This method takes a polynomial ring $R$ in $n$ variables and a $d\times n$ matrix $A$ and grades $R$ by assigning the i-th variable of $R$ to have degree being the i-th column of $A$.
i1 : A=matrix{{1,1,1,1,1},{0,0,1,1,0},{0,1,1,0,-2}} o1 = | 1 1 1 1 1 | | 0 0 1 1 0 | | 0 1 1 0 -2 | 3 5 o1 : Matrix ZZ <--- ZZ |
i2 : R=QQ[a..e] o2 = R o2 : PolynomialRing |
i3 : S=toGradedRing(A,R) o3 = S o3 : PolynomialRing |
i4 : describe S o4 = QQ[a..e, Degrees => {{1}, {1}, {1}, {1}, {1 }}, Heft => {1, 2:0}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 3] {0} {0} {1} {1} {0 } {GRevLex => {5:1} } {0} {1} {1} {0} {-2} {Position => Up } |
The object toGradedRing is a method function.