mapToTriangleRing -- embeds a ring of the form R[d,f]/d^2 in its triangle ring R[d,e,f]/(d^2,e^3)

Synopsis

Usage:

mapToTriangleRing Q
Inputs:
- Q, a ring, of the form R[d,f]/d^2
Outputs:
- a ring map, from Q to its triangle ring R[d,e,f]/(d^2,e^3)

Description

The external degrees of d and f double, and the external degree of the new variable "e" is the difference of external degrees (degree d) - (degree f).

i1 : R = QQ[x];

i2 : Q = R[d,f,Degrees=>{{1,2,3},{10,11,12}}]/d^2

o2 = Q

o2 : QuotientRing

i3 : phi = mapToTriangleRing Q

         R[d, e, f]
o3 = map(----------,Q,{d, f, x})
            2   3
          (d , e )

             R[d, e, f]
o3 : RingMap ---------- <--- Q
                2   3
              (d , e )

i4 : T = target phi

o4 = T

o4 : QuotientRing

i5 : degree \ {Q_0, Q_1}

o5 = {{1, 2, 3, 0}, {10, 11, 12, 0}}

o5 : List

i6 : degree \ {T_0, T_1, T_2}

o6 = {{2, 4, 6, 0}, {-9, -9, -9, 0}, {20, 22, 24, 0}}

o6 : List

Caveat

The input ring Q must be valid for expectChainSequenceRing.

Ways to use `mapToTriangleRing`:

mapToTriangleRing(Ring)

For the programmer