|\^/| 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, `NEWVARS` is implicitly declared local to procedure `IsSingularMohab` Warning, `VEC` is implicitly declared local to procedure `IsSingularMohab` Warning, `NEWVEC` is implicitly declared local to procedure `IsSingularMohab` Warning, `NEWPOLS` is implicitly declared local to procedure `IsSingularMohab` 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, `GB` 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, [[-36-202*X1-23*X2,35+251*X1+47*X2,34+115*X1+40*X2,-1-172*X1+66*X2,-34-10*X1-63*X2,185-150*X1+80*X2],[13+76*X1+60*X2,80+52*X1-63*X2,43+60*X1+75*X2,38-178*X1+60*X2,-100-114*X1+44*X2,-210-9*X1-51*X2],[-21+19*X1-8*X2,-84+138*X1-140*X2,-1+179*X1-147*X2,-80+110*X1+14*X2,16+144*X1-7*X2,181+315*X1+21*X2],[-76-6*X1-45*X2,-50+160*X1-211*X2,-55+203*X1-170*X2,-144-69*X1+173*X2,-61-16*X1+131*X2,-125-130*X1+87*X2],[-43+17*X1+118*X2,114+27*X1+129*X2,-168+70*X1+155*X2,301+46*X1-24*X2,55-191*X1+64*X2,-87+100*X1+8*X2],[38+104*X1+11*X2,-135-79*X1+17*X2,-18-66*X1-96*X2,-17+36*X1-148*X2,-22-41*X1-22*X2,91-178*X1-2*X2]]), 6, [X1, X2], 3):lprint(time()-st): [34 - 7 Y11 - 7 Y21 - 6 Y31 , 81 - 7 Y12 - 7 Y22 - 6 Y32 , -27 - 7 Y13 - 7 Y23 - 6 Y33] [83 - 9 Y11 - 7 Y21 - 4 Y31 , 9 - 9 Y12 - 7 Y22 - 4 Y32 , -12 - 9 Y13 - 7 Y23 - 4 Y33] [-46 - 4 Y11 - 5 Y21 - 9 Y31 , -30 - 4 Y12 - 5 Y22 - 9 Y32 , -70 - 4 Y13 - 5 Y23 - 9 Y33] [Y11 , Y12 , Y13] [Y21 , Y22 , Y23] [Y31 , Y32 , Y33] Set tr to 1 INCREASE HEAP 14470848 [2](18x30)100%/[3](201x180)60.5%/100%/ #C Dimension: -1, Degree: -1 Elapsed time (empty case): 0.029000 .53e-1 > quit memory used=6.9MB, alloc=40.3MB, time=0.19