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AbstractPoint -- a type used to store a point in complex space


The type Point inherited from AbstractPoint is used to store a solution to a polynomial system obtained by such functions as solveSystem, track. The following methods can be used to access a AbstractPoint: Possible return values of status reflect the status with respect to a homotopy continuation procedure that obtained this point: Only coordinates are displayed (by net); other attributes of a Point p are stored in p.cache. Different algorithms attach different information describing the point. For example, solveSystem produces the following.

i1 : loadPackage "NumericalAlgebraicGeometry";
i2 : R = CC[x,y];
i3 : sols = solveSystem{x^2+y^2-3, x^3-y^3-7}

o3 = {{-1.7957-1.31322*ii, 1.7957-1.31322*ii}, {-.101284+.779159*ii,
     -1.89699-.041601*ii}, {-1.7957+1.31322*ii, 1.7957+1.31322*ii},
     {-.101284-.779159*ii, -1.89699+.041601*ii}, {1.89699+.041601*ii,
     .101284-.779159*ii}, {1.89699-.041601*ii, .101284+.779159*ii}}

o3 : List
i4 : pt = first sols

o4 = pt

o4 : Point
i5 : peek pt

o5 = Point{cache => CacheTable{...5...}                          }
           Coordinates => {-1.7957-1.31322*ii, 1.7957-1.31322*ii}
i6 : coordinates pt

o6 = {-1.7957-1.31322*ii, 1.7957-1.31322*ii}

o6 : List
i7 : status pt

o7 = Regular

o7 : Symbol

The other keys that may be attached include

Basic service functions:

Types of point :

Methods that use a point :

For the programmer

The object AbstractPoint is a type, with ancestor classes HashTable < Thing.