getSmoothingFamilyWithVersalDeformation -- Get a smoothing family using versal deformations

Usage:

(worked,fibz)=getSmoothingFamilyWithVersalDeformation(L)

L:List

list of generators of a semigroup
Optional inputs:
- BaseField => ..., default value ZZ/10000019
- Bound => ..., default value 1
- CoeffBound => ..., default value 10000
- CoeffSize => ..., default value 1
- HighestOrder1 => ..., default value 20
- Verbose => ..., default value 0
Outputs:
- worked, a Boolean value, true if successful
- fibz, an ideal, the ideal of a 1-parameter smoothing family defined over QQ

Description

Using the package VersalDeformations we try compute a smoothing family

i1 : L = {5,7,11}

o1 = {5, 7, 11}

o1 : List

i2 : (worked,fibz)=getSmoothingFamilyWithVersalDeformation(L,Verbose=>2,Bound=>4)
Calculating first order relations
Calculating standard expressions for obstructions
Starting lifting
Order 2
Order 3
Order 4
Solution is polynomial
 -- .253354s elapsed

                    3    2      2   4        5    3 6    2 7        9      10
o2 = (true, ideal (x  - x x  - x x z  - x x z  - x z  - x z  + x x z  - x z  
                    2    0 1    0 2      0 1      0      2      0 2      1   
     ------------------------------------------------------------------------
        2 11      14       16     21   3      2        4    2   5        6  
     - x z   + x z   - 3x z   - 2z  , x x  - x  - x x z  - x x z  - x x z  -
        0       2        0             0 2    1    2 1      0 2      0 1    
     ------------------------------------------------------------------------
      3 7    2 8         10    2 12      15       17     22   5    2    
     x z  - x z  - 2x x z   + x z   - x z   + 2x z   + 2z  , x  - x x  -
      0      2       0 2       0       2        0             0    2 1  
     ------------------------------------------------------------------------
      2   8         9     3 10        13       14     2 15      18       20  
     x x z  - 2x x z  - 2x z   - x x z   - 2x z   - 5x z   - x z   - 4x z   -
      0 2       0 1       0       0 2        1        0       2        0
     ------------------------------------------------------------------------
       25
     2z  ))

o2 : Sequence

Caveat

If the versal deformation computation does finished with "Solution is polynomial" one needs to increase the default value HighestOrder1=>20 to a larger number.

Ways to use getSmoothingFamilyWithVersalDeformation:

getSmoothingFamilyWithVersalDeformation(List)

For the programmer

The object getSmoothingFamilyWithVersalDeformation is a method function with options.

The source of this document is in WeierstrassSemigroups.m2:3015:0.