|\^/| Maple 18 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. [&x, *, +, -, ., <,>, <|>, About, AddCoordinates, ArcLength, BasisFormat, Binormal, Compatibility, ConvertVector, CrossProduct, Curl, Curvature, D, Del, DirectionalDiff, Divergence, DotProduct, Flux, GetCoordinateParameters, GetCoordinates, GetNames, GetPVDescription, GetRootPoint, GetSpace, Gradient, Hessian, IsPositionVector, IsRootedVector, IsVectorField, Jacobian, Laplacian, LineInt, MapToBasis, Nabla, Norm, Normalize, PathInt, PlotPositionVector, PlotVector, PositionVector, PrincipalNormal, RadiusOfCurvature, RootedVector, ScalarPotential, SetCoordinateParameters, SetCoordinates, SpaceCurve, SurfaceInt, TNBFrame, Tangent, TangentLine, TangentPlane, TangentVector, Torsion, Vector, VectorField, VectorPotential, VectorSpace, Wronskian, diff, eval, evalVF, int, limit, series] Path set to /dsk/l1/fgb/13379/FGblib/../libfgbunid.so FGb/Maple interface package Version 1.63 JC Faugere (Jean-Charles.Faugere@inria.fr) Type ?FGb for documentation Warning, `n` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `EQUS` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `linear` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `var` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `S` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `par` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `ls` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `myrand1` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `myrand` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `myprime` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `gb` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `rr1` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `DEG` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `boo` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `i` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `NEWVARS` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `LS` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `param` is implicitly declared local to procedure `FGbRationalParametrization` FGbRationalParametrization := proc(EQUATIONS, VARS) local n, EQUS, linear, var, S, par, ls, myrand1, myrand, myprime, gb, rr1, DEG, boo, i, NEWVARS, LS, param; n := nops(VARS); EQUS := expand(EQUATIONS); if indets(VARS) <> indets(EQUS) then print(indets(EQUS) <> indets(VARS)); error "Variables do not match" end if; if n = 1 then error "Univariate Case" end if; if member(1, map(degree, EQUS)) then linear := map(_pol -> if degree(_pol) = 1 then _pol end if, EQUS); var := indets(linear[1])[1]; S := solve(linear[1], var); par, ls := FGbRationalParametrization(subs(var = S, EQUATIONS), remove(member, VARS, [var])); return par, {op(ls), var = S} end if; myrand1 := rand(1 .. 10); myrand := rand(9000 .. 65519); myprime := nextprime(myrand()); gb := FGb:-fgb_gbasis_lm([VectorCalculus:-`+`( add(VectorCalculus:-`*`(myrand(), VARS[i]), i = 1 .. n), myrand()), op(EQUS)], myprime, [], VARS, {"index" = 99886600, "verb" = 0}); if gb[1] <> [1] then printf("\t\n\n Positive dimension \n\n"); error "Positive dimension" end if; gb := FGb:-fgb_gbasis(EQUS, myprime, [], VARS, {"index" = 99886600, "verb" = 0}); if member(1, map(degree, gb)) then FGb:-fgb_gbasis(EQUS, 0, [], VARS, {"index" = 99886600, "verb" = 0}) ; return [1], {}; error "There is a linear polynomial in the Gb" end if; if gb = [1] then return [seq(1, i = 1 .. nops(vars))], {} end if; rr1 := FGb:-fgb_matrixn(subs(VARS[n] = VectorCalculus:-`+`(add( VectorCalculus:-`*`(myrand(), VARS[i]), i = 1 .. VectorCalculus:-`+`(n, -1)), VARS[n]), gb), myprime, VARS, {"index" = 99886600, "verb" = 0}); if 1 <= nops(map(_sqr -> if 1 < _sqr[2] then _sqr[2] end if, (Sqrfree(rr1[nops(rr1)]) mod myprime)[2])) then printf("Non radical case\n", degree(rr1[nops(rr1)]), add( degree(_pol[1]), _pol in (Sqrfree(rr1[nops(rr1)]) mod myprime)[2])); error "Non radical case" end if; DEG := degree(rr1[nops(rr1)]); printf("\n\nDegree is %d\n\n", DEG); boo := false; for i from nops(VARS) by -1 to 1 do NEWVARS := [op(remove(member, VARS, VARS[i .. i])), VARS[i]]; try rr1 := FGb:-fgb_matrixn(gb, myprime, NEWVARS, {"index" = 99886600, "verb" = 0}); if 0 < nops(rr1) then boo := true; break end if catch: end try end do; if boo then LS := {}; if 0 = 0 then param := FGb:-fgb_matrixn(EQUS, 0, NEWVARS, {"index" = 99886600, "verb" = 0}) else param := FGb:-fgb_matrixn(EQUS, 65521, NEWVARS, {"index" = 99886600, "verb" = 0}) end if else printf("\n\nChange of variables requested\n\n"); LS := {VARS[n] = VectorCalculus:-`+`(VARS[n], add(VectorCalculus:-`*`(myrand1(), VARS[i]), i = 1 .. n))}; if 0 = 0 then param := FGb:-fgb_matrixn( map(expand, subs(LS, EQUS)), 0, VARS, {"index" = 99886600, "verb" = 0}) else param := FGb:-fgb_matrixn(map(expand, subs(LS, EQUS)), 65521, VARS, {"index" = 99886600, "verb" = 0}) end if end if; return param, LS end proc MyIsolation := proc(rrform) local newrr, elimvars, othervars, reg, SOLS, vars, DEG; elimvars := indets(rrform[1])[1]; othervars := map(_eqs -> indets(_eqs) minus {elimvars}, rrform[2 .. nops(rrform)]); othervars := map(_v -> _v[1], othervars); DEG := degree(rrform[1]); newrr := [rrform[1], VectorCalculus:-diff(rrform[1], elimvars), [rem( VectorCalculus:-`*`(VectorCalculus:-diff(rrform[1], elimvars), elimvars), rrform[1], elimvars), seq(VectorCalculus:-`-`( VectorCalculus:-`*`( coeff(rrform[i], othervars[VectorCalculus:-`+`(i, -1)], 0), DEG)), i = 2 .. nops(rrform))]]; reg := lcm(op(map(denom, newrr[3])), denom(newrr[2])); newrr := [numer(newrr[1]), expand(VectorCalculus:-`*`(reg, newrr[2])), map(_eqs -> expand(VectorCalculus:-`*`(_eqs, reg)), newrr[3])]; SOLS := fgbrs:-rs_isolate_rur(newrr[1], newrr[2], newrr[3], elimvars, verbose = 0); vars := [elimvars, op(othervars)]; SOLS := map(_point -> [seq(vars[i] = VectorCalculus:-`*`( VectorCalculus:-`+`(_point[i][1], _point[i][2]), 1/2), i = 1 .. nops(vars))], SOLS); return SOLS end proc my_rs_rur_sys := proc( sys::depends(list(polynom(integer, vars))), vars::list(name), v::name := _Z , {constraints := [], fulloutput::boolean := false, noresult::boolean := false, sepvector::list(integer) := [], useblockingerror::boolean := FAIL, verbose::nonnegint := 0}, $) fgbrs:-rs_rur_gb( fgbrs:-rs_gbasis(sys, vars, ':-useblockingerror' = useblockingerror), vars, v, ':-constraints' = constraints, ':-verbose' = verbose, ':-noresult' = noresult, ':-sepvector' = sepvector, ':-fulloutput' = fulloutput, ':-useblockingerror' = useblockingerror) end proc > read "load.mpl": Warning, `X` is implicitly declared local to procedure `MyRand` Warning, `S` is implicitly declared local to procedure `LittleRankPosDef` Warning, `i` is implicitly declared local to procedure `LittleRankPosDef` Warning, `v` is implicitly declared local to procedure `LittleRankPosDef` Warning, `j` is implicitly declared local to procedure `LittleRankPosDef` Warning, `S` is implicitly declared local to procedure `Deformation` Warning, `i` is implicitly declared local to procedure `Deformation` Warning, `j` is implicitly declared local to procedure `Deformation` Warning, `one` is implicitly declared local to procedure `MyRand2` Warning, `two` is implicitly declared local to procedure `MyRand2` Warning, `rr2` is implicitly declared local to procedure `MyRand2` Warning, `i` is implicitly declared local to procedure `RowElementaryOperation` Warning, `lambda` is implicitly declared local to procedure `RowElementaryOperation` Warning, `j` is implicitly declared local to procedure `RowElementaryOperation` Warning, `i` is implicitly declared local to procedure `ColumnElementaryOperation` Warning, `j` is implicitly declared local to procedure `ColumnElementaryOperation` Warning, `lambda` is implicitly declared local to procedure `ColumnElementaryOperation` Warning, `r` is implicitly declared local to procedure `ApplyAffineTransf` Warning, `c` is implicitly declared local to procedure `ApplyAffineTransf` Warning, `out` is implicitly declared local to procedure `LinearChangeOfVariables` Warning, `t` is implicitly declared local to procedure `LinearChangeOfVariables` Warning, `r` is implicitly declared local to procedure `MakeTriangular` Warning, `c` is implicitly declared local to procedure `MakeTriangular` Warning, `out` is implicitly declared local to procedure `MakeTriangular` Warning, `i` is implicitly declared local to procedure `MakeTriangular` Warning, `j` is implicitly declared local to procedure `MakeTriangular` Warning, `J` is implicitly declared local to procedure `RandomSymmMatrix` Warning, `var` is implicitly declared local to procedure `RandomLinearMatrix` Warning, `M` is implicitly declared local to procedure `RandomLinearMatrix` Warning, `s` is implicitly declared local to procedure `RandomLinearMatrix` Warning, `t` is implicitly declared local to procedure `RandomLinearMatrix` Warning, `var` is implicitly declared local to procedure `RandomSymmetricLinearMatrix` Warning, `M` is implicitly declared local to procedure `RandomSymmetricLinearMatrix` Warning, `s` is implicitly declared local to procedure `RandomSymmetricLinearMatrix` Warning, `t` is implicitly declared local to procedure `RandomSymmetricLinearMatrix` Warning, `vec` is implicitly declared local to procedure `Vectorize` Warning, `i` is implicitly declared local to procedure `Vectorize` Warning, `j` is implicitly declared local to procedure `Vectorize` Warning, `MIN` is implicitly declared local to procedure `SetOfSubMatrices` Warning, `j` is implicitly declared local to procedure `SetOfSubMatrices` Warning, `l` is implicitly declared local to procedure `SetOfSubMatrices` Warning, `listofsubmatrices` is implicitly declared local to procedure `SetOfSubMatrices` Warning, `MIN` is implicitly declared local to procedure `Minors` Warning, `j` is implicitly declared local to procedure `Minors` Warning, `l` is implicitly declared local to procedure `Minors` Warning, `listofminors` is implicitly declared local to procedure `Minors` Warning, `e` is implicitly declared local to procedure `MaxMinorsJacobian` Warning, `v` is implicitly declared local to procedure `MaxMinorsJacobian` Warning, `lv` is implicitly declared local to procedure `MaxMinorsJacobian` Warning, `ld` is implicitly declared local to procedure `MaxMinorsJacobian` Warning, `eqs` is implicitly declared local to procedure `SingularLocus` Warning, `var` is implicitly declared local to procedure `SingularLocus` Warning, `n` is implicitly declared local to procedure `SingularLocus` Warning, `out` is implicitly declared local to procedure `SingularLocus` Warning, `Mat` is implicitly declared local to procedure `MatrixCombination` Warning, `var` is implicitly declared local to procedure `ComputeDimension` Warning, `n` is implicitly declared local to procedure `ComputeDimension` Warning, `eqs` is implicitly declared local to procedure `ComputeDimension` Warning, `GB` is implicitly declared local to procedure `ComputeDimension` Warning, `d` is implicitly declared local to procedure `ComputeDimension` Warning, `var` is implicitly declared local to procedure `ComputeCodimension` Warning, `var` is implicitly declared local to procedure `ComputeDegree` Warning, `eqs` is implicitly declared local to procedure `ComputeDegree` Warning, `dimen` is implicitly declared local to procedure `ComputeDegree` Warning, `i` is implicitly declared local to procedure `ComputeDegree` Warning, `eqs` is implicitly declared local to procedure `EliminateRelations` Warning, `e` is implicitly declared local to procedure `EliminateRelations` Warning, `var` is implicitly declared local to procedure `EliminateRelations` Warning, `v` is implicitly declared local to procedure `EliminateRelations` Warning, `dim` is implicitly declared local to procedure `EliminateRelations` Warning, `cod` is implicitly declared local to procedure `EliminateRelations` Warning, `neweqs` is implicitly declared local to procedure `EliminateRelations` Warning, `i` is implicitly declared local to procedure `EliminateRelations` Warning, `eqs` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `e` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `var` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `v` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `neweqs` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `i` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `vars` is implicitly declared local to procedure `TestTheMembership` Warning, `pol` is implicitly declared local to procedure `TestTheMembership` Warning, `listofpol` is implicitly declared local to procedure `TestTheMembership` Warning, `newlist` is implicitly declared local to procedure `TestTheMembership` Warning, `GB1` is implicitly declared local to procedure `TestTheMembership` Warning, `GB2` is implicitly declared local to procedure `TestTheMembership` Warning, `vars` is implicitly declared local to procedure `TestTheEquality` Warning, `GB1` is implicitly declared local to procedure `TestTheEquality` Warning, `GB2` is implicitly declared local to procedure `TestTheEquality` Warning, `vars` is implicitly declared local to procedure `TestTheInclusion` Warning, `newlist` is implicitly declared local to procedure `TestTheInclusion` Warning, `GB1` is implicitly declared local to procedure `TestTheInclusion` Warning, `GB2` is implicitly declared local to procedure `TestTheInclusion` Warning, `vars` is implicitly declared local to procedure `TestSingularity` Warning, `ss` is implicitly declared local to procedure `TestSingularity` Warning, `GB` is implicitly declared local to procedure `TestSingularity` Warning, `out` is implicitly declared local to procedure `ChangeLines` Warning, `r` is implicitly declared local to procedure `ChangeLines` Warning, `c` is implicitly declared local to procedure `ChangeLines` Warning, `j` is implicitly declared local to procedure `ChangeLines` Warning, `ch` is implicitly declared local to procedure `ChangeLines` Warning, `out` is implicitly declared local to procedure `ChangeColumns` Warning, `r` is implicitly declared local to procedure `ChangeColumns` Warning, `c` is implicitly declared local to procedure `ChangeColumns` Warning, `i` is implicitly declared local to procedure `ChangeColumns` Warning, `ch` is implicitly declared local to procedure `ChangeColumns` Warning, `linear` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `newset` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `var` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `S` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `par` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `ls` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `i` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `NEWVARS` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `LS` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `param` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `n` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `EQUS` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `linear` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `var` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `S` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `par` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `ls` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `myrand1` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `myrand` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `myprime` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `gb` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `boo` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `i` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `candidate` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `rr1` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `DEG` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `NEWVARS` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `LS` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `param` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `out` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `n` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `pos` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `i` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `val` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `j` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `MAT` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `v` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `z` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `out` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `n` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `pos` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `i` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `val` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `j` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `MAT` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `v` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `z` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `matY` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `s` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `i` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `g` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `BB` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `NEWEQ` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `j` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `st0` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `times` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `ldeg` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `deg` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `param` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `chgvar` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `st1` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `varsZ` is implicitly declared local to procedure `OldLagSyst` Warning, `varsXY` is implicitly declared local to procedure `OldLagSyst` Warning, `NEWEQS` is implicitly declared local to procedure `OldLagSyst` Warning, `zz` is implicitly declared local to procedure `OldLagSyst` Warning, `GB` is implicitly declared local to procedure `OldLagSyst` Warning, `SOLS` is implicitly declared local to procedure `OldLagSyst` Warning, `param` is implicitly declared local to procedure `LagSyst` Warning, `chgvar` is implicitly declared local to procedure `LagSyst` Warning, `SOLS` is implicitly declared local to procedure `LagSyst` Warning, `varsZ` is implicitly declared local to procedure `LagSyst` Warning, `varsXY` is implicitly declared local to procedure `LagSyst` Warning, `rr` is implicitly declared local to procedure `LagSyst` Warning, `NEWEQS` is implicitly declared local to procedure `LagSyst` Warning, `zz` is implicitly declared local to procedure `LagSyst` Warning, `lv` is implicitly declared local to procedure `LagSyst` Warning, `ld` is implicitly declared local to procedure `LagSyst` Warning, `varsZ` is implicitly declared local to procedure `PolarVarieties` Warning, `varsXY` is implicitly declared local to procedure `PolarVarieties` Warning, `J` is implicitly declared local to procedure `PolarVarieties` Warning, `jac` is implicitly declared local to procedure `PolarVarieties` Warning, `i` is implicitly declared local to procedure `PolarVarieties` Warning, `j` is implicitly declared local to procedure `PolarVarieties` Warning, `NEWEQS` is implicitly declared local to procedure `PolarVarieties` Warning, `rr` is implicitly declared local to procedure `IsSingular` Warning, `lv` is implicitly declared local to procedure `IsSingular` Warning, `ld` is implicitly declared local to procedure `IsSingular` Warning, `NEWEQUATIONS` is implicitly declared local to procedure `IsSingular` Warning, `GB` is implicitly declared local to procedure `IsSingular` Warning, `NEWEQS` is implicitly declared local to procedure `IsSingularMohab` Warning, `GB` is implicitly declared local to procedure `IsSingularMohab` Warning, `n` is implicitly declared local to procedure `RealSmallRank` Warning, `varsX` is implicitly declared local to procedure `RealSmallRank` Warning, `matY2` is implicitly declared local to procedure `RealSmallRank` Warning, `i` is implicitly declared local to procedure `RealSmallRank` Warning, `j` is implicitly declared local to procedure `RealSmallRank` Warning, `U` is implicitly declared local to procedure `RealSmallRank` Warning, `matY1` is implicitly declared local to procedure `RealSmallRank` Warning, `matY` is implicitly declared local to procedure `RealSmallRank` Warning, `varsY` is implicitly declared local to procedure `RealSmallRank` Warning, `rr` is implicitly declared local to procedure `RealSmallRank` Warning, `EQS` is implicitly declared local to procedure `RealSmallRank` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRank` Warning, `st` is implicitly declared local to procedure `RealSmallRank` Warning, `st0` is implicitly declared local to procedure `RealSmallRank` Warning, `times` is implicitly declared local to procedure `RealSmallRank` Warning, `HYP` is implicitly declared local to procedure `RealSmallRank` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRank` Warning, `deg` is implicitly declared local to procedure `RealSmallRank` Warning, `st1` is implicitly declared local to procedure `RealSmallRank` Warning, `ldeg` is implicitly declared local to procedure `RealSmallRank` Warning, `s` is implicitly declared local to procedure `RealSmallRank` Warning, `myvar` is implicitly declared local to procedure `RealSmallRank` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRank` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `U` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `matY` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `i` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `j` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `ID` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `s` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankOld` Warning, `matY` is implicitly declared local to procedure `RealSmallRankOld` Warning, `i` is implicitly declared local to procedure `RealSmallRankOld` Warning, `j` is implicitly declared local to procedure `RealSmallRankOld` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankOld` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankOld` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankOld` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankOld` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankOld` Warning, `s` is implicitly declared local to procedure `RealSmallRankOld` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankOld` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankOld` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankChange` Warning, `matY` is implicitly declared local to procedure `RealSmallRankChange` Warning, `i` is implicitly declared local to procedure `RealSmallRankChange` Warning, `j` is implicitly declared local to procedure `RealSmallRankChange` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankChange` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankChange` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankChange` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankChange` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankChange` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankChange` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `matY` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `i` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `j` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `s` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `matY` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `i` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `j` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `J` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `NEW` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `s` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `matY` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `i` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `j` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `J` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `matY` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `i` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `j` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `J` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `s` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `matY` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `i` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `j` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `J` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `s` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `matY` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `i` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `j` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `s` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `varsX` is implicitly declared local to procedure `RealSmallRank2` Warning, `matY` is implicitly declared local to procedure `RealSmallRank2` Warning, `i` is implicitly declared local to procedure `RealSmallRank2` Warning, `j` is implicitly declared local to procedure `RealSmallRank2` Warning, `varsY` is implicitly declared local to procedure `RealSmallRank2` Warning, `EQS` is implicitly declared local to procedure `RealSmallRank2` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRank2` Warning, `HYP` is implicitly declared local to procedure `RealSmallRank2` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRank2` Warning, `myvar` is implicitly declared local to procedure `RealSmallRank2` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRank2` Warning, `fd` is implicitly declared local to procedure `PrintFiles` Warning, `N` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `varsXX` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `VV` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `i` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `M` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `s` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `j` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `varsXX` is implicitly declared local to procedure `MyGenerateMatrix` Warning, `M` is implicitly declared local to procedure `MyGenerateMatrix` Warning, `i` is implicitly declared local to procedure `MyGenerateMatrix` Warning, `j` is implicitly declared local to procedure `MyGenerateMatrix` Warning, `r` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `script1` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `fd1` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `script2` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `fd2` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `n` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `M` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `F` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `str1` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `logstr1` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `varsXX` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `str2` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `logstr2` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `M` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `F` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `str1` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `varsXX` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `str2` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `script1` is implicitly declared local to procedure `GenerateFiles` Warning, `script2` is implicitly declared local to procedure `GenerateFiles` Warning, `F` is implicitly declared local to procedure `GenerateFiles` Warning, `str1` is implicitly declared local to procedure `GenerateFiles` Warning, `logstr1` is implicitly declared local to procedure `GenerateFiles` Warning, `varsXX` is implicitly declared local to procedure `GenerateFiles` Warning, `str2` is implicitly declared local to procedure `GenerateFiles` Warning, `logstr2` is implicitly declared local to procedure `GenerateFiles` Warning, `M` is implicitly declared local to procedure `GenerateSingleFile` Warning, `F` is implicitly declared local to procedure `GenerateSingleFile` Warning, `str1` is implicitly declared local to procedure `GenerateSingleFile` Warning, `varsXX` is implicitly declared local to procedure `GenerateSingleFile` Warning, `str2` is implicitly declared local to procedure `GenerateSingleFile` > > st:=time():RealSmallRank(Matrix(6, 6, [[-69+2*X1+103*X2-17*X3-48*X4-132*X5+83*X6,-55-19*X1+13*X2+2*X3+109*X4-97*X5+231*X6,77-11*X1+119*X2+40*X3+45*X4+60*X5-94*X6,-46+47*X1+43*X2-139*X3-86*X4-40*X5-66*X6,-36+104*X1-36*X2+4*X3-71*X4-177*X5+77*X6,63-33*X1+10*X2-30*X3+21*X4+132*X5-202*X6],[55+9*X1-140*X2+30*X3+120*X4+79*X5+55*X6,-74-98*X1+63*X2+22*X3+52*X4-13*X5-31*X6,69+43*X1-97*X2+128*X3+54*X4-109*X5+46*X6,131-58*X1-32*X2+131*X3+13*X4+114*X5+85*X6,40-16*X1-33*X2+55*X3+37*X4-143*X5+27*X6,-58-180*X1-87*X2+104*X3+24*X4+121*X5+24*X6],[199-37*X1-13*X2+23*X3-230*X4-187*X5-49*X6,-19-170*X1+17*X2+29*X3-113*X4+38*X5-64*X6,-39-53*X1+30*X2-72*X3-19*X4+100*X5+23*X6,129+197*X2+139*X3-9*X4+7*X5+72*X6,43-82*X1+66*X2-73*X3-45*X4+23*X5+188*X6,172-105*X1-14*X2+135*X3-152*X4+138*X5-59*X6],[81-40*X1+18*X2-152*X3-80*X4-13*X5-19*X6,-121+16*X1+45*X2+60*X3-14*X4+X5-71*X6,-118-7*X1+91*X2+96*X3-101*X4+48*X5+196*X6,3-168*X1-211*X2-143*X3+21*X4-17*X5+89*X6,142-49*X1-129*X2-12*X3-82*X4-114*X5-131*X6,147-29*X1+111*X2-76*X3-4*X4+144*X5-196*X6],[1+30*X1+47*X2+43*X3+34*X4-67*X5-171*X6,20+56*X1-67*X2-17*X3+28*X4-140*X5-146*X6,122-88*X1-36*X2+37*X3-91*X4-167*X5+55*X6,113+43*X1-23*X2-23*X3-55*X4+13*X5-32*X6,-41-120*X1+111*X2+209*X3+13*X4-X5+15*X6,-67+106*X1-160*X2-235*X3-74*X4-45*X5+91*X6],[123+59*X1-143*X2+7*X3+98*X4+12*X5+137*X6,-19-44*X1-231*X2+48*X3+100*X4+22*X5-44*X6,-25-69*X1+6*X2+43*X3+23*X4-49*X5-46*X6,-81-147*X1+39*X2+277*X3+50*X4-78*X5+54*X6,124+2*X1+20*X2+80*X3+141*X4-64*X5+107*X6,48+219*X1+123*X2-16*X3+125*X4-85*X5+54*X6]]), 6, [X1, X2, X3, X4, X5, X6], 4):lprint(time()-st): [13 - 10 Y11 - Y21 - Y31 - 7 Y41 , -35 - 10 Y12 - Y22 - Y32 - 7 Y42] [ ] [-84 - Y11 - 8 Y21 - 4 Y31 - 5 Y41 , 15 - Y12 - 8 Y22 - 4 Y32 - 5 Y42] [ ] [Y11 , Y12] [ ] [Y21 , Y22] [ ] [Y31 , Y32] [ ] [Y41 , Y42] Checking regularity assumptions Execution Stopped: Unhandled signal caught (UNKNOWN: 1)GC Thread signalAbort 0x7ff58b4b4700 Execution Stopped: Unhandled signal caught (UNKNOWN: 1)