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CompPoly.Bivariate.GuruswamiSudan.Root.FieldRoots.KoalaBear

KoalaBear Guruswami-Sudan Field-Root Backends #

Concrete finite-field root backends for canonical KoalaBear and native-word fast KoalaBear. Both use the generic finite-field algorithm directly over their field carriers.

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def CompPoly.GuruswamiSudan.koalaBearFiniteFieldContext :
CPolynomial.Roots.FiniteField.FiniteFieldContext KoalaBear.Field

Finite-field context for canonical KoalaBear.

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    def CompPoly.GuruswamiSudan.koalaBearSmoothCyclicRootContext :
    CPolynomial.Roots.FiniteField.SmoothCyclicRootContext KoalaBear.Field

    Smooth cyclic splitter context for canonical KoalaBear.

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      def CompPoly.GuruswamiSudan.koalaBearFieldRootContext :
      FieldRootContext KoalaBear.Field

      Complete GS-facing finite-field root backend for canonical KoalaBear.

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        def CompPoly.GuruswamiSudan.koalaBearNttFieldRootContext :
        FieldRootContext KoalaBear.Field

        Complete GS-facing finite-field root backend for canonical KoalaBear with NTT arithmetic.

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          def CompPoly.GuruswamiSudan.koalaBearNttFastFieldRootContext :
          FieldRootContext KoalaBear.Field

          Complete GS-facing finite-field root backend for canonical KoalaBear with NTTFast arithmetic.

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            def CompPoly.GuruswamiSudan.fastKoalaBearFiniteFieldContext :
            CPolynomial.Roots.FiniteField.FiniteFieldContext KoalaBear.Fast.Field

            Finite-field context for native-word fast KoalaBear.

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              def CompPoly.GuruswamiSudan.fastKoalaBearPrimitiveRoot :
              KoalaBear.Fast.Field

              Primitive generator transported to native-word fast KoalaBear.

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                theorem CompPoly.GuruswamiSudan.fastKoalaBearPrimitiveRoot_order :
                orderOf fastKoalaBearPrimitiveRoot = KoalaBear.fieldSize - 1

                The transported fast KoalaBear generator has full multiplicative order.

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                def CompPoly.GuruswamiSudan.fastKoalaBearSmoothCyclicRootContext :
                CPolynomial.Roots.FiniteField.SmoothCyclicRootContext KoalaBear.Fast.Field

                Smooth cyclic splitter context for native-word fast KoalaBear.

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                  def CompPoly.GuruswamiSudan.fastKoalaBearFieldRootContext :
                  FieldRootContext KoalaBear.Fast.Field

                  Complete GS-facing finite-field root backend for native-word fast KoalaBear.

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                    def CompPoly.GuruswamiSudan.fastKoalaBearNttFieldRootContext :
                    FieldRootContext KoalaBear.Fast.Field

                    Complete GS-facing finite-field root backend for native-word fast KoalaBear with NTT arithmetic.

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                      def CompPoly.GuruswamiSudan.fastKoalaBearNttFastFieldRootContext :
                      FieldRootContext KoalaBear.Fast.Field

                      Complete GS-facing finite-field root backend for native-word fast KoalaBear with NTTFast arithmetic.

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