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Solving an issue with isBinomial #1

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4cb5c17
Fixing an error which was causing the function monomialParameterizati…
Oct 12, 2018
118cd45
removing a blank line
Oct 12, 2018
7ffa6df
solving a problem which was causing isBinomial to compute a Groebner …
Apr 18, 2019
a4f3572
Solving an issue with the function monomialParameterization: When the…
Jun 4, 2019
b5b1e9a
Slighlty improving the last commit. Now the last implemented error ap…
Jun 4, 2019
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25 changes: 16 additions & 9 deletions Binomials.m2
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Original file line number Diff line number Diff line change
Expand Up @@ -380,6 +380,7 @@ isBinomial Ideal := Ideal => o -> I -> (
if not o#GroebnerFree then return isBinomialGroebner I;

isB := (isBinomialGroebnerFree I)#0;
if isB then return isB;
if isHomogeneous I then return isB;
if not isB then
print "Gröbner free method failed.\nStarting computation of Gröbner basis...\n";
Expand Down Expand Up @@ -532,8 +533,9 @@ monomialParameterization = I ->(
if not char R == 0 then eligible = false;
if not isBinomial I then eligible = false;
if not binomialIsPrime I then eligible = false;
if dim I == 0 then eligible = false;
if not eligible then (
error "Sorry, only implemented for prime binomial ideals in characteristic zero";
error "Sorry, only implemented for prime binomial ideals of dimension greater than zero in characteristic zero.";
);

n := numgens R;
Expand Down Expand Up @@ -561,12 +563,12 @@ monomialParameterization = I ->(
imageDimension := rank exponentMatrix_{0..(numColumns exponentMatrix-2)};
i := 0;
while (imageDimension =!= numRows exponentMatrix) do (
if rank submatrix'(exponentMatrix,{i},) == imageDimension then (
exponentMatrix = submatrix'(exponentMatrix,{i},);
i = i-1;
if rank (submatrix'(exponentMatrix,{i},))_{0..(numColumns matrix exponentList-2)} == imageDimension then (
exponentMatrix = (submatrix'(exponentMatrix,{i},));
i = i-1;
);
i = i+1;
);
i = i+1;
);
r := numRows exponentMatrix;
v := symbol v;
S := R[v_1..v_r,MonomialOrder => Lex];
Expand All @@ -587,8 +589,8 @@ monomialParameterization = I ->(
-- construct the Laurent polynomial ring by hand.
numv := numColumns solution-r;
G := K[tt_1..tt_numv, ti_1..ti_numv];
posvars := unique (gens G)_{0, numv-1}; -- unique solves the case L_{0,0};
invvars := unique (gens G)_{numv, 2*numv-1};
posvars := unique (gens G)_{0..numv-1}; -- unique solves the case L_{0,0};
invvars := unique (gens G)_{numv..2*numv-1};
laurentRels := ideal for i from 1 to (numColumns solution-r) list tt_i*ti_i - 1;
H := G/laurentRels;
charValues := flatten entries sub(sub(vars S, storeVarMap),K);
Expand Down Expand Up @@ -2369,6 +2371,11 @@ K = frac(QQ[a,b])
R = K[x,y]
I = ideal(a*x-b*y)
assert (ker monomialParameterization I == I)

R = QQ[a,b,c,d,e,f]
A = matrix {{1,1,1,1,1,1},{1,2,3,5,7,11},{1,2,4,6,8,10}}
I = toricMarkov_A R
assert (ker monomialParameterization I == I)
///


Expand Down Expand Up @@ -2454,4 +2461,4 @@ end
restart
uninstallPackage "Binomials"
installPackage "Binomials"
check "Binomials"
check "Binomials"