getNorm -- Computes the norm over $k$ for an element in a finite dimensional $k$-algebra

• Usage:

  getNorm(C,a)

  getNorm(S,I,b)

• Inputs:
  • C, a ring, a finite dimensional $k$-algebra
  • a, a thing, an element in C
  • S, a ring, a polynomial ring
  • I, an ideal, an ideal in the polynomial ring S
  • b, a thing, an element in S
• Outputs:
  • a ring element, the norm over $k$ for an element in the algebra

i1 : L = QQ[x]/(x^6+x^5+x^4+x^3+x^2+x+1);

i2 : F = toField L;

i3 : getNorm(F[a,b,c], ideal(a^2,b^2,c^2),1+a*b+b*c+c*a)

o3 = 1

o3 : F

i4 : R = QQ[x,y]/(x^2+y^2+1, 3*x+2);

i5 : getNorm(R, 1+y*x^2)

     937
o5 = ---
     729

o5 : QQ