By default, the homotopy is created with tDegree equal to 2. This option allows the user to give another value for tDegree; e.g., a linear homotopy between start system q and target system f is of the form (1-t)*q + t*f.
In general, if tDegree is k, then the homotopy is of the form (1-t)^k*q + t^k*f.
A reason for changing the tDegree would be the following: higher degree homotopies ensure that the system doesn't change as fast in the beginning and at the end of the homotopy; that is, they force smaller step sizes in the beginning and end. The default value, 2, is usually sufficient.
|
|
|
|
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/PHCpack/PHCpackDoc.m2:1432:0.