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
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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 }
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The object toGradedRing is a method function.