checkSmoothnessOfOneParameterFamilies -- Check smoothness of 1-parameter families

Usage:

(answer,toDoAgain)=checkSmoothnessOfOneParameterFamilies(LL,name)
Inputs:
- LL, a list, list of semigroups
- name, a string, name of a " .dbm" file on the hard disk.
Optional inputs:
- BaseField => ..., default value ZZ/10000019
- Verbose => ..., default value 0
Outputs:
- answer, a Boolean value, true if all 1-parameter family are smoothing families
- toDoAgain, a list, list of elements L in LL where the smoothness check failed

Description

The database Y=openDatabase name contains an entries Y#(toString L|"ring") and Y#(toString L|"ideal") of a ring and an ideal over QQ for every L in LL; The function reads the corresponding list of ideals of one parameter smoothing families, and checks whether they are indeed smoothing families. The smoothness is checked by reduction to a finite field. Picking a bad prime field might give a few cases where the test fails. The corresponding semigroups are collected in the list toDoAgain.

Caveat

If for L there are no entries in Y an error occurs.

Ways to use checkSmoothnessOfOneParameterFamilies:

checkSmoothnessOfOneParameterFamilies(List,String)

For the programmer

The object checkSmoothnessOfOneParameterFamilies is a method function with options.

The source of this document is in WeierstrassSemigroups.m2:3576:0.