internalUseDirectSum -- Compute direct sum of two rings.

Synopsis

• Usage:

  internalUseDirectSum(A,C)

• Inputs:
  • f
  • g
• Outputs:
  • The ring A times C
  • The idempotent (1_A, 0)

Description

A method which computes the product of two rings in the category of rings.This function requires that $A$ and $C$ have the same coefficient field and that the variable names of $A$ and $C$ are distinct. The variable names of the two rings in the direct sum ring remain the same. This function was originally going to be internal (hence the name), but may be useful in other cases too. We compute an example

i1 : A = QQ[x];

i2 : C = QQ[y];

i3 : (internalUseDirectSum(A,C))#0 QQ[x, e1, y] o3 = -------------------------- 2 (e1 - e1, x*e1 - x, e1*y) o3 : QuotientRing