest(Mat,1)),
 445     [append([[first(first(Mat))]],result),append([rest(first(Mat),1)],left)]
 446     );
 447
 448
 449 glu(Mat1,Mat2):=
 450   if equal(Mat2,[]) then Mat1
 451   else append([append(first(Mat1),first(Mat2))],glu(rest(Mat1,1),rest(Mat2,1)));
 452
 453 firstcolumnisntusefull(Mat):=
 454   if equal(Mat,[]) then true
 455   elseif not(first(first(Mat))=s) then
 456     false
 457   else
 458     firstcolumnisntusefull(rest(Mat,1));
 459
 460 compression(Info,Sigma,I):=
 461   if equal(Info,[]) or equal(first(Info),[]) then [[],[],[]]
 462   elseif firstcolumnisntusefull(Info) then
 463     (compression(deletefirstcolumn(Info),deletefirstcolumn(Sigma),rest(I,1))
 464     )
 465   else
 466     (block([CompInfo,CompSigma,comp,A,B,C,D],
 467     [A,B] : extractfirstcolumn2(Info),
 468     [C,D] : extractfirstcolumn2(Sigma),
 469     [CompInfo,CompSigma,comp] : compression(B,D,rest(I,1)),
 470     [glu(A,CompInfo),glu(C,CompSigma),append([first(I)],comp)]
 471     )
 472     );
 473
 474 extractInfoSign1(Info,temprow):=
 475   if equal(Info,[]) then [[],[],[],[],[],[],[],[],[],[],[],[]]
 476   else
 477     block([lp1,lp2,lp3,l0,l01,l0m1,l1m1,ls,l1,l10,lm10,lm11],
 478     [lp1,lp2,lp3,l0,l01,l0m1,l1m1,ls,l1,l10,lm10,lm11] : extractInfoSign1(rest(Info,1),temprow+1),
 479     if first(first(Info))=0 then
 480       [append([temprow],lp1),lp2,lp3,append([temprow],l0),l01,l0m1,l1m1,ls,l1,l10,lm10,lm11]
 481     elseif first(first(Info))=e01 then
 482        [append([temprow],lp1),lp2,lp3,l0,append([temprow],l01),l0m1,l1m1,ls,l1,l10,lm10,lm11]
 483     elseif first(first(Info))=e0m1 then
 484        [append([temprow],lp1),lp2,lp3,l0,l01,append([temprow],l0m1),l1m1,ls,l1,l10,lm10,lm11]
 485     elseif first(first(Info))=e1m1 then
 486        [append([temprow],lp1),lp2,lp3,l0,l01,l0m1,append([temprow],l1m1),ls,l1,l10,lm10,lm11]
 487     elseif first(first(Info))=s then
 488        [append([temprow],lp1),lp2,lp3,l0,l01,l0m1,l1m1,append([temprow],ls),l1,l10,lm10,lm11]
 489     elseif first(first(Info))=1 then
 490        [lp1,append([temprow],lp2),lp3,l0,l01,l0m1,l1m1,ls,append([temprow],l1),l10,lm10,lm11]
 491     elseif first(first(Info))=e10 then
 492        [lp1,append([temprow],lp2),lp3,l0,l01,l0m1,l1m1,ls,l1,append([temprow],l10),lm10,lm11]
 493     elseif first(first(Info))=em10 then
 494        [lp1,append([temprow],lp2),lp3,l0,l01,l0m1,l1m1,ls,l1,l10,append([temprow],lm10),lm11]
 495     elseif first(first(Info))=em11 then
 496        [lp1,append([temprow],lp2),lp3,l0,l01,l0m1,l1m1,ls,l1,l10,lm10,append([temprow],lm11)]
 497     else
 498        [lp1,lp2,append([temprow],lp3),l0,l01,l0m1,l1m1,ls,l1,l10,lm10,lm11]
 499     );
 500
 501 extractInfoSign(Info):=extractInfoSign1(Info,1);
 502
 503 extractl1l2l3rows1(Mat,l1,l2,l3,templine):=
 504   if equal(Mat,[]) then [[],[],[]]
 505   else
 506     block([M1,M2,M3],
 507     if notequal(l1,[]) and equal(first(l1),templine) then
 508       ([M1,M2,M3] : extractl1l2l3rows1(rest(Mat,1),rest(l1,1),l2,l3,templine+1),
 509       [append([first(Mat)],M1),M2,M3]
 510       )
 511     elseif notequal(l2,[]) and equal(first(l2),templine) then
 512       ([M1,M2,M3] : extractl1l2l3rows1(rest(Mat,1),l1,rest(l2,1),l3,templine+1),
 513       [M1,append([first(Mat)],M2),M3]
 514       )
 515     else
 516       ([M1,M2,M3] : extractl1l2l3rows1(rest(Mat,1),l1,l2,rest(l3,1),templine+1),
 517       [M1,M2,append([first(Mat)],M3)]
 518       )
 519     );
 520
 521 extractl1l2l3rows(Mat,l1,l2,l3):=extractl1l2l3rows1(Mat,l1,l2,l3,1);
 522
 523 extractl1l2l3columns(Mat,l1,l2,l3):=
 524   if equal(Mat,[]) then [[],[],[]]
 525   else
 526     block([A,B,C,D,E,F],
 527     [A,B,C] : extractl1l2l3rows(first(Mat),l1,l2,l3),
 528     [D,E,F] : extractl1l2l3columns(rest(Mat),l1,l2,l3),
 529     [append([A],D),append([B],E),append([C],F)]
 530     );
 531
 532 add(alpha,v,beta,w):=
 533   if equal(v,[]) then []
 534   else append([alpha*first(v)+beta*first(w)],add(alpha,rest(v,1),beta,rest(w,1))) ;
 535
 536 multiplypartofvect(alpha,indexvect,indexpart,vect):=
 537   if equal(indexpart,[]) then vect
 538   elseif equal(first(indexpart),first(indexvect)) then
 539     append([alpha*first(vect)],multiplypartofvect(alpha,rest(indexvect,1),rest(indexpart,1),rest(vect,1)))
 540   else
 541     append([first(vect)],multiplypartofvect(alpha,rest(indexvect,1),indexpart,rest(vect,1)));
 542
 543 listSigma2insideSigma1(lp1,ls):=
 544   if equal(ls,[]) then lp1
 545   elseif equal(first(lp1),first(ls)) then
 546     listSigma2insideSigma1(rest(lp1,1),rest(ls,1))
 547   else
 548     append([first(lp1)],listSigma2insideSigma1(rest(lp1,1),ls)) ;
 549
 550 mult(alpha,v):=
 551   if equal(v,[]) then []
 552   else
 553     append([alpha*first(v)],mult(alpha,rest(v,1)));
 554
 555 sumvinsidew(alpha,v,listv,beta,w,listw):=
 556   if equal(v,[]) then mult(beta,w)
 557   elseif equal(first(listv),first(listw)) then
 558     append([alpha*first(v)+beta*first(w)],sumvinsidew(alpha,rest(v,1),rest(listv,1),beta,rest(w,1),rest(listw,1)))
 559   else
 560     append([beta*first(w)],sumvinsidew(alpha,v,listv,beta,rest(w,1),rest(listw,1)));
 561
 562 put0atrows(vect,Index,rows):=
 563   if equal(rows,[]) then vect
 564   elseif equal(first(Index),first(rows)) then
 565     append([0],put0atrows(rest(vect,1),rest(Index,1),rest(rows,1)))
 566   else
 567     append([first(vect)],put0atrows(rest(vect,1),rest(Index,1),rows))
 568 ;
 569
 570 put0atcolumns(Mat,Index,columns):=
 571   if equal(Mat,[]) then []
 572   else
 573     append([put0atrows(first(Mat),Index,columns)],put0atcolumns(rest(Mat,1),Index,columns));
 574
 575 assemblec1(clp1,clp2,clp3,lp1,lp2,lp3,temprow):=
 576   if equal(clp1,[]) and equal(clp2,[]) and equal(clp3,[]) then []
 577   elseif notequal(lp1,[]) and equal(first(lp1),temprow) then
 578     append([first(clp1)],assemblec1(rest(clp1,1),clp2,clp3,rest(lp1,1),lp2,lp3,temprow+1))
 579   elseif notequal(lp2,[]) and equal(first(lp2),temprow) then
 580     append([first(clp2)],assemblec1(clp1,rest(clp2,1),clp3,lp1,rest(lp2,1),lp3,temprow+1))
 581   else
 582     append([first(clp3)],assemblec1(clp1,clp2,rest(clp3,1),lp1,lp2,rest(lp3,1),temprow+1)) ;
 583
 584 assemblec(clp1,clp2,clp3,lp1,lp2,lp3):= assemblec1(clp1,clp2,clp3,lp1,lp2,lp3,1);
 585
 586 extractthelines(Mat,linesMat,extractedlines):=
 587   if equal(extractedlines,[]) then [[],Mat]
 588   else block([extr,restmat],
 589   if equal(first(linesMat),first(extractedlines)) then
 590     ([extr,restmat] : extractthelines(rest(Mat,1),rest(linesMat,1),rest(extractedlines,1)),
 591     [append([first(Mat)],extr),restmat])
 592   else
 593     ([extr,restmat] : extractthelines(rest(Mat,1),rest(linesMat,1),extractedlines),
 594     [extr,append([first(Mat)],restmat)])
 595   );
 596
 597 Special_linear_solving(Sigma,Q,Info,Mat,v):=
 598   if equal(Q,[]) then v
 599   else
 600     block([lp1,lp2,lp3,l0,l01,l0m1,l1m1,ls,l1,l10,lm10,lm11,M1,M2,M3,M11,M12,M13,M21,M22,M23,M31,M32,M33,A,B,C,D,Sigma1,Sigma2,Sigma3,restSigma1,restSigma2,restSigma3,Info1,Info2,Info3,restInfo1,restInfo2,restInfo3,vlp1,vlp2,vlp3,t1lp1,t1lp2,t1lp3,t2lp2,t2lp1,t2lp3,N32,CompInfo3,CompSigma3,Comp3,clp1,clp2,clp3, CompInfo2,CompSigma2,Comp2],
 601     [lp1,lp2,lp3,l0,l01,l0m1,l1m1,ls,l1,l10,lm10,lm11] : extractInfoSign(Info),
 602     [M1,M2,M3] : extractl1l2l3rows(Mat,lp1,lp2,lp3),
 603     [M11,M12,M13] : extractl1l2l3columns(M1,lp1,lp2,lp3),
 604     [M21,M22,M23] : extractl1l2l3columns(M2,lp1,lp2,lp3),
 605     [M31,M32,M33] : extractl1l2l3columns(M3,lp1,lp2,lp3),
 606     [A,B] : extractthelines(M12,lp1,ls),
 607     [C,D] : extractthelines(M13,lp1,l0),
 608     [Sigma1,Sigma2,Sigma3] : extractl1l2l3rows(Sigma,lp1,lp2,lp3),
 609     [restSigma1,restSigma2,restSigma3] :[deletefirstcolumn(Sigma1),deletefirstcolumn(Sigma2),deletefirstcolumn(Sigma3)],
 610     [Info1,Info2,Info3] : extractl1l2l3rows(Info,lp1,lp2,lp3),
 611     [restInfo1,restInfo2,restInfo3] :[deletefirstcolumn(Info1),deletefirstcolumn(Info2),deletefirstcolumn(Info3)],
 612     [vlp1,vlp2,vlp3] : extractl1l2l3rows(v,lp1,lp2,lp3),
 613     t1lp1 : Special_linear_solving(restSigma1,rest(Q,1),restInfo1,M11,vlp1),
 614     t1lp2 : add(-1,evaluation(M21,t1lp1),1,vlp2),
 615     (if notequal(lp3,[]) then
 616       t1lp3 : add(-1,evaluation(M31,t1lp1),1,vlp3)
 617     else
 618       t1lp3 : []),
 619     [CompInfo2,CompSigma2,Comp2] : compression(restInfo2,restSigma2,rest(Q,1)),
 620     t2lp2 : Special_linear_solving(CompSigma2,Comp2,CompInfo2,newMat(CompSigma2,CompInfo2),t1lp2),
 621     t2lp2 : multiplypartofvect(-1,lp2,lm10,t2lp2),
 622     t2lp2 : multiplypartofvect(-(1/2),lp2,lm11,t2lp2),
 623     t2lp1 : sumvinsidew(-1,t2lp2,listSigma2insideSigma1(lp1,ls),1,t1lp1,lp1),
 624     N32 : put0atcolumns(M32,lp2,lm11),
 625     t2lp3 : add(-1,evaluation(N32,t2lp2),1,t1lp3),
 626     if notequal(lp3,[]) then
 627       ([CompInfo3,CompSigma3,Comp3] : compression(restInfo3,restSigma3,rest(Q,1)),
 628       clp3 : mult(1/2,Special_linear_solving(CompSigma3,Comp3,CompInfo3,newMat(CompSigma3,CompInfo3),t2lp3)),
 629       clp1 : sumvinsidew(-2,clp3,l0,1,t2lp1,lp1),
 630       clp2 : sumvinsidew(1,clp3,l1,1,t2lp2,lp2)
 631       )
 632     else
 633       (clp1 : t2lp1,
 634       clp2 : t2lp2,
 635       clp3 : t2lp3
 636       ),
 637     assemblec(clp1,clp2,clp3,lp1,lp2,lp3)
 638     );
 639
 640 extractSig1Sig2Sig3lp1lp2lp3firstcolumnInfo1(Sigma,temprow):=
 641   block([size,R1,R2,R3,Sig1,Sig2,Sig3,lp1,lp2,lp3,firstcolumnInfo],
 642   if equal(Sigma,[]) then size : 0
 643   elseif equal(rest(Sigma,1),[]) then (size : 1 , R1 : first(Sigma))
 644   elseif equal(rest(rest(Sigma,1),1),[]) then
 645     (size :2, R1 : first(Sigma), R2 : second(Sigma))
 646   else
 647     (size : 3,
 648     R1 : first(Sigma),
 649     R2 : second(Sigma),
 650     R3 : third(Sigma) ),
 651   if equal(size,0) or equal(first(Sigma),[]) then [[],[],[],[],[],[],[]]
 652   elseif equal(size,1) or not(rest(R1,1)=rest(R2,1)) then
 653     ([Sig1,Sig2,Sig3,lp1,lp2,lp3,firstcolumnInfo] : extractSig1Sig2Sig3lp1lp2lp3firstcolumnInfo1(rest(Sigma,1),temprow+1),
 654      [append([rest(R1)],Sig1),Sig2,Sig3,append([temprow],lp1),lp2,lp3,append([[s]],firstcolumnInfo)]
 655     )
 656   elseif equal(size,2) or not(rest(R2,1)=rest(R3,1)) then
 657     ([Sig1,Sig2,Sig3,lp1,lp2,lp3,firstcolumnInfo] : extractSig1Sig2Sig3lp1lp2lp3firstcolumnInfo1(rest(Sigma,2),temprow+2),
 658     if equal(first(R1),0) and equal(first(R2),1) then
 659       [append([rest(R1)],Sig1),append([rest(R1)],Sig2),Sig3,append([temprow],lp1),append([temprow+1],lp2),lp3,append([[e01],[e10]],firstcolumnInfo)]
 660     elseif equal(first(R1),0) and equal(first(R2),-1) then
 661       [append([rest(R1)],Sig1),append([rest(R1)],Sig2),Sig3,append([temprow],lp1),append([temprow+1],lp2),lp3,append([[e0m1],[em10]],firstcolumnInfo)]
 662     else
 663       [append([rest(R1)],Sig1),append([rest(R1)],Sig2),Sig3,append([temprow],lp1),append([temprow+1],lp2),lp3,append([[e1m1],[em11]],firstcolumnInfo)]
 664     )
 665   else
 666     ([Sig1,Sig2,Sig3,lp1,lp2,lp3,firstcolumnInfo] : extractSig1Sig2Sig3lp1lp2lp3firstcolumnInfo1(rest(Sigma,3),temprow+3),
 667     [append([rest(R1)],Sig1),append([rest(R1)],Sig2),append([rest(R1)],Sig3),append([temprow],lp1),append([temprow+1],lp2),append([temprow+2],lp3),append([[0],[1],[m1]],firstcolumnInfo)]
 668     )
 669   );
 670
 671
 672 newassembleInfo(Info1,Info2,Info3,lp1,lp2,lp3,firstcolumnInfo,temprow):=
 673   if equal(Info1,[]) and equal(Info2,[]) and equal(Info3,[]) then firstcolumnInfo
 674   elseif notequal(lp1,[]) and equal(first(lp1),temprow) then
 675     (
 676
 677   append([append(first(firstcolumnInfo),first(Info1))],newassembleInfo(rest(Info1,1),Info2,Info3,rest(lp1,1),lp2,lp3,rest(firstcolumnInfo,1),temprow+1)) )
 678   elseif notequal(lp2,[]) and equal(first(lp2),temprow) then
 679     (
 680     append([append(first(firstcolumnInfo),first(Info2))],newassembleInfo(Info1,rest(Info2,1),Info3,lp1,rest(lp2,1),lp3,rest(firstcolumnInfo,1),temprow+1))
 681 )
 682   else
 683     (
 684     append([append(first(firstcolumnInfo),first(Info3))],newassembleInfo(Info1,Info2,rest(Info3,1),lp1,lp2,rest(lp3,1),rest(firstcolumnInfo,1),temprow+1)) ) ;
 685
 686
 687
 688 newInfo(Sigma):=
 689   if equal(Sigma,[]) or equal(first(Sigma),[]) then Sigma
 690   else
 691   block([Sig1,Sig2,Sig3,lp1,lp2,lp3,firstcolumnInfo,Info1,Info2,Info3],
 692   [Sig1,Sig2,Sig3,lp1,lp2,lp3,firstcolumnInfo] : extractSig1Sig2Sig3lp1lp2lp3firstcolumnInfo1(Sigma,1),
 693   Info1 : newInfo(Sig1),
 694   Info2 : newInfo(Sig2),
 695   Info3 : newInfo(Sig3),
 696   newassembleInfo(Info1,Info2,Info3,lp1,lp2,lp3,firstcolumnInfo,1)
 697   );
 698
 699 newAdarow(temppolylist,rowInfo):=
 700   if equal(temppolylist,[]) then 1
 701   else
 702   block([P],
 703   P : newAdarow(rest(temppolylist,1),rest(rowInfo,1)),
 704   if first(rowInfo)=1 or first(rowInfo)=e10 or first(rowInfo)=em10 or first(rowInfo)=em11 then
 705     first(temppolylist)*P
 706   elseif first(rowInfo)=m1 then
 707     first(temppolylist)^2*P
 708   else P
 709   );
 710
 711 newAda(Info,polylist):=
 712   if equal(Info,[]) then []
 713   else append([newAdarow(polylist,first(Info))],newAda(rest(Info,1),polylist));
 714
 715 makecolumn(v):=
 716   if equal(v,[]) then []
 717   else append([[first(v)]],makecolumn(rest(v,1)));
 718
 719 newfirstcolumn(v,Mat):=
 720   if equal(Mat,[]) then makecolumn(v)
 721   else append([append([first(v)],first(Mat))],newfirstcolumn(rest(v,1),rest(Mat,1)));
 722
 723 newMat(Sigma,Info):=
 724   if equal(Sigma,[]) then []
 725   else newfirstcolumn(newAda(Info,first(Sigma)),newMat(rest(Sigma,1),Info)) ;
 726   multlistby(list,elem) :=
 727   if equal(list,[]) then []
 728   else append([elem*first(list)],multlistby(rest(list,1),elem));
 729
 730 Tarskiquerylist(P,polylist,TaQu,var):=
 731   if equal(polylist,[]) then []
 732   else
 733     append([TaQu(first(polylist),P,var)],Tarskiquerylist(P,rest(polylist,1),TaQu,var)) ;
 734
 735 rowNewAuxMat1(row):=
 736   if equal(row,[]) then []
 737   else append([first(row),first(row),first(row)],rowNewAuxMat1(rest(row,1)));
 738
 739 rowNewAuxMat2(row):=
 740   if equal(row,[]) then []
 741   else append([0,first(row),-first(row)],rowNewAuxMat2(rest(row,1)));
 742
 743 rowNewAuxMat3(row):=
 744   if equal(row,[]) then []
 745   else append([0,first(row),first(row)],rowNewAuxMat3(rest(row,1)));
 746
 747 NewAuxMat(oldMat):=
 748   if equal(oldMat,[]) then []
 749   else append([rowNewAuxMat1(first(oldMat)),rowNewAuxMat2(first(oldMat)),rowNewAuxMat3(first(oldMat))],NewAuxMat(rest(oldMat,1))) ;
 750
 751 createvector(v1,v2,v3):=
 752   if equal(v1,[]) then []
 753   else append([first(v1),first(v2),first(v3)],createvector(rest(v1,1),rest(v2,1),rest(v3,1)));
 754
 755 makeauxSigma(Sigma):=
 756   if equal(Sigma,[]) then []
 757   else
 758     append([append([0],first(Sigma)),append([1],first(Sigma)),append([-1],first(Sigma))],makeauxSigma(rest(Sigma,1))) ;
 759
 760 makenewSigma(c,AuxSigma,AuxCompSigma,temprow):=
 761   if equal(c,[]) then [[],[],[],[],[],[],[],[],[],[],[],[],[],[]]
 762   else
 763     block([tempc,tempSigma,tempSigma1,tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3],
 764     if notequal(first(c),0) and notequal(second(c),0) and notequal(third(c),0) then
 765       ([tempc,tempSigma,tempCompSigma,tempSigma1,tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] :
 766     makenewSigma(rest(c,3),rest(AuxSigma,3),rest(AuxCompSigma,3),temprow+3),
 767       [append([first(c),second(c),third(c)],tempc),append([first(AuxSigma),second(AuxSigma),third(AuxSigma)],tempSigma),append([first(AuxCompSigma),second(AuxCompSigma),third(AuxCompSigma)],tempCompSigma),append([first(AuxCompSigma)],tempSigma1),append([second(AuxCompSigma)],tempSigma2),append([third(AuxCompSigma)],tempSigma3),append([temprow],l0),l01,l0m1,l1m1,ls,append([temprow],lp1),append([temprow+1],lp2),append([temprow+2],lp3)] )
 768     elseif notequal(first(c),0) and notequal(second(c),0) then
 769       ([tempc,tempSigma,tempCompSigma,tempSigma1,tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] :
 770     makenewSigma(rest(c,3),rest(AuxSigma,3),rest(AuxCompSigma,3),temprow+2),
 771       [append([first(c),second(c)],tempc),append([first(AuxSigma),second(AuxSigma)],tempSigma),append([first(AuxCompSigma),second(AuxCompSigma)],tempCompSigma),append([first(AuxCompSigma)],tempSigma1),append([second(AuxCompSigma)],tempSigma2),tempSigma3,l0,append([temprow],l01),l0m1,l1m1,ls,append([temprow],lp1),append([temprow+1],lp2),lp3])
 772     elseif notequal(first(c),0) and notequal(third(c),0) then
 773       ([tempc,tempSigma,tempCompSigma,tempSigma1,tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] :
 774     makenewSigma(rest(c,3),rest(AuxSigma,3),rest(AuxCompSigma,3),temprow+2),
 775       [append([first(c),third(c)],tempc),append([first(AuxSigma),third(AuxSigma)],tempSigma),append([first(AuxCompSigma),third(AuxCompSigma)],tempCompSigma),append([first(AuxCompSigma)],tempSigma1),append([third(AuxCompSigma)],tempSigma2),tempSigma3,l0,l01,append([temprow],l0m1),l1m1,ls,append([temprow],lp1),append([temprow+1],lp2),lp3])
 776     elseif notequal(second(c),0) and notequal(third(c),0) then
 777       ([tempc,tempSigma,tempCompSigma,tempSigma1,tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] :
 778     makenewSigma(rest(c,3),rest(AuxSigma,3),rest(AuxCompSigma,3),temprow+2),
 779       [append([second(c),third(c)],tempc),append([second(AuxSigma),third(AuxSigma)],tempSigma),append([second(AuxCompSigma),third(AuxCompSigma)],tempCompSigma),append([second(AuxCompSigma)],tempSigma1),append([third(AuxCompSigma)],tempSigma2),tempSigma3,l0,l01,l0m1,append([temprow],l1m1),ls,append([temprow],lp1),append([temprow+1],lp2),lp3])
 780     elseif notequal(first(c),0) then
 781       ([tempc,tempSigma,tempCompSigma,tempSigma1,tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] :
 782     makenewSigma(rest(c,3),rest(AuxSigma,3),rest(AuxCompSigma,3),temprow+1),
 783       [append([first(c)],tempc),append([first(AuxSigma)],tempSigma),append([first(AuxCompSigma)],tempCompSigma),append([first(AuxCompSigma)],tempSigma1),tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,append([temprow],ls),append([temprow],lp1),lp2,lp3])
 784     elseif notequal(second(c),0) then
 785     ([tempc,tempSigma,tempCompSigma,tempSigma1,tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] :
 786     makenewSigma(rest(c,3),rest(AuxSigma,3),rest(AuxCompSigma,3),temprow+1),
 787       [append([second(c)],tempc),append([second(AuxSigma)],tempSigma),append([second(AuxCompSigma)],tempCompSigma),append([second(AuxCompSigma)],tempSigma1),tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,append([temprow],ls),append([temprow],lp1),lp2,lp3])
 788     else
 789       ([tempc,tempSigma,tempCompSigma,tempSigma1,tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] :
 790     makenewSigma(rest(c,3),rest(AuxSigma,3),rest(AuxCompSigma,3),temprow+1),
 791       [append([third(c)],tempc),append([third(AuxSigma)],tempSigma),append([third(AuxCompSigma)],tempCompSigma),append([third(AuxCompSigma)],tempSigma1),tempSigma2,tempSigma3,l0,l01,l0m1,l1m1,append([temprow],ls),append([temprow],lp1),lp2,lp3])
 792     );
 793
 794 rowpart1ofNewMat(rowoldMat,l0,l01,l0m1,l1m1,ls,tempplace):=
 795   if equal(rowoldMat,[]) then []
 796   elseif notequal(l0,[]) and equal(tempplace,first(l0)) then
 797     append([first(rowoldMat),first(rowoldMat),first(rowoldMat)],rowpart1ofNewMat(rest(rowoldMat,1),rest(l0,1),l01,l0m1,l1m1,ls,tempplace+3))
 798   elseif notequal(l01,[]) and equal(tempplace,first(l01)) then
 799     append([first(rowoldMat),first(rowoldMat)],rowpart1ofNewMat(rest(rowoldMat,1),l0,rest(l01,1),l0m1,l1m1,ls,tempplace+2))
 800   elseif notequal(l0m1,[]) and equal(tempplace,first(l0m1)) then
 801     append([first(rowoldMat),first(rowoldMat)],rowpart1ofNewMat(rest(rowoldMat,1),l0,l01,rest(l0m1,1),l1m1,ls,tempplace+2))
 802   elseif notequal(l1m1,[]) and equal(tempplace,first(l1m1)) then
 803     append([first(rowoldMat),first(rowoldMat)],rowpart1ofNewMat(rest(rowoldMat,1),l0,l01,l0m1,rest(l1m1,1),ls,tempplace+2))
 804   elseif notequal(rowoldMat,[]) then
 805      append([first(rowoldMat)],rowpart1ofNewMat(rest(rowoldMat,1),l0,l01,l0m1,l1m1,rest(ls,1),tempplace+1))
 806   else [] ;
 807
 808 part1ofNewMat(oldMat,l0,l01,l0m1,l1m1,ls):=
 809   if equal(oldMat,[]) then []
 810   else append([rowpart1ofNewMat(first(oldMat),l0,l01,l0m1,l1m1,ls,1)],part1ofNewMat(rest(oldMat,1),l0,l01,l0m1,l1m1,ls));
 811
 812 assembletwoparts(part1,part2,lp1,lp2):=
 813   if equal(lp2,[]) then part1
 814   elseif equal(lp1,[]) then part2
 815   elseif first(lp1)<first(lp2) then
 816     append([first(part1)],assembletwoparts(rest(part1,1),part2,rest(lp1,1),lp2))
 817   else
 818     append([first(part2)],assembletwoparts(part1,rest(part2,1),lp1,rest(lp2,1)))
 819 ;
 820
 821 assemblethreeparts(part1,part2,part3,lp1,lp2,lp3):=
 822   if equal(lp2,[]) and equal(lp3,[]) then part1
 823   elseif equal(lp2,[]) then append(part3,part1)
 824   elseif equal(lp3,[]) then assembletwoparts(part1,part2,lp1,lp2)
 825   elseif equal(lp1,[]) then append(part2,part3)
 826   elseif first(lp1)<first(lp2) and first(lp1)<first(lp3) then
 827     append([first(part1)],assemblethreeparts(rest(part1,1),part2,part3,rest(lp1,1),lp2,lp3))
 828   elseif first(lp2)<first(lp1) and first(lp2)<first(lp3) then
 829     append([first(part2)],assemblethreeparts(part1,rest(part2,1),part3,lp1,rest(lp2,1),lp3))
 830   else
 831     append([first(part3)],assemblethreeparts(part1,part2,rest(part3),lp1,lp2,rest(lp3,1))) ;
 832
 833 createfirstcolumnInfomat(l0,l01,l0m1,l1m1,ls,temprow):=
 834   if notequal(l0,[]) and equal(first(l0),temprow) then
 835     append([0,1,m1],createfirstcolumnInfomat(rest(l0,1),l01,l0m1,l1m1,ls,temprow+3))
 836   elseif notequal(l01,[]) and equal(first(l01),temprow) then
 837     append([e01,e10],createfirstcolumnInfomat(l0,rest(l01,1),l0m1,l1m1,ls,temprow+2))
 838   elseif notequal(l0m1,[]) and equal(first(l0m1),temprow) then
 839     append([e0m1,em10],createfirstcolumnInfomat(l0,l01,rest(l0m1,1),l1m1,ls,temprow+2))
 840   elseif notequal(l1m1,[]) and equal(first(l1m1),temprow) then
 841     append([e1m1,em11],createfirstcolumnInfomat(l0,l01,l0m1,rest(l1m1,1),ls,temprow+2))
 842   elseif notequal(ls,[]) and equal(first(ls),temprow) then
 843     append([s],createfirstcolumnInfomat(l0,l01,l0m1,l1m1,rest(ls),temprow+1))
 844   else
 845     []
 846   ;
 847
 848 createInformationmat(Info1,Info2,Info3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3):=
 849   block([column,M],
 850   column : createfirstcolumnInfomat(l0,l01,l0m1,l1m1,ls,1),
 851   M : assemblethreeparts(Info1,Info2,Info3,lp1,lp2,lp3),
 852   newfirstcolumn(column,M)
 853   );
 854
 855 addnewfirstcolumn(elem,Mat):=
 856   if equal(Mat,[]) then []
 857   else append([append([elem],first(Mat))],addnewfirstcolumn(elem,rest(Mat,1)));
 858
 859
 860
 861 rowpart2ofNewMat(rowoldMat,l0,l01,l0m1,l1m1,ls,tempplace,Sigma):=
 862   if equal(rowoldMat,[]) then []
 863   elseif notequal(l0,[]) and equal(tempplace,first(l0)) then
 864     append([0,first(rowoldMat),-first(rowoldMat)],rowpart2ofNewMat(rest(rowoldMat,1),rest(l0,1),l01,l0m1,l1m1,ls,tempplace+3,rest(Sigma,3)))
 865   elseif notequal(l01,[]) and equal(tempplace,first(l01)) then
 866     append([0,first(rowoldMat)],rowpart2ofNewMat(rest(rowoldMat,1),l0,rest(l01,1),l0m1,l1m1,ls,tempplace+2,rest(Sigma,2)))
 867   elseif notequal(l0m1,[]) and equal(tempplace,first(l0m1)) then
 868     append([0,-first(rowoldMat)],rowpart2ofNewMat(rest(rowoldMat,1),l0,l01,rest(l0m1,1),l1m1,ls,tempplace+2,rest(Sigma,2)))
 869   elseif notequal(l1m1,[]) and equal(tempplace,first(l1m1)) then
 870     append([first(rowoldMat),-first(rowoldMat)],rowpart2ofNewMat(rest(rowoldMat,1),l0,l01,l0m1,rest(l1m1,1),ls,tempplace+2,rest(Sigma,2)))
 871   elseif notequal(rowoldMat,[]) then
 872      append([first(rowoldMat)*first(first(Sigma))],rowpart2ofNewMat(rest(rowoldMat,1),l0,l01,l0m1,l1m1,rest(ls,1),tempplace+1,rest(Sigma,1)))
 873   else [] ;
 874
 875 part2ofNewMat(oldMat,l0,l01,l0m1,l1m1,ls,Sigma):=
 876   if equal(oldMat,[]) then []
 877   else append([rowpart2ofNewMat(first(oldMat),l0,l01,l0m1,l1m1,ls,1,Sigma)],part2ofNewMat(rest(oldMat,1),l0,l01,l0m1,l1m1,ls,Sigma));
 878
 879 rowpart3ofNewMat(rowoldMat,l0,l01,l0m1,l1m1,ls,tempplace,Sigma):=
 880   if equal(rowoldMat,[]) then []
 881   elseif notequal(l0,[]) and equal(tempplace,first(l0)) then
 882     append([0,first(rowoldMat),first(rowoldMat)],rowpart3ofNewMat(rest(rowoldMat,1),rest(l0,1),l01,l0m1,l1m1,ls,tempplace+3,rest(Sigma,3)))
 883   elseif notequal(l01,[]) and equal(tempplace,first(l01)) then
 884     append([0,first(rowoldMat)],rowpart3ofNewMat(rest(rowoldMat,1),l0,rest(l01,1),l0m1,l1m1,ls,tempplace+2,rest(Sigma,2)))
 885   elseif notequal(l0m1,[]) and equal(tempplace,first(l0m1)) then
 886     append([0,first(rowoldMat)],rowpart3ofNewMat(rest(rowoldMat,1),l0,l01,rest(l0m1,1),l1m1,ls,tempplace+2,rest(Sigma,2)))
 887   elseif notequal(l1m1,[]) and equal(tempplace,first(l1m1)) then
 888     append([first(rowoldMat),first(rowoldMat)],rowpart3ofNewMat(rest(rowoldMat,1),l0,l01,l0m1,rest(l1m1,1),ls,tempplace+2,rest(Sigma,2)))
 889   elseif notequal(rowoldMat,[]) then
 890      append([first(rowoldMat)*(first(first(Sigma)))^2],rowpart2ofNewMat(rest(rowoldMat,1),l0,l01,l0m1,l1m1,rest(ls,1),tempplace+1,rest(Sigma,1)))
 891   else [] ;
 892
 893 part3ofNewMat(oldMat,l0,l01,l0m1,l1m1,ls,Sigma):=
 894   if equal(oldMat,[]) then []
 895   else append([rowpart3ofNewMat(first(oldMat),l0,l01,l0m1,l1m1,ls,1,Sigma)],part3ofNewMat(rest(oldMat,1),l0,l01,l0m1,l1m1,ls,Sigma));
 896
 897
 898 Special_linear_solvingstep1(Sigma,Q,Info,Mat,v,oldc):=
 899   if equal(Q,[]) then v
 900   else
 901     block([lp1,lp2,lp3,l0,l01,l0m1,l1m1,ls,l1,l10,lm10,lm11,M1,M2,M3,M11,M12,M13,M21,M22,M23,M31,M32,M33,Sigma1,Sigma2,Sigma3,restSigma1,restSigma2,restSigma3,Info1,Info2,Info3,restInfo1,restInfo2,restInfo3,vlp1,vlp2,vlp3,t1lp1,t1lp2,t1lp3,t2lp2,t2lp1,t2lp3,N32,CompInfo3,CompSigma3,Comp3,clp1,clp2,clp3],
 902     [lp1,lp2,lp3,l0,l01,l0m1,l1m1,ls,l1,l10,lm10,lm11] : extractInfoSign(Info),
 903     [M1,M2,M3] : extractl1l2l3rows(Mat,lp1,lp2,lp3),
 904     [M11,M12,M13] : extractl1l2l3columns(M1,lp1,lp2,lp3),
 905     [M21,M22,M23] : extractl1l2l3columns(M2,lp1,lp2,lp3),
 906     [M31,M32,M33] : extractl1l2l3columns(M3,lp1,lp2,lp3),
 907     [Sigma1,Sigma2,Sigma3] : extractl1l2l3rows(Sigma,lp1,lp2,lp3),
 908     [restSigma1,restSigma2,restSigma3] :[deletefirstcolumn(Sigma1),deletefirstcolumn(Sigma2),deletefirstcolumn(Sigma3)],
 909     [Info1,Info2,Info3] : extractl1l2l3rows(Info,lp1,lp2,lp3),
 910     [restInfo1,restInfo2,restInfo3] :[deletefirstcolumn(Info1),deletefirstcolumn(Info2),deletefirstcolumn(Info3)],
 911     [vlp1,vlp2,vlp3] : extractl1l2l3rows(v,lp1,lp2,lp3),
 912     t1lp1 : oldc,
 913     t1lp2 : add(-1,evaluation(M21,t1lp1),1,vlp2),
 914     (if notequal(lp3,[]) then
 915       t1lp3 : add(-1,evaluation(M31,t1lp1),1,vlp3)
 916     else
 917       t1lp3 : []),
 918     [CompInfo2,CompSigma2,Comp2] : compression(restInfo2,restSigma2,rest(Q,1)),
 919     t2lp2 : Special_linear_solving(CompSigma2,Comp2,CompInfo2,newMat(CompSigma2,CompInfo2),t1lp2),
 920     t2lp2 : multiplypartofvect(-1,lp2,lm10,t2lp2),
 921     t2lp2 : multiplypartofvect(-(1/2),lp2,lm11,t2lp2),
 922     t2lp1 : sumvinsidew(-1,t2lp2,listSigma2insideSigma1(lp1,ls),1,t1lp1,lp1),
 923     N32 : put0atcolumns(M32,lp2,lm11),
 924     t2lp3 : add(-1,evaluation(N32,t2lp2),1,t1lp3),
 925     if notequal(lp3,[]) then
 926       ([CompInfo3,CompSigma3,Comp3] : compression(restInfo3,restSigma3,rest(Q,1)),
 927       clp3 : mult(1/2,Special_linear_solving(CompSigma3,Comp3,CompInfo3,newMat(CompSigma3,CompInfo3),t2lp3)),
 928       clp1 : sumvinsidew(-2,clp3,l0,1,t2lp1,lp1),
 929       clp2 : sumvinsidew(1,clp3,l1,1,t2lp2,lp2)
 930       )
 931     else
 932       (clp1 : t2lp1,
 933       clp2 : t2lp2,
 934       clp3 : t2lp3
 935       ),
 936     assemblec(clp1,clp2,clp3,lp1,lp2,lp3)
 937     );
 938
 939 newc1m1(c):=
 940   if equal(c,[]) then []
 941   else append([0,first(c),second(c)],newc1m1(rest(c,2)));
 942
 943 newc0m1(c):=
 944   if equal(c,[]) then []
 945   else append([first(c),0,second(c)],newc0m1(rest(c,2)));
 946
 947 newc01(c):=
 948   if equal(c,[]) then []
 949   else append([first(c),second(c),0],newc01(rest(c,2)));
 950
 951 threepartvect(a,b,c):=
 952   if equal(a,[]) then []
 953   else append([first(a),first(b),first(c)],threepartvect(rest(a,1),rest(b,1),rest(c,1)));
 954
 955 Special_linear_solvingthreesigns(CompSigma,Q,Info,Mat,v0,v1,v2,c_i):=
 956   block([tprime,t2prime,cl2,cl3,cl1],
 957   tprime : Special_linear_solving(CompSigma,Q,Info,Mat,v1),
 958   t2prime : Special_linear_solving(CompSigma,Q,Info,Mat,v2),
 959   cl2 : add(1/2,tprime,1/2,t2prime),
 960   cl3 : add(-1/2,tprime,1/2,t2prime),
 961   cl1 : add(1,c_i,-1,t2prime),
 962   threepartvect(cl1,cl2,cl3)
 963   );
 964
 965 Special_linear_solving01(CompSigma,Q,Info,Mat,v0,v1,c_i):=
 966   block([cl2,cl1],
 967   cl2 : Special_linear_solving(CompSigma,Q,Info,Mat,v1),
 968   cl1 : add(1,c_i,-1,cl2),
 969   join(cl1,cl2)
 970   );
 971
 972 Special_linear_solving0m1(CompSigma,Q,Info,Mat,v0,v1,c_i):=
 973   block([cl2,cl1],
 974   cl2 : multlistby(Special_linear_solving(CompSigma,Q,Info,Mat,v1),-1),
 975   cl1 : add(1,c_i,-1,cl2),
 976   join(cl1,cl2)
 977   );
 978
 979 Special_linear_solving1m1(CompSigma,Q,Info,Mat,v0,v1,c_i):=
 980   block([c2prime,cl1,cl2],
 981   c2prime : Special_linear_solving(CompSigma,Q,Info,Mat,v1),
 982   cl1 : add(1/2,c_i,1/2,c2prime),
 983   cl2 : add(1/2,c_i,-1/2,c2prime),
 984   join(cl1,cl2)
 985   );
 986
 987 quickSignDeterminationwithcardinals(polylist,P,TaQu,var):=
 988   block([r,Sigma_i,CompressedSigma_i,c_i,comp_i,Info_i,Ada_i,Mat_i,AdaQulist,i,temppolylist,usefullpoly,cdet,cplus,cminus,czero,v1,v2,AuxCompSigma,AuxSigma,InfoAux,AuxMat,v,c,tempCompSigma,Sigma1,Sigma2,Sigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3,Info1,Info2,Info3,Ada1,Ada2,Ada3,TaQu1,TaQu2,TaQu3,Mat1,Mat2,Mat3, Mat2prime, Mat3prime],
 989   r : TaQu(1,P,var),
 990   if equal(r,0) then [[],[]]
 991   else
 992     (Sigma_i : [[]],
 993     CompressedSigma_i : [[]],
 994     c_i : [r],
 995     comp_i : [],
 996     Info_i : [[]],
 997     Ada_i : [1],
 998     Mat_i : [[1]],
 999     AdaQulist : [r],
1000     i : 0,
1001     temppolylist : polylist,
1002     usefullpoly : [],
1003     while notequal(temppolylist,[]) do
1004       (i : i+1,
1005       cdet : evaluation([[1/2,1/2],[-1/2,1/2]],[TaQu(first(temppolylist),P,var),TaQu((first(temppolylist))^2,P,var)]),
1006       [cplus,cminus] : cdet,
1007       czero : r-(cplus+cminus),
1008       if notequal(cplus,0) and notequal(cminus,0) and notequal(czero,0) then
1009         (v1 : Tarskiquerylist(P,multlistby(Ada_i,first(temppolylist)),TaQu,var),
1010         v2 : Tarskiquerylist(P,multlistby(Ada_i,(first(temppolylist))^2),TaQu,var),
1011         c :Special_linear_solvingthreesigns(CompressedSigma_i,comp_i,Info_i,Mat_i,AdaQulist,v1,v2,c_i),
1012         [c_i,Sigma_i,tempCompSigma,Sigma1,Sigma2,Sigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] : makenewSigma(c,makeauxSigma(Sigma_i),makeauxSigma(CompressedSigma_i),1) )
1013       elseif equal(cplus,0) and equal(cminus,0) then
1014         (Sigma_i : addnewfirstcolumn(0,Sigma_i),
1015         lp2 : [])
1016       elseif equal(czero,0) and equal(cminus,0) then
1017         (Sigma_i : addnewfirstcolumn(1,Sigma_i),
1018         lp2 : [])
1019       elseif equal(cplus,0) and equal(czero,0) then
1020         (Sigma_i : addnewfirstcolumn(-1,Sigma_i),
1021         lp2 : [])
1022       elseif equal(czero,0) then
1023         (v1 : Tarskiquerylist(P,multlistby(Ada_i,first(temppolylist)),TaQu,var),
1024         c : Special_linear_solving1m1(CompressedSigma_i,comp_i,Info_i,Mat_i,AdaQulist,v1,c_i),
1025         c : newc1m1(c),
1026         [c_i,Sigma_i,tempCompSigma,Sigma1,Sigma2,Sigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] : makenewSigma(c,makeauxSigma(Sigma_i),makeauxSigma(CompressedSigma_i),1)
1027         )
1028       elseif equal(cplus,0) then
1029         (v1 : Tarskiquerylist(P,multlistby(Ada_i,first(temppolylist)),TaQu,var),
1030         c : Special_linear_solving0m1(CompressedSigma_i,comp_i,Info_i,Mat,AdaQulist,v1,c_i),
1031         c : newc0m1(c),
1032         [c_i,Sigma_i,tempCompSigma,Sigma1,Sigma2,Sigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] : makenewSigma(c,makeauxSigma(Sigma_i),makeauxSigma(CompressedSigma_i),1)
1033         )
1034       else
1035         (v1 : Tarskiquerylist(P,multlistby(Ada_i,first(temppolylist)),TaQu,var),
1036         c : Special_linear_solving01(CompressedSigma_i,comp_i,Info_i,Mat_i,AdaQulist,v1,c_i),
1037         c : newc01(c),
1038         [c_i,Sigma_i,tempCompSigma,Sigma1,Sigma2,Sigma3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3] : makenewSigma(c,makeauxSigma(Sigma_i),makeauxSigma(CompressedSigma_i),1)
1039         ),
1040       if equal(lp2,[]) then (1=1)
1041       else
1042         (CompressedSigma_i : tempCompSigma,
1043         comp_i : append([i],comp_i),
1044         usefullpoly : append([first(temppolylist)],usefullpoly),
1045         Info1 : Info_i,
1046         Info2 : newInfo(deletefirstcolumn(Sigma2)),
1047         Info3 : newInfo(deletefirstcolumn(Sigma3)),
1048         Info_i : createInformationmat(Info1,Info2,Info3,l0,l01,l0m1,l1m1,ls,lp1,lp2,lp3),
1049         Mat1 : part1ofNewMat(Mat_i,l0,l01,l0m1,l1m1,ls),
1050         Mat2prime : newMat(deletefirstcolumn(Sigma1),Info2),
1051         Mat2 : part2ofNewMat(Mat2prime,l0,l01,l0m1,l1m1,ls,CompressedSigma_i),
1052         Mat3prime : newMat(deletefirstcolumn(Sigma1),Info3),
1053         Mat3 : part3ofNewMat(Mat3prime,l0,l01,l0m1,l1m1,ls,CompressedSigma_i),
1054         Mat_i : assemblethreeparts(Mat1,Mat2,Mat3,lp1,lp2,lp3),
1055         Info2 : addnewfirstcolumn(1,Info2),
1056         Info3 : addnewfirstcolumn(m1,Info3),
1057         Ada1 : Ada_i,
1058         Ada2 : newAda(Info2,usefullpoly),
1059         Ada3 : newAda(Info3,usefullpoly),
1060         Ada_i : assemblethreeparts(Ada1,Ada2,Ada3,lp1,lp2,lp3),
1061         TaQu1 : AdaQulist,
1062         TaQu2 : Tarskiquerylist(P,Ada2,TaQu,var),
1063         TaQu3 : Tarskiquerylist(P,Ada3,TaQu,var),
1064         AdaQulist : assemblethreeparts(TaQu1,TaQu2,TaQu3,lp1,lp2,lp3)
1065
1066         )
1067       ,
1068       temppolylist : rest(temppolylist,1)
1069       ),
1070     [c_i,Reverserows(Sigma_i)]
1071     )
1072
1073   );
1074
1075 quickSignDetermination(polylist,P,TaQu,var):=
1076   second(quickSignDeterminationwithcardinals(polylist,P,TaQu,var));