next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Quasidegrees :: toGradedRing

toGradedRing -- grade a polynomial ring by a matrix

Synopsis

Description

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    }

Ways to use toGradedRing :

For the programmer

The object toGradedRing is a method function.