III.3 - Function AddCoefficientChains adds two Coefficients Chains into one, by appending them together .

III.2 - Function AppendChain appends a Coefficient-Chain to a Coefficient-Chain of Chains.

III.2 - Function AppendCoefficient appends a Coefficient to a Coefficient-Chain.

III.4 - Function AddCoefficientChains adds two Coefficients Chains into one, by appending them together .

VI.3 - Function ComposePolynom creates a Polynom from its composing Elements It is used in Polynom multiplication.

Counts how many primes are needed to compute T modulo these primes,for the given Elliptic Finite Prime Field PWe need as many primes as to reach a product between them greater than 4*Sqrt(PrimeField).

VII.2 - Function DPolynomCube multiplies a DivisionPolynom with itself two times.

====================================================================================================================== Part VII - DivisionPolynom Operation Functions VII.1 - Function DPolynomMul multiplies two DivisionPolynom together.

VII.2 - Function DPolynomSqr multiplies a DivisionPolynom with itself.

Outputs two big.Int, the result of the division of the YCoefficient with their GCD.Assuming their Y exponent is equal the correct output are two ig.Int.

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Creates a Slice with the first 1 million Prime numbers as big.Int.

VI.2 - Function ModifyRank increases the uint64 slice elements by a given Value It is used in Polynom multiplication.

V.2 - Function MulCoefficient multiplies two Coefficient.

V.3 - Function MulCoefficients multiplies two Coefficient-Chains.

====================================================================================================================== Part V - Coefficient Operation Functions, needed for Polynom Operation Function.

IV.4 - Function NegatePolynom multiplies a Polynom by a -1 Scalar, which in effect negates it.

VI.4 - Function PolynomAdd adds two Polynom together It is also a part of Polynom multiplication.

VI.8 - Function PolynomCube multiplies a Polynom with itself two times.

VI.6 - Function PolynomMul multiplies two Polynom together It is used in computing the DivisionPolynom .

VI.7 - Function PolynomSqr multiplies a Polynom with itself.

VI.5 - Function PolynomSub subtracts a Polynom from another Polynom.

II.5 PrintCoefficient prints a single Coefficient.

II.3 PrintCoefficients prints a Chain of Coefficients .

====================================================================================================================== Part II - Printing Functions II.1 PrintDPolynom prints a Division-Polynom .

II.2 PrintPolynom prints a simple AB-Polynom; The AB-Polynom is the nonY Part of the Division Polynom .

II.4 PrintYCoefficient prints the YCoefficient, the Y Polynom Part of the DivisionPolynom.

III.4 - Function ReduceCoefficients reduces multiple similar Coefficient values, if they exist (values that have the same AB exponent), to a single value.

====================================================================================================================== Part III - Auxiliary Function III.1 - Function RemoveCoefficient remove a Coefficient from the specified Position .

====================================================================================================================== Part IV - Coefficient and Polynom Scalar Multiplication Function IV.1 - Function ScalarMulCoefficient multiplies a Coefficient by a Scalar, which is a big.Int number.

IV.2 - Function ScalarMulCoefficients multiplies a Coefficient-Chain by a Scalar, which is a big.Int number.

IV.3 - Function ScalarPolynomMul multiplies a Polynom by a Scalar, which is a big.Int number.

The Core of the Schoof Algorithm, Computing Trace mod many smaller Primes.

====================================================================================================================== Part VI - Polynom Operation Functions VI.1 - Function UniqueSlice creates a Unique uint64 Slice from two uint64 Slices that might have similar elements.

Defining Letters.

Division Polynom Three.

Division Polynom Four.

Division Polynom Minus One.

Division Polynom One.

Division Polynom Two.

Division Polynom 0.

No Y Coefficient.

1/2Y as DivisionPolynom.

Division Polynom One, defined as Polynom, used in the Definition of Division Polynom 2.

Defining Y^2.

====================================================================================================================== PART I - Type Definitions .