/. Good-divisors-d1, , p.2

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, Q := Decomposition(F,Zeros(Kx!q

, K<b>:=ResidueClassField(Q)

, degree of Q is, Degree(Q

. //-n,

, D1 := RandomIrreduciblePolynomial, vol.16, p.1

, D1 a

, D1:=Decomposition(F,Zeros(Kx!D1

, D1:=1*D1

, D2:=RandomIrreduciblePolynomial(F16, p.1

, D2 := x^14 + x^2 + a*x + 1

, D2:=Decomposition(F,Zeros(Kx!D2

, D2:=1*D2

, D1-Q is special ?, Check D1 and D2 are suitable

. //-n, D2-Q is special ?

, Is D1 equivalent to D2 ?

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, LD1, vol.1, p.=RiemannRochSpace

, LD2, vol.2, p.=RiemannRochSpace

H. Ld1d2 and . Riemannrochspace, , vol.1

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, Construction of E1=Evalf(Q) and set a

, E1:=Transpose(Matrix(L))

, BasisLD1 := Matrix(F,1,n,BD1)*Matrix(F, pp.1-1

. //basisld1,

, Construction of E2=Evalf(Q) and set a

, E2:=Transpose(Matrix(L))

, BasisLD2 := Matrix(F,1,n,BD2)*Matrix(F, pp.2-3

. //basisld2,

, L2 := ElementToSequence, vol.2

, addition

, b^5 * (1 + a^2*b^3 + b^4) = b^9 + a^2*b^8 + b^5 X2 := Matrix

, Y2 := Matrix(F16,n,1,ElementToSequence(1 + a^2*b^3 + b^4

, *b + b^2 + a*b^4) * (a*b + b^2 + a*b^4) = a^2*b^8 + b^4 + a^2*b^2 X3 := Matrix, vol.3

, Y3 := Matrix(F16,n,1,ElementToSequence(a*b + b^2 + a*b^4

, Y4 := Matrix(F16,n,1,ElementToSequence(a*b + b^2 + a*b^4

, A

/. ,

, F4<a>:=GF(4)

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, Kx<x> := FunctionField(F4)

, Kxy<y> := PolynomialRing(Kx

, =y^2 + y + x/(x^3 + x +, vol.1

, F<c> := FunctionField(f)

, // 10 degree 1 places LP2:=Places

/. Good-divisors-d1, , p.2

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, Q := Decomposition(F,Zeros(Kx!q

, K<b>:=ResidueClassField(Q)

, degree of Q is, Degree(Q

. //-n,

, D1 := RandomIrreduciblePolynomial, vol.4, p.1

, D1 := x^6 + a*x^4 + a*x^2 + x + a^2

, D1:=Decomposition(F,Zeros(Kx!D1

, D1:=1*D1

, D2:=RandomIrreduciblePolynomial(F4, p.1

, D2 := x^6 + a*x^3 + a^2*x^2 + a^2

, D2:=Decomposition(F,Zeros(Kx!D2

, D2:=1*D2

, D1-Q is special ?, Check D1 and D2 are suitable

. //-n, D2-Q is special ?

, Is D1 equivalent to D2 ?

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, LD1, vol.1, p.=RiemannRochSpace

, LD2, vol.2, p.=RiemannRochSpace

H. Ld1d2 and . Riemannrochspace, , vol.1

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, Construction of E1=Evalf(Q) and set a

, E1:=Transpose(Matrix(L))

, BasisLD1 := Matrix(F,1,n,BD1)*Matrix(F, pp.1-1

. //basisld1,

, Construction of E2=Evalf(Q) and set a

, E2:=Transpose(Matrix(L))

, BasisLD2 := Matrix(F,1,n,BD2)*Matrix(F, pp.2-3

. //basisld2,

, L2 := ElementToSequence, vol.2

, addition

, TT := Matrix

. Basisld1d2,

, BLD1D2 := ExtendBasis

, Vectors of BLD1D2 are independent ?

, Basis of BLD1D2

:. Stemp and . St,

, place such that the 11x11-matrix T has rank 11 numPlace:=0

, ST1:=Append

, Matrix(2*n+g-1,2*n+g-1, ST

, Rank(T) eq 11 then numPlace:=j; break; end if

, num of the chosen 2 degree place : ", numPlace

, TI := T^-1

/. @parameter, VarY are the coordinates in a canonical basis // of the elements of (F4)^n to multipliate // @return : the result of VarX * VarY in the canonical basis of (F4)^n mult := function

, Matrix, vol.4

, TFX:=T*fx

, TFY:=T*fy

*. Kk!,

, mp:=ElementToSequence(mb,F4)

, E_Q(TI(u)) : T^-1 then evaluation in Q uu:=Matrix(F,TI*u)

, Evaluate(Matrix(1,2*n+g-1,BasisLD1D2)*uu,Q)

, Y1 := Matrix(F4,n,1,ElementToSequence(1+a*b+a*b^2

, Y2 := Matrix(F4,n,1,ElementToSequence(1 + a^2*b^3 + b^4

, X3 := Matrix(F4,n,1,ElementToSequence(a*b + b^2 + a*b^4

, Y3 := Matrix(F4,n,1,ElementToSequence(a*b + b^2 + a*b^4

, F2:=GF

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, Kx<x> := FunctionField, vol.2

, Kxy<y> := PolynomialRing(Kx

, F<c> := FunctionField(f)

, // 3 degree 1 places LP2:=Places

/. Good-divisors-d1, , p.2

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, x^5 + x^3 + 1

, Q := Decomposition(F,Zeros(Kx!q

, K<b>:=ResidueClassField(Q)

, D1 := RandomIrreduciblePolynomial, vol.2, p.1

, D1 := x^6 + x^5 + x^4 + x + 1

, D1:=Decomposition(F,Zeros(Kx!D1

, D1:=1*D1

, D2:=RandomIrreduciblePolynomial(F2, p.1

, D2 := x^6 + x^5 + x^2 + x + 1

, D2:=Decomposition(F,Zeros(Kx!D2

, D2:=1*D2

, D1-Q is special ?, Check D1 and D2 are suitable

. //-n, D2-Q is special ?

, Is D1 equivalent to D2 ?

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, LD1, vol.1, p.=RiemannRochSpace

, LD2, vol.2, p.=RiemannRochSpace

H. Ld1d2 and . Riemannrochspace, , vol.1

/. %%%%%%%%%%%%%%%%%%%%%%%%%%%,

, Construction of E1 : E1=Evalf(Q) and set a

, E1:=Transpose(Matrix(L))

, BasisLD1 := Matrix(F,1,n,BD1)*Matrix(F, pp.1-1

. //basisld1,

, Construction of E2 : E2=Evalf(Q) and set a

, E2:=Transpose(Matrix(L))

, BasisLD2 := Matrix(F,1,n,BD2)*Matrix(F, pp.2-3

. //basisld2,

, L2 := ElementToSequence, vol.2

, addition

, TT := Matrix

. Basisld1d2,

, BLD1D2 := ExtendBasis

, Vectors of BLD1D2 are independent ?

, Basis of BLD1D2

, ST2:=Append

, ST4:=Append

, Matrix(2*n+g-1,2*n+g-1, ST

, Rank of T

, TI := T^-1

/. @parameter, VarY are the coordinates in a canonic basis // of the elements of (F4)^n to multiply // @return : the result of VarX * VarY in the canonic basis of (F2)^n mult := function

, Matrix, vol.2

, TFX:=T*fx

. Tfy:=t*fy,

*. Kk!,

, mp:=ElementToSequence(mb,F2)

*. Kk4!,

, mp:=ElementToSequence(mb,F2)

, = mp, vol.9

, = mp, vol.10

, E_Q(TI(u)) : T^-1 then evaluation in Q uu:=Matrix(F,TI*u)

, Evaluate(Matrix(1,2*n+g-1,BasisLD1D2)*uu,Q)

, Y1 := Matrix

, b^4*(b^2+b^3) = b^20 X2 := Matrix, vol.2

, Y2 := Matrix

, Y3 := Matrix(F2,n,1,ElementToSequence

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