# 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, , 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, , the outcome of LRtriple(n,m), wrapped into string.
• Optional inputs:
• Verbose => ..., default value true, request verbose feedback
• Outputs:
• t, , 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. This is similar in function to changeFlags

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); i5 : w := wrapTriplet(t);

## Ways to use LRcheater :

• "LRcheater(ZZ,Matrix,String)"

## For the programmer

The object LRcheater is .