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LinearTruncations > irrelevantIdeal

irrelevantIdeal -- gives the irrelevant ideal of the coordinate ring of a product of projective spaces

Synopsis

Description

Given the coordinate ring of a product of projective spaces, this function produces the irrelevant ideal (in the sense of toric geometry) by listing the unique degrees of generators of R, creating an ideal from the generators of each degree, and intersecting them.

i1 : R = multigradedPolynomialRing {1,2}

o1 = R

o1 : PolynomialRing
i2 : irrelevantIdeal R

o2 = ideal (x   x   , x   x   , x   x   , x   x   , x   x   , x   x   )
             0,1 1,2   0,0 1,2   0,1 1,1   0,0 1,1   0,1 1,0   0,0 1,0

o2 : Ideal of R
i3 : R = multigradedPolynomialRing 3

o3 = R

o3 : PolynomialRing
i4 : irrelevantIdeal R

o4 = ideal (x   x   x   , x   x   x   , x   x   x   , x   x   x   ,
             0,1 1,1 2,1   0,0 1,1 2,1   0,1 1,0 2,1   0,0 1,0 2,1 
     ------------------------------------------------------------------------
     x   x   x   , x   x   x   , x   x   x   , x   x   x   )
      0,1 1,1 2,0   0,0 1,1 2,0   0,1 1,0 2,0   0,0 1,0 2,0

o4 : Ideal of R

Caveat

This function will not give the correct irrelevant ideal for the Cox ring of a toric variety that is not a product of projective spaces. Use the package NormalToricVarieties instead.

See also

Ways to use irrelevantIdeal :

For the programmer

The object irrelevantIdeal is a method function.