RealRoots : Index
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BudanFourierBound -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,InfiniteNumber,InfiniteNumber) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,InfiniteNumber,QQ) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,InfiniteNumber,RR) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,InfiniteNumber,ZZ) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,QQ,InfiniteNumber) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,QQ,QQ) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,QQ,RR) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,QQ,ZZ) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,RR,InfiniteNumber) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,RR,QQ) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,RR,RR) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,RR,ZZ) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,ZZ,InfiniteNumber) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,ZZ,QQ) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,ZZ,RR) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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BudanFourierBound(RingElement,ZZ,ZZ) -- a bound for the number of real roots of a univariate polynomial with rational coefficients
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characteristicPolynomial -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
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characteristicPolynomial(...,Variable=>...) -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
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characteristicPolynomial(Matrix) -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
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characteristicPolynomial(RingElement) -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
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characteristicPolynomial(RingElement,Ideal) -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
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HurwitzMatrix -- a specified principle submatrix of the Hurwitz matrix of a univariate polynomial
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HurwitzMatrix(RingElement) -- a specified principle submatrix of the Hurwitz matrix of a univariate polynomial
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HurwitzMatrix(RingElement,ZZ) -- a specified principle submatrix of the Hurwitz matrix of a univariate polynomial
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isHurwitzStable -- determines whether or not a rational univariate polynomial is Hurwitz stable
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isHurwitzStable(RingElement) -- determines whether or not a rational univariate polynomial is Hurwitz stable
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minimalPolynomial -- the minimal polynomial of an element of an Artinian ring
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minimalPolynomial(...,Strategy=>...) -- the minimal polynomial of an element of an Artinian ring
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minimalPolynomial(RingElement) -- the minimal polynomial of an element of an Artinian ring
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minimalPolynomial(RingElement,Ideal) -- the minimal polynomial of an element of an Artinian ring
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Multiplicity
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Multiplicity(RealRoots)
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rationalUnivariateRepresentation -- the rational univariate representation of a zero-dimensional ideal
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rationalUnivariateRepresentation(Ideal) -- the rational univariate representation of a zero-dimensional ideal
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realRootIsolation -- a list that isolates the real roots of a rational univariate polynomial
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realRootIsolation(RingElement,QQ) -- a list that isolates the real roots of a rational univariate polynomial
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realRootIsolation(RingElement,RR) -- a list that isolates the real roots of a rational univariate polynomial
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realRootIsolation(RingElement,ZZ) -- a list that isolates the real roots of a rational univariate polynomial
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RealRoots -- Package for exploring, counting and locating real solutions to polynomial systems
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regularRepresentation -- the regular representation of a rational polynomial
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regularRepresentation(RingElement) -- the regular representation of a rational polynomial
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regularRepresentation(RingElement,Ideal) -- the regular representation of a rational polynomial
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SturmCount -- the number of real roots of a rational univariate polynomial
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SturmCount(...,Multiplicity=>...)
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SturmCount(RingElement) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,InfiniteNumber,InfiniteNumber) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,InfiniteNumber,QQ) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,InfiniteNumber,RR) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,InfiniteNumber,ZZ) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,QQ,InfiniteNumber) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,QQ,QQ) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,QQ,RR) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,QQ,ZZ) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,RR,InfiniteNumber) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,RR,QQ) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,RR,RR) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,RR,ZZ) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,ZZ,InfiniteNumber) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,ZZ,QQ) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,ZZ,RR) -- the number of real roots of a rational univariate polynomial
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SturmCount(RingElement,ZZ,ZZ) -- the number of real roots of a rational univariate polynomial
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SturmSequence -- the Sturm sequence of a rational univariate polynomial
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SturmSequence(RingElement) -- the Sturm sequence of a rational univariate polynomial
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SylvesterCount -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(...,Multiplicity=>...)
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SylvesterCount(RingElement,RingElement) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,InfiniteNumber,InfiniteNumber) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,InfiniteNumber,QQ) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,InfiniteNumber,RR) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,InfiniteNumber,ZZ) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,QQ,InfiniteNumber) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,QQ,QQ) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,QQ,RR) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,QQ,ZZ) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,RR,InfiniteNumber) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,RR,QQ) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,RR,RR) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,RR,ZZ) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,ZZ,InfiniteNumber) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,ZZ,QQ) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,ZZ,RR) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterCount(RingElement,RingElement,ZZ,ZZ) -- the difference in variations of the Sylvester sequence of two rational univariate polynomials
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SylvesterSequence -- the Sylvester sequence of two rational univariate polynomials
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SylvesterSequence(RingElement,RingElement) -- the Sylvester sequence of two rational univariate polynomials
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traceCount -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
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traceCount(Ideal) -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
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traceCount(List) -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
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traceCount(QuotientRing) -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
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traceCount(RingElement) -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
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traceForm -- the trace quadratic form of a rational polynomial in an Artinian ring
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traceForm(RingElement) -- the trace quadratic form of a rational polynomial in an Artinian ring
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traceForm(RingElement,Ideal) -- the trace quadratic form of a rational polynomial in an Artinian ring
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univariateEliminant -- the univariate eliminant of an element of an Artinian ring
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univariateEliminant(...,Strategy=>...) -- the univariate eliminant of an element of an Artinian ring
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univariateEliminant(RingElement) -- the univariate eliminant of an element of an Artinian ring
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univariateEliminant(RingElement,Ideal) -- the univariate eliminant of an element of an Artinian ring
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variations -- the number of sign changes of an ordered list of numbers
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variations(List) -- the number of sign changes of an ordered list of numbers