-- -*- M2-comint -*- {* hash: -1204366786 *} i1 : A = QQ[x,y]; i2 : I = ideal "x10+x9y2,y8-x2y7"; o2 : Ideal of A i3 : transpose gens gb I o3 = {-9} | x2y7-y8 | {-11} | x9y2+x10 | {-13} | x12y+xy11 | {-13} | x13-xy12 | {-14} | y14+xy12 | {-14} | xy13+y12 | 6 1 o3 : Matrix A <--- A i4 : A1 = QQ[x,y,MonomialOrder=>Lex]; i5 : I = substitute(I,A1) 10 9 2 2 7 8 o5 = ideal (x + x y , - x y + y ) o5 : Ideal of A1 i6 : transpose gens gb I o6 = {-15} | y15-y12 | {-14} | xy12+y14 | {-9} | x2y7-y8 | {-11} | x10+x9y2 | 4 1 o6 : Matrix A1 <--- A1 i7 : B = QQ[x,y,MonomialOrder=>{Weights=>{-1,-1},2},Global=>false]; i8 : I = substitute(I,B) 10 9 2 8 2 7 o8 = ideal (x + x y , y - x y ) o8 : Ideal of B i9 : transpose gens gb I o9 = {-11} | x10+x9y2 | {-9} | y8-x2y7 | 2 1 o9 : Matrix B <--- B i10 : B = QQ[x,y,MonomialOrder=>{Weights=>{-1,0},Weights=>{0,-1}},Global=>false]; i11 : I = substitute(I,B) 9 2 10 8 2 7 o11 = ideal (x y + x , y - x y ) o11 : Ideal of B i12 : transpose gens gb I o12 = {-16} | x13-x13y3 | {-11} | x9y2+x10 | {-9} | y8-x2y7 | 3 1 o12 : Matrix B <--- B i13 : M = matrix{{1,1,1},{0,-1,-1},{0,0,-1}} o13 = | 1 1 1 | | 0 -1 -1 | | 0 0 -1 | 3 3 o13 : Matrix ZZ <--- ZZ i14 : mo = apply(entries M, e -> Weights => e) o14 = {Weights => {1, 1, 1}, Weights => {0, -1, -1}, Weights => {0, 0, -1}} o14 : List i15 : C = QQ[t,x,y,MonomialOrder=>mo]; i16 : I = homogenize(substitute(I,C),t) 10 9 2 8 2 7 o16 = ideal (t*x + x y , t*y - x y ) o16 : Ideal of C i17 : transpose gens gb I o17 = {-9} | ty8-x2y7 | {-11} | tx10+x9y2 | {-19} | x12y7+x9y10 | 3 1 o17 : Matrix C <--- C i18 : substitute(transpose gens gb I, {t=>1}) o18 = {-9} | -x2y7+y8 | {-11} | x9y2+x10 | {-19} | x12y7+x9y10 | 3 1 o18 : Matrix C <--- C i19 :