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# GateSystem ^ List -- a subsystem with specified equations

- Operator: ^
- Usage:
    `G^L`
- Inputs:
  - G, an instance of the type GateSystem,
  - L, a list, indices of the equations,

## Description

    i1 : variables = declareVariable \ {x,y}

    o1 = {x, y}

    o1 : List

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

    o2 = gate system: 2 input(s) ---> 3 output(s)

    o2 : GateSystem

    i3 : gateMatrix F

    o3 = {{((x * y) + -1)}, {(((x * x * x) + (y * y)) + (-1 * 2))}, {(((x * x) +
         ------------------------------------------------------------------------
         (2 * y)) + (-1 * 3))}}

    o3 : GateMatrix

    i4 : G = F^{0,2}

    o4 = gate system: 2 input(s) ---> 2 output(s)

    o4 : GateSystem

    i5 : gateMatrix G

    o5 = {{((x * y) + -1)}, {(((x * x) + (2 * y)) + (-1 * 3))}}

    o5 : GateMatrix

## Ways to use this method:

- GateSystem ^ List -- a subsystem with specified equations

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NumericalAlgebraicGeometry/doc.m2:1104:0.