# 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(CoherentSheaf)"
• "ring(GroebnerBasis)"
• "ring(Ideal)"
• "ring(Matrix)"
• "ring(Module)"
• "ring(MonomialIdeal)"
• "ring(MutableMatrix)"
• "ring(Number)"
• "ring(Resolution)"
• "ring(RingElement)"
• "ring(RR)"
• "ring(RRi)"
• "ring(SheafOfRings)"
• "ring(Variety)"
• "ring(Vector)"

## For the programmer

The object ring is .