parity -- parity of an element of a super ring.

Synopsis

Usage:

N = parity(f, R, L)
Inputs:
- f, a ring element,
- R, a ring, superRing
- L, a list,
Outputs:
- N, a number, 0 for even, 1 for odd and-1 for Nonhomogeneous

Description

Let we have a super algebra (ring), $R=R_0 \oplus R_1$. A homogeneous element of $R$ is an element belongs to $R_0$ or $R_1$. This function has three outputs,-1 for non-homogeneous, 0 for homogeneous and even, and 1 for homogeneous and odd elements.

i1 : R1=QQ[x_0..x_4];

i2 : R2=QQ[e_0, e_1];

i3 : R= superRing(R1, R2)

o3 = R

o3 : QuotientRing

i4 : L={e_0, e_1}

o4 = {e , e }
       0   1

o4 : List

i5 : f=x_1*x_2*x_3+x_1*e_0+e_1*e_0-4*x_2*e_1*e_0+4

o5 = x x x  + x e  + 4x e e  - e e  + 4
      1 2 3    1 0     2 0 1    0 1

o5 : R

i6 : parity(f, R, L)

o6 = -1

i7 : g=x_1*x_2*x_3+e_0*e_1+4;

i8 : parity(g, R, L)

o8 = 0

Caveat

Ways to use parity :

parity(RingElement,Ring,List)
parity(Number,Ring,List) (missing documentation)

For the programmer