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NumericalAlgebraicGeometry :: gateHomotopy(GateMatrix,GateMatrix,InputGate)

gateHomotopy(GateMatrix,GateMatrix,InputGate) -- homotopy implemented via straight line programs

Synopsis

Description

Optional arguments:
i1 : X = inputGate symbol X

o1 = X

o1 : InputGate
i2 : Y = inputGate symbol Y

o2 = Y

o2 : InputGate
i3 : T = inputGate symbol T

o3 = T

o3 : InputGate
i4 : F = {X*X-1, Y*Y*Y-1}

o4 = {((X * X) + -1), (((Y * Y) * Y) + -1)}

o4 : List
i5 : G = {X*X+Y*Y-1, X*X*X+Y*Y*Y-1}

o5 = {(((X * X) + (Y * Y)) + -1), ((((X * X) * X) + ((Y * Y) * Y)) + -1)}

o5 : List
i6 : H = (1 - T) * F + T * G

o6 = {(((1 + (-1 * T)) * ((X * X) + -1)) + (T * (((X * X) + (Y * Y)) + -1))),
     ------------------------------------------------------------------------
     (((1 + (-1 * T)) * (((Y * Y) * Y) + -1)) + (T * ((((X * X) * X) + ((Y *
     ------------------------------------------------------------------------
     Y) * Y)) + -1)))}

o6 : List
i7 : HS = gateHomotopy(transpose matrix {H},matrix{{X,Y}},T)

o7 = GateHomotopy{...11...}

o7 : GateHomotopy

Caveat

The order of inputs for unexported internal evaluation functions (evaluateH, etc.) is fixed as follows: Parameters, X, T.

See also