--- NEAR FUTURE ---
engine track:
DMat submatrix operations
(A,B are submatrices given by a rectangular window; c is a scalar)
set_zero(A), copy i.e. A=B, A+=B,
A *= c
A = c*B
A += c*B
)
MatOps vs MatrixOps???
adaptive precision:
proposed heuristic? if (log(cond number) + log(rel.error) + safety bits?) > precision then status = INCREASE_PRECISION
decide when to decrease?
mechanism: (1) engine returns with a flag "increase/decrease" precision
(2) M2 code decides what to do:
for example, the current approximation for x gets promoted to CC_prec where prec is new precision
also, create a (rawEvaluatorK?) evaluator for the homotopy with the new precision
--- ISSUES ---
Normalize=>true: is probably a good default for the blackbox... but causes checks to fail in NumericalSchubertCalculus
movePoints: fails if the new points are not regular -- there should be a blackbox combining endgame/refine before this is fixed
isSolution?
isOn: merge two versions?
numericalIntersection: need to handle witness sets with ProjectionDimension key
engine track: problem with the origin (change handling relative error tolerance, see witness-set examples)
NAGtrace: separate "progress update" from other "talk"?
hypersurfaceSection does not remove junk
numericalIrreducibleDecomposition fails on a singular point: e.g., ideal(x_1^2,x_2^2,x_3^3)
movePoints should take a list of Points
deflation needs work
points WitnessSet -- should return list of Points not list of lists (check if external packages use it)
decompose -- still not robust for nonreduced components
---functions that we may forget---
segmentHomotopyProjective