resolution(EagonData) -- outputs the resolution that is the 0th row of the Eagon double complex

Synopsis

Function: resolution
Usage:

C = resolution E
Inputs:
- E, an instance of the type EagonData,
Optional inputs:
- DegreeLimit => ..., default value null,
- FastNonminimal => ..., default value false,
- HardDegreeLimit => ..., default value {},
- LengthLimit => ..., default value infinity,
- PairLimit => ..., default value infinity,
- ParallelizeByDegree (missing documentation) => ..., default value false,
- SortStrategy => ..., default value 0,
- StopBeforeComputation => ..., default value false,
- Strategy => ..., default value null,
- SyzygyLimit => ..., default value infinity,
Outputs:
- C, a chain complex,

Description

This command is equivalent to eagonResolution(EagonData).

i1 : R = ZZ/101[a,b]/ideal"a2,b2"

o1 = R

o1 : QuotientRing

i2 : E = eagon(R,4)

o2 = EagonData in <ring>.cache computed to length 4

o2 : EagonData

i3 : C = resolution E

      1      2      3      5      8
o3 = R  <-- R  <-- R  <-- R  <-- R
                                  
     0      1      2      3      4

o3 : ChainComplex

i4 : picture C

     +----------------------------------------+
     |+-------+-------+                       |
o4 = ||       |(1, {})|                       |
     |+-------+-------+                       |
     ||(0, {})|   *   |                       |
     |+-------+-------+                       |
     +----------------------------------------+
     |+-------+-------+--------+              |
     ||       |(2, {})|(0, {1})|              |
     |+-------+-------+--------+              |
     ||(1, {})|   *   |    *   |              |
     |+-------+-------+--------+              |
     +----------------------------------------+
     |+--------+--------+--------+            |
     ||        |(0, {2})|(1, {1})|            |
     |+--------+--------+--------+            |
     || (2, {})|    *   |    *   |            |
     |+--------+--------+--------+            |
     ||(0, {1})|    .   |    *   |            |
     |+--------+--------+--------+            |
     +----------------------------------------+
     |+--------+--------+--------+-----------+|
     ||        |(1, {2})|(2, {1})|(0, {1, 1})||
     |+--------+--------+--------+-----------+|
     ||(0, {2})|    *   |    .   |    1,1    ||
     |+--------+--------+--------+-----------+|
     ||(1, {1})|    .   |    *   |     *     ||
     |+--------+--------+--------+-----------+|
     +----------------------------------------+

Ways to use this method: