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

- 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.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/K3Carpets.m2:1882:0.