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#############################################################################
##
## solveeq.gi CRISP Burkhard Höfling
##
## Copyright © 2000-2002 Burkhard Höfling
##
#############################################################################
##
#F LinearSystem(nrvars, nrsolutions, field, conv, convsol)
##
InstallGlobalFunction(LinearSystem,
function(nrvars, nrsolutions, field, conv, convsol)
local sys, i;
sys := rec(
nrvars := nrvars,
nrsolutions := nrsolutions,
field := field,
fieldsize := Size(field),
zero := Zero(field),
one := One(field),
equations := [],
nrequations := 0,
solutions := [],
soluble := ListWithIdenticalEntries(nrsolutions,true),
conv := conv,
convsol := convsol,
nullrow := ListWithIdenticalEntries(nrvars, Zero(field)),
nullsol := ListWithIdenticalEntries(nrsolutions, Zero(field)));
if conv then
ConvertToVectorRep(sys.nullrow, sys.fieldsize);
fi;
if convsol then
ConvertToVectorRep(sys.nullsol, sys.fieldsize);
fi;
return sys;
end);
#############################################################################
##
#F AddEquation(sys, row, sol)
##
InstallGlobalFunction(AddEquation,
function(sys, r, s)
local row, sol, i, solv, oldsolv, coeff;
if Length(r) <> sys.nrvars or Length(s) <> sys.nrsolutions
or(sys.conv and sys.fieldsize <> ConvertToVectorRep(r, sys.fieldsize))
or(sys.convsol and sys.fieldsize <> ConvertToVectorRep(s, sys.fieldsize)) then
Error("vectors must be of the right length and over the correct field");
fi;
row := ShallowCopy(r);
sol := ShallowCopy(s);
i := 1;
while i <= sys.nrvars do
coeff := row[i];
if coeff <> sys.zero then
if IsBound(sys.equations[i]) then
# row := row - row[i] * sys.equations[i];
AddRowVector(row, sys.equations[i], - coeff);
if sys.nrsolutions > 0 then
AddRowVector(sol, sys.solutions[i], - coeff);
fi;
elif coeff = sys.one then
sys.equations[i] := row;
if sys.nrsolutions > 0 then
sys.solutions[i] := sol;
fi;
sys.nrequations := sys.nrequations + 1;
return true;
else
sys.equations[i] := row / coeff;
if sys.nrsolutions > 0 then
sys.solutions[i] := sol / coeff;
fi;
sys.nrequations := sys.nrequations + 1;
return true;
fi;
fi;
i := i + 1;
od;
solv := true;
for i in [1..sys.nrsolutions] do
if sys.soluble[i] and sol[i] <> sys.zero then
sys.soluble[i] := false;
solv := false;
fi;
od;
return solv;
end);
#############################################################################
##
#F HasSolution(sys, n)
##
InstallGlobalFunction(HasSolution,
function(sys, n)
return sys.soluble[n];
end);
#############################################################################
##
#F DimensionOfNullspace(sys)
##
InstallGlobalFunction(DimensionOfNullspace,
function(sys)
return sys.nrvars - sys.nrequations;
end);
#############################################################################
##
#F OneSolution(sys, n)
##
InstallGlobalFunction(OneSolution,
function(sys, n)
local s, i;
if not sys.soluble[n] then
return fail;
fi;
s := ShallowCopy(sys.nullrow);
for i in [sys.nrvars, sys.nrvars-1..1] do
# treat the i-th row
if IsBound(sys.equations[i]) then
s[i] := sys.solutions[i][n] - s*sys.equations[i];
fi;
od;
return s;
end);
#############################################################################
##
#F BasisNullspaceSolution(sys)
##
InstallGlobalFunction(BasisNullspaceSolution,
function(sys)
local v, i, j, basis, nullspace;
nullspace := [];
for i in [sys.nrvars, sys.nrvars-1..1] do
# treat the i-th row
if not IsBound(sys.equations[i]) then
v := ShallowCopy(sys.nullrow);
v[i] := sys.one;
for j in [i-1, i-2 .. 1] do
if IsBound(sys.equations[j]) then
v[j] := - v * sys.equations[j];
fi;
od;
Add(nullspace, v{[1..sys.nrvars]});
fi;
od;
return nullspace;
end);
############################################################################
##
#E
##
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