LRcheater -- A cheater's homotopy to a real Schubert triple intersection problem

Synopsis

Usage:

t = LRcheater(n,m,w)
Inputs:
- n, an integer, the ambient dimension
- m, a matrix, in the rows are the intersection conditions, the first element of each row is the number of times the intersection bracket must be taken.
- w, a string, the outcome of LRtriple(n,m), wrapped into string.
Outputs:
- t, a string, solutions to a a real triple Schubert intersection problem.

Description

A cheater's homotopy between two polynomial systems connects a generic instance to a specific instance.

The example below solves a generic instance of [2 4 6]^3, followed by a cheater homotopy to a real instance.

i1 : R := ZZ;

i2 : n := 6;

i3 : m := matrix{{3, 2, 4, 6}};

              1        4
o3 : Matrix ZZ  <--- ZZ

i4 : t := LRtriple(n,m);
PHCv2.4.77 released 2020-06-12

the input data for phc -e : 
5
6
[ 2 4 6 ]^3;
0
0
0
/var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-96022-0/3PHCout
0
y
y
0
0
0

writing data to file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-96022-0/2PHCip
running phc -e, session output to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-96022-0/4PHCses
                writing output to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-96022-0/3PHCout
opening output file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-96022-0/5PHCsolutions

i5 : w := wrapTriplet(t);

Ways to use `LRcheater` :

"LRcheater(ZZ,Matrix,String)"

For the programmer

The object LRcheater is a method function.

LRcheater -- A cheater's homotopy to a real Schubert triple intersection problem

Synopsis

Description

Ways to use LRcheater :

For the programmer

Ways to use `LRcheater` :