-- Example 7c: the genus 7 balanced K3 carpet
load "K3Carpets.m2";
S=QQ[X_14, X_15, X_23, X_25, X_35, X_1245, X_1345, X_2345];
X_0=0;
X_12=X_1345;
X_13=X_2345;
X_24=2*X_15;
X_34=1/2*X_25;
X_45=0;
X_1234=0;
X_1235=0;
LK3Carpet7 = {X_0, X_12-X_1345, X_13-X_2345, X_24-2*X_15, X_34-1/2*X_25, X_45, X_1234, X_1235};
all(LK3Carpet7, i -> i==0)
PcapOG510 = {X_0*X_2345-X_23*X_45+X_24*X_35-X_25*X_34,
X_12*X_1345-X_13*X_1245+X_14*X_1235-X_15*X_1234,
X_0*X_1345-X_13*X_45+X_14*X_35-X_15*X_34,
X_12*X_2345-X_23*X_1245+X_24*X_1235-X_25*X_1234,
X_0*X_1245-X_12*X_45+X_14*X_25-X_15*X_24,
X_13*X_2345-X_23*X_1345+X_34*X_1235-X_35*X_1234,
X_0*X_1235-X_12*X_35+X_13*X_25-X_15*X_23,
X_14*X_2345-X_24*X_1345+X_34*X_1245-X_45*X_1234,
X_0*X_1234-X_12*X_34+X_13*X_24-X_14*X_23,
X_15*X_2345-X_25*X_1345+X_35*X_1245-X_45*X_1235};
K3Carpet7 = carpet(3,3,Characteristic=>0);
R=ring(K3Carpet7);
F = map(R,S,{R_0,R_1,R_7,2*R_2,R_3,R_4,R_5,R_6});
F(ideal(PcapOG510))==ideal(K3Carpet7)