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				|  |  | +package utils
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				|  |  | +
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				|  |  | +type GFPoly struct {
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				|  |  | +	gf           *GaloisField
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				|  |  | +	Coefficients []int
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				|  |  | +}
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				|  |  | +
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				|  |  | +func (gp *GFPoly) Degree() int {
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				|  |  | +	return len(gp.Coefficients) - 1
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				|  |  | +}
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				|  |  | +
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				|  |  | +func (gp *GFPoly) Zero() bool {
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				|  |  | +	return gp.Coefficients[0] == 0
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				|  |  | +}
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				|  |  | +
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				|  |  | +// GetCoefficient returns the coefficient of x ^ degree
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				|  |  | +func (gp *GFPoly) GetCoefficient(degree int) int {
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				|  |  | +	return gp.Coefficients[gp.Degree()-degree]
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				|  |  | +}
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				|  |  | +
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				|  |  | +func (gp *GFPoly) AddOrSubstract(other *GFPoly) *GFPoly {
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				|  |  | +	if gp.Zero() {
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				|  |  | +		return other
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				|  |  | +	} else if other.Zero() {
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				|  |  | +		return gp
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				|  |  | +	}
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				|  |  | +	smallCoeff := gp.Coefficients
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				|  |  | +	largeCoeff := other.Coefficients
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				|  |  | +	if len(smallCoeff) > len(largeCoeff) {
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				|  |  | +		largeCoeff, smallCoeff = smallCoeff, largeCoeff
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				|  |  | +	}
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				|  |  | +	sumDiff := make([]int, len(largeCoeff))
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				|  |  | +	lenDiff := len(largeCoeff) - len(smallCoeff)
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				|  |  | +	copy(sumDiff, largeCoeff[:lenDiff])
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				|  |  | +	for i := lenDiff; i < len(largeCoeff); i++ {
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				|  |  | +		sumDiff[i] = int(gp.gf.AddOrSub(int(smallCoeff[i-lenDiff]), int(largeCoeff[i])))
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				|  |  | +	}
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				|  |  | +	return NewGFPoly(gp.gf, sumDiff)
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				|  |  | +}
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				|  |  | +
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				|  |  | +func (gp *GFPoly) MultByMonominal(degree int, coeff int) *GFPoly {
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				|  |  | +	if coeff == 0 {
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				|  |  | +		return gp.gf.Zero()
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				|  |  | +	}
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				|  |  | +	size := len(gp.Coefficients)
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				|  |  | +	result := make([]int, size+degree)
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				|  |  | +	for i := 0; i < size; i++ {
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				|  |  | +		result[i] = int(gp.gf.Multiply(int(gp.Coefficients[i]), int(coeff)))
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				|  |  | +	}
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				|  |  | +	return NewGFPoly(gp.gf, result)
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				|  |  | +}
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				|  |  | +
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				|  |  | +func (gp *GFPoly) Multiply(other *GFPoly) *GFPoly {
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				|  |  | +	if gp.Zero() || other.Zero() {
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				|  |  | +		return gp.gf.Zero()
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				|  |  | +	}
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				|  |  | +	aCoeff := gp.Coefficients
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				|  |  | +	aLen := len(aCoeff)
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				|  |  | +	bCoeff := other.Coefficients
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				|  |  | +	bLen := len(bCoeff)
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				|  |  | +	product := make([]int, aLen+bLen-1)
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				|  |  | +	for i := 0; i < aLen; i++ {
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				|  |  | +		ac := int(aCoeff[i])
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				|  |  | +		for j := 0; j < bLen; j++ {
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				|  |  | +			bc := int(bCoeff[j])
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				|  |  | +			product[i+j] = int(gp.gf.AddOrSub(int(product[i+j]), gp.gf.Multiply(ac, bc)))
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				|  |  | +		}
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				|  |  | +	}
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				|  |  | +	return NewGFPoly(gp.gf, product)
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				|  |  | +}
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				|  |  | +
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				|  |  | +func (gp *GFPoly) Divide(other *GFPoly) (quotient *GFPoly, remainder *GFPoly) {
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				|  |  | +	quotient = gp.gf.Zero()
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				|  |  | +	remainder = gp
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				|  |  | +	fld := gp.gf
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				|  |  | +	denomLeadTerm := other.GetCoefficient(other.Degree())
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				|  |  | +	inversDenomLeadTerm := fld.Invers(int(denomLeadTerm))
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				|  |  | +	for remainder.Degree() >= other.Degree() && !remainder.Zero() {
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				|  |  | +		degreeDiff := remainder.Degree() - other.Degree()
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				|  |  | +		scale := int(fld.Multiply(int(remainder.GetCoefficient(remainder.Degree())), inversDenomLeadTerm))
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				|  |  | +		term := other.MultByMonominal(degreeDiff, scale)
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				|  |  | +		itQuot := NewMonominalPoly(fld, degreeDiff, scale)
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				|  |  | +		quotient = quotient.AddOrSubstract(itQuot)
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				|  |  | +		remainder = remainder.AddOrSubstract(term)
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				|  |  | +	}
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				|  |  | +	return
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				|  |  | +}
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				|  |  | +
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				|  |  | +func NewMonominalPoly(field *GaloisField, degree int, coeff int) *GFPoly {
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				|  |  | +	if coeff == 0 {
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				|  |  | +		return field.Zero()
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				|  |  | +	}
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				|  |  | +	result := make([]int, degree+1)
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				|  |  | +	result[0] = coeff
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				|  |  | +	return NewGFPoly(field, result)
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				|  |  | +}
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				|  |  | +
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				|  |  | +func NewGFPoly(field *GaloisField, coefficients []int) *GFPoly {
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				|  |  | +	for len(coefficients) > 1 && coefficients[0] == 0 {
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				|  |  | +		coefficients = coefficients[1:]
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				|  |  | +	}
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				|  |  | +	return &GFPoly{field, coefficients}
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				|  |  | +}
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