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# isGolodAInf -- Determines if the ring is Golod or not

- Usage:
    `h = isGolod R`
- Inputs:
  - R, a ring,
- Outputs:
  - h, a Boolean value, Whether or not the ring is Golod

## Description

This function computes the A-infinity multiplications to all required orders, and reduces them modulo the maximal ideal. If all reductions are zero, then the ring R is Golod.

Below is an example of an artinian ring R (based on an example of Roos and Katthan) which has minimal multiplications of order two, but is not Golod.

    i1 : kk = ZZ/101

    o1 = kk

    o1 : QuotientRing

    i2 : S = kk[x,y,z,u]

    o2 = S

    o2 : PolynomialRing

    i3 : I = ideal(u^3, x*y^2, (x+y)*z^2, x^2*u+z*u^2, y^2*u+x*z*u, y^2*z+y*z^2)

                 3     2     2      2   2       2   2            2       2
    o3 = ideal (u , x*y , x*z  + y*z , x u + z*u , y u + x*z*u, y z + y*z )

    o3 : Ideal of S

    i4 : J = trim (I + (ideal vars S)^6)

                 3   2            2       2     2      2   2       2     2   5
    o4 = ideal (u , y u + x*z*u, x u + z*u , x*z  + y*z , y z + y*z , x*y , z u,
         ------------------------------------------------------------------------
          6   4      5    6   5    6
         z , x y*z, x z, y , x y, x )

    o4 : Ideal of S

    i5 : hasMinimalMult(quotient J, 2)

    o5 = true

    i6 : isGolodAInf quotient J

    o6 = false

## Ways to use isGolodAInf:

- `isGolodAInf(Ring)`

## For the programmer

The object isGolodAInf is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/AInfinity.m2:1518:0.