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# RealRoots : Index

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

- budanFourierBound -- a bound for the number of real roots with multiplicity of a univariate polynomial with rational coefficients
- budanFourierBound(RingElement) -- a bound for the number of real roots with multiplicity of a univariate polynomial with rational coefficients
- budanFourierBound(RingElement,QQ,QQ) -- a bound for the number of real roots with multiplicity of a univariate polynomial with rational coefficients
- characteristicPolynomial -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
- characteristicPolynomial(...,Variable=>...) -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
- characteristicPolynomial(Matrix) -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
- characteristicPolynomial(RingElement) -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
- characteristicPolynomial(RingElement,Ideal) -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial
- hurwitzMatrix -- the principal submatrix of the Hurwitz matrix of a univariate polynomial
- hurwitzMatrix(RingElement) -- the principal submatrix of the Hurwitz matrix of a univariate polynomial
- hurwitzMatrix(RingElement,ZZ) -- the principal submatrix of the Hurwitz matrix of a univariate polynomial
- isHurwitzStable -- determines if a univariate polynomial with rational coefficients is Hurwitz-stable
- isHurwitzStable(RingElement) -- determines if a univariate polynomial with rational coefficients is Hurwitz-stable
- minimalPolynomial -- the minimal polynomial of an element of an Artinian ring
- minimalPolynomial(...,Strategy=>...) -- the minimal polynomial of an element of an Artinian ring
- minimalPolynomial(...,Variable=>...) -- the minimal polynomial of an element of an Artinian ring
- minimalPolynomial(RingElement) -- the minimal polynomial of an element of an Artinian ring
- minimalPolynomial(RingElement,Ideal) -- the minimal polynomial of an element of an Artinian ring
- Multiplicity
- Multiplicity(RealRoots)
- rationalUnivariateRepresentation -- the rational univariate representation of a zero-dimensional ideal in a polynomial ring
- rationalUnivariateRepresentation(Ideal) -- the rational univariate representation of a zero-dimensional ideal in a polynomial ring
- rationalUnivariateRepresentation(QuotientRing) -- the rational univariate representation of a zero-dimensional ideal in a polynomial ring
- realCount -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
- realCount(Ideal) -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
- realCount(List) -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
- realCount(QuotientRing) -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
- realCount(RingElement) -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)
- realRootIsolation -- a list that isolates the real roots of a univariate polynomial with rational coefficients
- realRootIsolation(RingElement,QQ) -- a list that isolates the real roots of a univariate polynomial with rational coefficients
- RealRoots -- Package for exploring, counting and locating real solutions to polynomial systems
- regularRepresentation -- the regular representation of an element of an Artinian ring
- regularRepresentation(RingElement) -- the regular representation of an element of an Artinian ring
- regularRepresentation(RingElement,Ideal) -- the regular representation of an element of an Artinian ring
- signature -- the signature of a symmetric matrix with rational entries
- signature(Matrix) -- the signature of a symmetric matrix with rational entries
- sturmCount -- the number of real roots of a univariate polynomial with rational coefficients
- sturmCount(...,Multiplicity=>...)
- sturmCount(RingElement) -- the number of real roots of a univariate polynomial with rational coefficients
- sturmCount(RingElement,QQ,QQ) -- the number of real roots of a univariate polynomial with rational coefficients
- sturmSequence -- the Sturm sequence of a univariate polynomial with rational coefficients
- sturmSequence(RingElement) -- the Sturm sequence of a univariate polynomial with rational coefficients
- sylvesterCount -- a signed count of the real roots of a univariate polynomial with rational coefficients
- sylvesterCount(...,Multiplicity=>...)
- sylvesterCount(RingElement,RingElement) -- a signed count of the real roots of a univariate polynomial with rational coefficients
- sylvesterCount(RingElement,RingElement,QQ,QQ) -- a signed count of the real roots of a univariate polynomial with rational coefficients
- sylvesterSequence -- the Sylvester sequence of two univariate polynomials with rational coefficients
- sylvesterSequence(RingElement,RingElement) -- the Sylvester sequence of two univariate polynomials with rational coefficients
- traceCount -- the degree of the reduced scheme of an Artinian ring
- traceCount(Ideal) -- the degree of the reduced scheme of an Artinian ring
- traceCount(List) -- the degree of the reduced scheme of an Artinian ring
- traceCount(QuotientRing) -- the degree of the reduced scheme of an Artinian ring
- traceCount(RingElement) -- the degree of the reduced scheme of an Artinian ring
- traceForm -- the trace symmetric form of a polynomial in an Artinian ring
- traceForm(RingElement) -- the trace symmetric form of a polynomial in an Artinian ring
- traceForm(RingElement,Ideal) -- the trace symmetric form of a polynomial in an Artinian ring
- univariateEliminant -- the univariate eliminant of an element of an Artinian ring
- univariateEliminant(...,Strategy=>...) -- the univariate eliminant of an element of an Artinian ring
- univariateEliminant(...,Variable=>...) -- the univariate eliminant of an element of an Artinian ring
- univariateEliminant(RingElement,Ideal) -- the univariate eliminant of an element of an Artinian ring
- variations -- the number of sign changes of an ordered list of numbers
- variations(List) -- the number of sign changes of an ordered list of numbers