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SuperLinearAlgebra :: superRing

superRing -- Makes a super ring from two polynomial rings.

Synopsis

Description

Let $R_1$ and $R_2$ be Two Polynomial rings on different set of variables A superRing is a new polynomial ring with three sets of variables. One set comes from $R_1$ and the second one is the inverse of it.

For example, if we have x as a variable in $R_1$, then there is a new variable, say $inverseVariable_0$ which is the inverse of $x$. The third set of variables comes from $R_2$. We redefine this set to be a set of skew-symmetric variables. So superRing of $R_1$ and $R_2$ is a quotient ring, which has both invertible and skew symmetric variables. If the coefficient ring is a field, then we get a super algebra.

i1 : R1=QQ[x_1..x_5]

o1 = R1

o1 : PolynomialRing
i2 : R2=QQ[z_1..z_3]

o2 = R2

o2 : PolynomialRing
i3 : superRing(R1, R2)

                                      QQ[x ..x , inverseVariable ..inverseVariable , z ..z ]
                                          1   5                 0                 4   1   3
o3 = ------------------------------------------------------------------------------------------------------------------------
     (x inverseVariable  - 1, x inverseVariable  - 1, x inverseVariable  - 1, x inverseVariable  - 1, x inverseVariable  - 1)
       1               0       2               1       3               2       4               3       5               4

o3 : QuotientRing

Caveat

Ways to use superRing :

For the programmer

The object superRing is a method function.