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NAGtypes :: PolySystem

PolySystem -- a polynomial system

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

See also

Methods that use a polynomial system :

For the programmer

The object PolySystem is a type, with ancestor classes System < MutableHashTable < HashTable < Thing.