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# ring -- get the associated ring of an object

## Synopsis

• Usage:
ring M
• Inputs:
• M, an object with a ring associated to it
• Outputs:
• a ring, associated to the input object

## Description

For example, ring elements, matrices, ideals, modules, chain complexes, varieties, coherent sheaves, etc., all have a base ring naturally associated to them.
 i1 : R = ZZ/101[x,y,z]; i2 : ring x o2 = R o2 : PolynomialRing i3 : M = matrix {{2*x, x+y},{y^3, z*y}}; 2 2 o3 : Matrix R <-- R i4 : ring M o4 = R o4 : PolynomialRing i5 : S = QQ[x,y,z]; i6 : ring x o6 = S o6 : PolynomialRing i7 : I = ideal (x*y, y*z); o7 : Ideal of S i8 : ring I o8 = S o8 : PolynomialRing

## Ways to use ring :

• ring(CC)
• ring(ChainComplex)
• ring(ChainComplexMap)
• ring(GradedModule)
• ring(GradedModuleMap)
• ring(GroebnerBasis)
• ring(Ideal)
• ring(Matrix)
• ring(Module)
• ring(MonomialIdeal)
• ring(MutableMatrix)
• ring(Number)
• ring(Resolution)
• ring(RingElement)
• ring(RR)
• ring(RRi)
• ring(Vector)
• ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• ring(SheafOfRings) -- see ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• ring(SumOfTwists) -- see ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• ring(SheafMap) (missing documentation)
• ring(Variety) -- coordinate ring of the variety

## For the programmer

The object ring is .