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); |
The object LRcheater is a method function.