Description
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
- parameters -- the list of parameter variables (if any)
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
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+10.6ii |
| -18.3+11ii |
2 1
o4 : Matrix CC <-- CC
53 53
|
i5 : evaluate(jacobian S, p)
o5 = | 2+6ii 4.6+2ii |
| 4+12ii -1 |
2 2
o5 : Matrix CC <-- CC
53 53
|
Basic service functions:
- polySystem -- construct a polynomial system
- evaluate -- evaluate a polynomial system or matrix at a point