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SuperLinearAlgebra :: parity

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

Synopsis

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

See also

Ways to use parity :

For the programmer

The object parity is a method function.