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EquivariantGB :: incOrbit

incOrbit -- the increasing map orbit of an element

Synopsis

Description

If F is an equivariant Gröbner basis for invariant ideal I with respect to a width order then this method produces a traditional Gröbner basis for the nth truncation of I.

If the optional argument Symmetrize is set to true, then the full Sn orbit is produced.

i1 : R = buildERing({symbol x}, {1}, QQ, 2);
i2 : O = incOrbit(x_0^2, 4)

       2   2   2   2
o2 = {x , x , x , x }
       0   1   2   3

o2 : List
i3 : P = incOrbit(x_0 + x_1^2, 3, Symmetrize=>true)

       2             2   2             2   2             2
o3 = {x  + x , x  + x , x  + x , x  + x , x  + x , x  + x }
       1    0   1    0   2    0   2    0   2    1   2    1

o3 : List

Caveat

The output is not necessarily in the same ring as the input. The width bound of the ring of the output will always be n.

Ways to use incOrbit :