Ring / Ideal

R/I -- form a quotient ring.

Here I may be: an element of R ; a sequence of elements of R ; or a submodule of R^1 .

The names of the variables are assigned values in the new quotient ring by automatically running use R , unless R has a name, or one of the rings R is a quotient ring of has a name.

Quotient rings are bulky objects, because they contain a Groebner basis for their ideals, so only quotients of ZZ are remembered forever. Typically the ring created by R/I will be a brand new ring, and its elements will be incompatible with the elements of previously created quotient rings for the same ideal.

     i1 = ZZ/2 === ZZ/(4,6)
     
     o1 = true

     i2 = R = ZZ/101[t]
     
     o2 = R
     
     o2 : PolynomialRing

     i3 = R/t === R/t
     
     o3 = false