gateSystem -- a constructor for GateSystem

Synopsis

Usage:

gateSystem(params,variables,M)

gateSystem(variables,M)
Inputs:
- M, an instance of the type GateMatrix,
- parameters, an instance of the type GateMatrix,
- variables, an instance of the type GateMatrix,

Description

GateMatrix M is expected to have 1 column. Matrices params and variables are expected to have 1 row. (Later addition: TO DO say something about less restritive syntax.)

i1 : variables = declareVariable \ {x,y}

o1 = {x, y}

o1 : List

i2 : F = gateSystem(matrix{variables}, matrix{{x*y-1},{x^3+y^2-2}})

o2 = gate system: 2 input(s) ---> 2 output(s)

o2 : GateSystem

i3 : evaluate(F,point{{0.1,0.2+ii}})

o3 = | -.98+.1ii -2.959+.4ii |

                1         2
o3 : Matrix CC    <-- CC
              53        53

i4 : evaluate(F,point{{1/2,1/3}})

o4 = | -5/6 -127/72 |

              1       2
o4 : Matrix QQ  <-- QQ

i5 : evaluate(F,point{{2_(ZZ/101),3}})

o5 = | 5 15 |

              ZZ 1       ZZ 2
o5 : Matrix (---)  <-- (---)
             101        101

Systems with parameters are allowed.

i6 : params = declareVariable \ {a,b}

o6 = {a, b}

o6 : List

i7 : Fab = gateSystem(matrix{params}, matrix{variables}, matrix{{a*x*y-1},{x^3+y^2-b}})

o7 = gate system: 2 input(s) ---> 2 output(s) (with 2 parameters)

o7 : GateSystem

i8 : evaluate(Fab,point{{1,2}},point{{0.1,0.2+ii}})

o8 = | -.98+.1ii -2.959+.4ii |

                1         2
o8 : Matrix CC    <-- CC
              53        53

Caveat

Note for developers: there is a version of the constructor that builds GateSystem from PolySystem. Its variant that takes the list of variables to treat as parameters is likely to disappear.

Ways to use gateSystem :

gateSystem(BasicList,BasicList,GateMatrix)
gateSystem(GateMatrix,GateMatrix)
gateSystem(GateMatrix,GateMatrix,GateMatrix)
gateSystem(Matrix)
gateSystem(PolySystem)
gateSystem(PolySystem,List)

For the programmer

The object gateSystem is a method function.