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Minors changes to KustinMiller package to get it working with Complexes
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@mikestillman
mikestillman committed Oct 7, 2024
1 parent 4f17a11 commit 79d3abe
Showing 1 changed file with 38 additions and 38 deletions.
76 changes: 38 additions & 38 deletions M2/Macaulay2/packages/KustinMiller.m2
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Original file line number Diff line number Diff line change
Expand Up @@ -311,7 +311,7 @@ kustinMillerComplex(Ideal,Ideal,PolynomialRing):=opt->(I,J,T0)->(
if ring I =!= ring J then error "expected the rings of the first and second argument to be the same";
if not isSubset(I,J) then error "expected first argument to be an ideal contained in the second";
if codim(I) != -1+codim(J) then error "expected an unprojection locus of codimension 1";
kustinMillerComplex(res I,res J,T0,opt))
kustinMillerComplex(freeResolution I,freeResolution J,T0,opt))


kustinMillerComplex(Complex,Complex,PolynomialRing):=opt->(cI0,cJ0,T0)->(
Expand Down Expand Up @@ -839,9 +839,9 @@ doc ///
Example
R = QQ[x_1..x_4,z_1..z_4]
I = ideal(z_2*z_3-z_1*z_4,x_4*z_3-x_3*z_4,x_2*z_2-x_1*z_4,x_4*z_1-x_3*z_2,x_2*z_1-x_1*z_3)
betti res I
betti freeResolution I
J = ideal (z_1..z_4)
betti res J
betti freeResolution J
cc=kustinMillerComplex(I,J,QQ[T]);
S=ring cc
cc
Expand Down Expand Up @@ -927,7 +927,7 @@ doc ///
C=delta(4,R)
fVector C
I=ideal C
betti res I
betti freeResolution I
///


Expand Down Expand Up @@ -1020,7 +1020,7 @@ doc ///
A=matrix {{0,x_1,x_2,x_3,x_4},{-x_1,0,0,z_1,z_2},{-x_2,0,0,z_3,z_4},{-x_3,-z_1,-z_3,0,0},{-x_4,-z_2,-z_4,0,0}}
resBE A
SeeAlso
res
freeResolution
///


Expand Down Expand Up @@ -1048,12 +1048,12 @@ doc ///
Example
R = QQ[x_1..x_4,z_1..z_4]
I = ideal(z_2*z_3-z_1*z_4,x_4*z_3-x_3*z_4,x_2*z_2-x_1*z_4,x_4*z_1-x_3*z_2,x_2*z_1-x_1*z_3)
cc= res I
cc= freeResolution I
isExactRes cc
isExactRes(cc[1])
isExactRes(cc[-1])
SeeAlso
res
freeResolution
///


Expand All @@ -1075,7 +1075,7 @@ doc ///

Example
R=QQ[x_1..x_4,z_1];
cc=res ideal(x_4*x_3, -x_1*x_2+x_4*z_1);
cc=freeResolution ideal(x_4*x_3, -x_1*x_2+x_4*z_1);
cs=substitute(cc,QQ[x_1..x_4])
cs.dd_1
SeeAlso
Expand Down Expand Up @@ -1110,13 +1110,13 @@ doc ///
Example
R=QQ[x_0..x_4];
I=monomialIdeal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0);
betti res I
betti freeResolution I
D=simplicialComplex I
fc=facets(D) / face
S=QQ[x_5]
D5=stellarSubdivision(D,fc#0,S)
I5=ideal D5
betti res I5
betti freeResolution I5
Text

Example
Expand All @@ -1125,7 +1125,7 @@ doc ///
D=simplicialComplex I
S=QQ[x_7]
Dsigma=stellarSubdivision(D,face {x_1,x_2,x_3},S)
betti res ideal Dsigma
betti freeResolution ideal Dsigma
SeeAlso
simplicialComplex
facets
Expand Down Expand Up @@ -1171,7 +1171,7 @@ assert(pfaffians(4,A)==ideal cc.dd_1);
///TEST
R = QQ[x_1..x_4,z_1..z_4];
I = ideal(z_2*z_3-z_1*z_4,x_4*z_3-x_3*z_4,x_2*z_2-x_1*z_4,x_4*z_1-x_3*z_2,x_2*z_1-x_1*z_3);
cc= res I;
cc= freeResolution I;
assert(isExactRes cc);
C=complex presentation QQ^1;
assert(isExactRes C);
Expand Down Expand Up @@ -1202,10 +1202,10 @@ TEST ///
C26=delta(2,K[z,x_2..x_6])
R=K[z,x_1..x_7]
J=sub(ideal C26,R)
c26=res J;
c26=freeResolution J;
C47=delta(4,K[x_1..x_7])
I=sub(ideal C47,R)
c47=res I;
c47=freeResolution I;
cc=kustinMillerComplex(c47,c26,K[x_8]);
assert(rank(cc_1)==16);
assert(rank(cc_2)==30);
Expand All @@ -1218,10 +1218,10 @@ TEST ///
C26=delta(2,K[z,x_2..x_6])
R=K[z,x_1..x_7]
J=sub(ideal C26,R)
c26=res J;
c26=freeResolution J;
C47=delta(4,K[x_1..x_7])
I=sub(ideal C47,R)
c47=res I;
c47=freeResolution I;
cc=kustinMillerComplex(c47,c26,K[x_8]);
R'=K[x_1..x_8];
C48=delta(4,R');
Expand All @@ -1234,10 +1234,10 @@ assert(I48==sub(ideal cc.dd_1,R'))
TEST ///
R = QQ[x_1..x_4,z_1..z_4]
I = ideal(z_2*z_3-z_1*z_4,x_4*z_3-x_3*z_4,x_2*z_2-x_1*z_4,x_4*z_1-x_3*z_2,x_2*z_1-x_1*z_3)
cI=res I
cI=freeResolution I
betti cI
J = ideal (z_1..z_4)
cJ=res J
cJ=freeResolution J
betti cJ
cc=kustinMillerComplex(cI,cJ,QQ[T]);
assert(rank(cc_1)==9);
Expand Down Expand Up @@ -1561,9 +1561,9 @@ doc ///
I=ideal(x_1*x_2*x_3)
Ilink=I:ideal(x_1*x_2)
J=Ilink+ideal(z_1)
cI=res I
cI=freeResolution I
betti cI
cJ=res J
cJ=freeResolution J
betti cJ
cc=kustinMillerComplex(cI,cJ,K[x_4]);
S=ring cc
Expand All @@ -1586,9 +1586,9 @@ doc ///
I=ideal(x_1*x_2*x_3,x_4*x_5*x_6)
Ilink=I:ideal(x_1*x_2*x_4*x_6)
J=Ilink+ideal(z_1*z_2*z_3)
cI=res I
cI=freeResolution I
betti cI
cJ=res J
cJ=freeResolution J
betti cJ
cc=kustinMillerComplex(cI,cJ,K[x_7]);
S=ring cc
Expand Down Expand Up @@ -1630,9 +1630,9 @@ doc ///
F=face {x_1,x_2}
Ilink=I:ideal(product vertices F)
J=Ilink+ideal(z_1)
cI=res I
cI=freeResolution I
betti cI
cJ=res J
cJ=freeResolution J
betti cJ
cc=kustinMillerComplex(cI,cJ,K[x_6]);
S=ring cc
Expand All @@ -1651,9 +1651,9 @@ doc ///
I=ideal(x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_5,x_5*x_1)
Ilink=I:ideal(x_1*x_3)
J=Ilink+ideal(z_1)
cI=res I
cI=freeResolution I
betti cI
cJ=res J
cJ=freeResolution J
betti cJ
cc=kustinMillerComplex(cI,cJ,K[x_10]);
betti cc
Expand All @@ -1666,9 +1666,9 @@ doc ///
I=monomialIdeal(x_1*x_2,x_3*x_4,x_5*x_6,x_7*x_8*x_9)
Ilink=I:ideal(x_1*x_3)
J=Ilink+ideal(z_1)
cI=res I
cI=freeResolution I
betti cI
cJ=res J
cJ=freeResolution J
betti cJ
cc=kustinMillerComplex(cI,cJ,K[x_10]);
S=ring cc;
Expand All @@ -1690,7 +1690,7 @@ doc ///
C'===simplicialComplex I'
SeeAlso
kustinMillerComplex
res
freeResolution
betti
///

Expand Down Expand Up @@ -1718,11 +1718,11 @@ doc ///
C26=delta(2,K[z,x_2..x_6])
R=K[z,x_1..x_7]
J=sub(ideal C26,R)
c26=res J;
c26=freeResolution J;
betti c26
C47=delta(4,K[x_1..x_7])
I=sub(ideal C47,R)
c47=res I;
c47=freeResolution I;
betti c47
cc=kustinMillerComplex(c47,c26,K[x_8]);
betti cc
Expand All @@ -1736,7 +1736,7 @@ doc ///
R'=K[x_1..x_8];
C48=delta(4,R')
I48=ideal C48
betti res I48
betti freeResolution I48
I48==sub(ideal cc.dd_1,R')
Text

Expand All @@ -1748,7 +1748,7 @@ doc ///
print cc.dd_3
SeeAlso
kustinMillerComplex
res
freeResolution
betti
///

Expand All @@ -1774,7 +1774,7 @@ doc ///
betti(cI=resBE b2)
b1 = cI.dd_1
J = ideal (z_1..z_4);
betti(cJ=res J)
betti(cJ=freeResolution J)
betti(cU=kustinMillerComplex(cI,cJ,QQ[T]))
S=ring cU
isExactRes cU
Expand All @@ -1784,7 +1784,7 @@ doc ///
print cU.dd_4
SeeAlso
kustinMillerComplex
res
freeResolution
betti
"Jerry"
///
Expand All @@ -1807,10 +1807,10 @@ doc ///
Example
R = QQ [x_1..x_3, z_1..z_4]
I = ideal(-z_2*z_3+z_1*x_1,-z_2*z_4+z_1*x_2,-z_3*z_4+z_1*x_3,-z_3*x_2+z_2*x_3,z_4*x_1-z_3*x_2)
cI=res I
cI=freeResolution I
betti cI
J = ideal (z_1..z_4)
cJ=res J
cJ=freeResolution J
betti cJ
cc=kustinMillerComplex(cI,cJ,QQ[T]);
S=ring cc
Expand All @@ -1823,7 +1823,7 @@ doc ///
print cc.dd_4
SeeAlso
kustinMillerComplex
res
freeResolution
betti
"Tom"
///
Expand Down

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