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 |
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 } |
The object makeGradedRing is a method function.