-- -*- M2-comint -*- {* hash: 113552450 *} i1 : R = QQ[a,b,c,d,e]; i2 : G = graph {a*b,b*c,c*d,d*e,e*a} -- graph of the 5-cycle o2 = Graph{edges => {{a, b}, {b, c}, {c, d}, {a, e}, {d, e}}} ring => R vertices => {a, b, c, d, e} o2 : Graph i3 : H1 = inducedGraph(G,{b,c,d,e}) o3 = Graph{edges => {{b, c}, {c, d}, {d, e}}} ring => QQ[b, c, d, e] vertices => {b, c, d, e} o3 : Graph i4 : H2 = inducedGraph(G,{a,b,d,e}) o4 = Graph{edges => {{a, b}, {a, e}, {d, e}}} ring => QQ[a, b, d, e] vertices => {a, b, d, e} o4 : Graph i5 : use ring H1 o5 = QQ[b, c, d, e] o5 : PolynomialRing i6 : inducedGraph(H1,{c,d,e}) o6 = Graph{edges => {{c, d}, {d, e}}} ring => QQ[c, d, e] vertices => {c, d, e} o6 : Graph i7 : use ring G o7 = R o7 : PolynomialRing i8 : inducedGraph(G,{b,c,d,e},OriginalRing=>true) --H1 but in bigger ring o8 = Graph{edges => {{b, c}, {c, d}, {d, e}}} ring => R vertices => {a, b, c, d, e} o8 : Graph i9 : R = QQ[a,b,c,d,e]; i10 : G = graph {a*b,b*c,c*d,d*e,e*a} -- graph of the 5-cycle o10 = Graph{edges => {{a, b}, {b, c}, {c, d}, {a, e}, {d, e}}} ring => R vertices => {a, b, c, d, e} o10 : Graph i11 : H = inducedGraph(G,{b,c,d}) o11 = Graph{edges => {{b, c}, {c, d}}} ring => QQ[b, c, d] vertices => {b, c, d} o11 : Graph i12 : graph changeRing(H,R,{b,c,d}) o12 = Graph{edges => {{d, c}, {c, b}} } ring => R vertices => {a, b, c, d, e} o12 : Graph i13 :