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

Methods that use a polynomial system :

"evaluate(PolySystem,Matrix)" -- see evaluate -- evaluate a polynomial system or matrix at a point
"evaluateJacobian(PolySystem,Point)" -- see evaluate -- evaluate a polynomial system or matrix at a point
homogenize(PolySystem,Ring,RingElement) -- homogenize a polynomial system
"equations(PolySystem)"
"ideal(PolySystem)"
"isHomogeneous(PolySystem)"
"jacobian(PolySystem)"
"net(PolySystem)"
"numFunctions(PolySystem)"
"numParameters(PolySystem)"
"numVariables(PolySystem)"
"parameters(PolySystem)"
"ring(PolySystem)"
"polySystem(PolySystem)" -- see polySystem -- construct a polynomial system
"residual(PolySystem,Point)" -- see residual -- residual of a polynomial function at a point
substitute(PolySystem,Ring) -- substitute a ring in a polynomial system
"texMath(PolySystem)" -- see texMath(PolySpace) -- convert to TeX math format
"witnessSet(PolySystem,Matrix,List)" -- see witnessSet -- construct a WitnessSet
"witnessSet(PolySystem,PolySystem,List)" -- see witnessSet -- construct a WitnessSet

For the programmer

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

PolySystem -- a polynomial system

Description

For developers:

See also

Methods that use a polynomial system :

For the programmer