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Macaulay2Doc :: Ring ^ List

Ring ^ List -- make a free module

Synopsis

Description

i1 : R = QQ[a..d]

o1 = R

o1 : PolynomialRing
i2 : R^{-1}

      1
o2 = R

o2 : R-module, free, degrees {1}
i3 : R^{-1,2:-2,-3}

      4
o3 = R

o3 : R-module, free, degrees {1..2, 2..3}

If i, j, ... are lists of integers, then they represent multi-degrees, as in graded and multigraded polynomial rings.

i4 : R = QQ[x,y,z,Degrees=>{{1,0},{1,-1},{1,-2}}]

o4 = R

o4 : PolynomialRing
i5 : R^{{1,2}}

      1
o5 = R

o5 : R-module, free, degrees {{-1, -2}}

See also