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irrelevantIdeal -- returns the irrelevant ideal of a multi-graded ring

Synopsis

Usage:

mm = irrelevantIdeal R
Inputs:
- R, a ring, (multi)-graded ring
Outputs:
- mm, an ideal, irrelevant ideal of R

Description

Returns the intersection of the ideals of variables in each single multi-degree.

i1 : R = productOfProjectiveSpaces 3

o1 = R

o1 : PolynomialRing

i2 : vars R

o2 = | x_(0,0) x_(1,0) x_(0,1) x_(1,1) x_(0,2) x_(1,2) |

             1      6
o2 : Matrix R  <-- R

i3 : (gens R)/degree

o3 = {{1, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 1, 0}, {0, 0, 1}, {0, 0, 1}}

o3 : List

i4 : irrelevantIdeal R

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

o4 : Ideal of R

See also

productOfProjectiveSpaces -- Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)

For the programmer

The object irrelevantIdeal is a function closure.