This type stores a polynomial system, the following methods can be used to access a
PolySystem:
- ideal -- the ideal generated by the system
- equations -- the list of polynomials in the system
- ring -- the ring containing the polynomials
- jacobian -- the jacobian of the polynomial map
Only polynomials are displayed (by
net); to see the data stored in a witness set use
peek.
For developers:
Required entries in a
PolySystem are
- NumberOfVariables of type ZZ
- NumberOfPolys of type ZZ
- PolyMap of type Matrix, a column matrix over a polynomial ring
- Jacobian of type Matrix, the jacobian of PolyMap
Basic methods for
polynomial homotopy use additional keys:
- ContinuationParameter -- stores one variable of the ring
- SpecializationRing -- stores the subring generated my all variables except the additional parameter (e.g., used by specializeContinuationParameter)
i1 : CC[x,y]
o1 = CC [x, y]
53
o1 : PolynomialRing
|
i2 : S = polySystem {x^2+y^2-6, 2*x^2-y}
o2 = S
o2 : PolySystem
|
i3 : p = point {{1.0+3*ii,2.3+ii}};
|
i4 : evaluate(S,p)
o4 = | -9.71+10.6i |
| -18.3+11i |
2 1
o4 : Matrix CC <--- CC
53 53
|
i5 : evaluate(jacobian S, p)
o5 = | 2+6i 4.6+2i |
| 4+12i -1 |
2 2
o5 : Matrix CC <--- CC
53 53
|
Basic service functions: