This method takes a $d\times n$ integer matrix $A$ and makes the polynomial ring $\QQ[x_0,..,x_{n-1}]$ with the degree of the i-th variable 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 = makeGradedRing(A,t) o2 = R o2 : PolynomialRing |
We can see that $R$ is graded by the columns of $A$
i3 : describe R
o3 = QQ[t ..t , Degrees => {{1}, {1}, {1}, {1}, {1 }}, Heft => {1, 2:0}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 3]
0 4 {0} {0} {1} {1} {0 } {GRevLex => {5:1} }
{0} {1} {1} {0} {-2} {Position => Up }
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The object makeGradedRing is a method function.