Computes the graded coordinate ring of the \PP^{n_1} x.... x \PP^{n_m} where {n_1,...,n_m} is the input list of dimensions. This method is used to quickly build the coordinate ring of a product of projective spaces for use in computations.
i1 : S=MultiProjCoordRing(QQ,symbol z,{1,3,3})
o1 = S
o1 : PolynomialRing
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i2 : degrees S
o2 = {{1, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 1, 0}, {0, 1, 0}, {0, 1, 0}, {0,
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0, 1}, {0, 0, 1}, {0, 0, 1}, {0, 0, 1}}
o2 : List
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i3 : R=MultiProjCoordRing {2,3}
o3 = R
o3 : PolynomialRing
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i4 : coefficientRing R
ZZ
o4 = -----
32749
o4 : QuotientRing
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i5 : describe R
ZZ
o5 = -----[x ..x , Degrees => {3:{1}, 4:{0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2]
32749 0 6 {0} {1} {GRevLex => {7:1} }
{Position => Up }
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i6 : A=ChowRing R o6 = A o6 : QuotientRing |
i7 : describe A
ZZ[h ..h ]
1 2
o7 = ----------
3 4
(h , h )
1 2
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i8 : Segre(A,ideal random({1,1},R))
2 3 2 2 3 2 2 3 2 2
o8 = 10h h - 6h h - 4h h + 3h h + 3h h + h - h - 2h h - h + h + h
1 2 1 2 1 2 1 2 1 2 2 1 1 2 2 1 2
o8 : A
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The object MultiProjCoordRing is a method function.