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DenseUnivariateRationalPolynomial Class Reference
The concrete class DenseUnivariateRationalPolynomial inherits from BPASUnivariatePolynomial and implements a univariate polynomial ring over the rational numbers with a dense representation. It overrides all the public member functions of BPASRing, BPASPolynomial and BPASUnivariatePolynomial. One can construct a DenseUnivariateRationalPolynomial object either by initializing a zero polynomial with or without its size, or from another DenseUnivariateRationalPolynomial object. Further, it supports some in-place operations, like integrate, reciprocal, homothetic, scaleTransform and taylorShift. One can also compute a bound for the positive real roots, isolate the real roots and refine the isolation interval of a given real root.
Inheritance diagram for DenseUnivariateRationalPolynomial:
BPASUnivariatePolynomial BPASPolynomial BPASRing

Public Member Functions

 DenseUnivariateRationalPolynomial ()
 
 DenseUnivariateRationalPolynomial (int s)
 
 DenseUnivariateRationalPolynomial (Integer e)
 
 DenseUnivariateRationalPolynomial (RationalNumber e)
 
 DenseUnivariateRationalPolynomial (const DenseUnivariateRationalPolynomial &b)
 
 ~DenseUnivariateRationalPolynomial ()
 
int degree ()
 
mpq_class leadingCoefficient ()
 
mpq_class * coefficients (int k=0)
 
mpq_class coefficient (int k)
 
void setCoefficient (int k, mpq_class value)
 
void setCoefficient (int k, RationalNumber value)
 
void setCoefficient (int k, double value)
 
std::string variable ()
 
void setVariableName (std::string x)
 
DenseUnivariateRationalPolynomialoperator= (DenseUnivariateRationalPolynomial b)
 
bool operator!= (DenseUnivariateRationalPolynomial &b)
 
bool operator== (DenseUnivariateRationalPolynomial &b)
 
bool isZero ()
 
void zero ()
 
bool isOne ()
 
void one ()
 
bool isNegativeOne ()
 
void negativeOne ()
 
int isConstant ()
 
int content ()
 
DenseUnivariateRationalPolynomial operator^ (int e)
 
DenseUnivariateRationalPolynomialoperator^= (int e)
 
DenseUnivariateRationalPolynomial operator<< (int k)
 
DenseUnivariateRationalPolynomialoperator<<= (int k)
 
DenseUnivariateRationalPolynomial operator>> (int k)
 
DenseUnivariateRationalPolynomialoperator>>= (int k)
 
DenseUnivariateRationalPolynomial operator+ (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomialoperator+= (DenseUnivariateRationalPolynomial b)
 
void add (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomial operator+ (RationalNumber c)
 
DenseUnivariateRationalPolynomial operator+ (mpq_class c)
 
DenseUnivariateRationalPolynomialoperator+= (RationalNumber c)
 
DenseUnivariateRationalPolynomialoperator+= (mpq_class c)
 
DenseUnivariateRationalPolynomial operator- (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomialoperator-= (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomial operator- ()
 
void subtract (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomial operator- (RationalNumber c)
 
DenseUnivariateRationalPolynomial operator- (mpq_class c)
 
DenseUnivariateRationalPolynomialoperator-= (RationalNumber c)
 
DenseUnivariateRationalPolynomialoperator-= (mpq_class c)
 
DenseUnivariateRationalPolynomial operator* (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomialoperator*= (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomial operator* (RationalNumber e)
 
DenseUnivariateRationalPolynomial operator* (mpq_class e)
 
DenseUnivariateRationalPolynomial operator* (sfixn e)
 
DenseUnivariateRationalPolynomialoperator*= (RationalNumber e)
 
DenseUnivariateRationalPolynomialoperator*= (mpq_class e)
 
DenseUnivariateRationalPolynomialoperator*= (sfixn e)
 
DenseUnivariateRationalPolynomial operator/ (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomialoperator/= (DenseUnivariateRationalPolynomial b)
 
DenseUnivariateRationalPolynomial operator/ (RationalNumber e)
 
DenseUnivariateRationalPolynomial operator/ (mpq_class e)
 
DenseUnivariateRationalPolynomialoperator/= (RationalNumber e)
 
DenseUnivariateRationalPolynomialoperator/= (mpq_class e)
 
DenseUnivariateRationalPolynomial monicDivide (DenseUnivariateRationalPolynomial &b)
 
DenseUnivariateRationalPolynomial monicDivide (DenseUnivariateRationalPolynomial &b, DenseUnivariateRationalPolynomial *rem)
 
DenseUnivariateRationalPolynomial lazyPseudoDivide (DenseUnivariateRationalPolynomial &b, mpq_class *c, mpq_class *d=NULL)
 
DenseUnivariateRationalPolynomial lazyPseudoDivide (DenseUnivariateRationalPolynomial &b, DenseUnivariateRationalPolynomial *rem, mpq_class *c, mpq_class *d)
 
DenseUnivariateRationalPolynomial pseudoDivide (DenseUnivariateRationalPolynomial &b, mpq_class *d=NULL)
 
DenseUnivariateRationalPolynomial pseudoDivide (DenseUnivariateRationalPolynomial &b, DenseUnivariateRationalPolynomial *rem, mpq_class *d)
 
DenseUnivariateRationalPolynomial halfExtendedEuclidean (DenseUnivariateRationalPolynomial b, DenseUnivariateRationalPolynomial *g)
 
void diophantinEquationSolve (DenseUnivariateRationalPolynomial a, DenseUnivariateRationalPolynomial b, DenseUnivariateRationalPolynomial *s, DenseUnivariateRationalPolynomial *t)
 
void differentiate (int k)
 
DenseUnivariateRationalPolynomial integrate ()
 
mpq_class evaluate (mpq_class x)
 
bool isTrailingCoefficientZero ()
 
DenseUnivariateRationalPolynomial gcd (DenseUnivariateRationalPolynomial q, int type=0)
 
std::vector
< DenseUnivariateRationalPolynomial
squareFree ()
 
bool divideByVariableIfCan ()
 
int numberOfSignChanges ()
 
void reciprocal ()
 
void homothetic (int k=1)
 
void scaleTransform (int k)
 
void negativeVariable ()
 
void negate ()
 
mpz_class rootBound ()
 
void taylorShift (int ts=-1)
 
Intervals positiveRealRootIsolate (mpq_class width, int ts=-1)
 
Intervals realRootIsolate (mpq_class width, int ts=-1)
 
void refineRoot (Interval *a, mpq_class width)
 
Intervals refineRoots (Intervals &a, mpq_class width)
 
- Public Member Functions inherited from BPASUnivariatePolynomial
BPASUnivariatePolynomialoperator+ (DataType)
 
BPASUnivariatePolynomialoperator+= (DataType)
 
BPASUnivariatePolynomialoperator- (DataType)
 
BPASUnivariatePolynomialoperator-= (DataType)
 
BPASUnivariatePolynomialoperator* (DataType)
 
BPASUnivariatePolynomialoperator*= (DataType)
 
BPASUnivariatePolynomialoperator/ (DataType)
 
BPASUnivariatePolynomialoperator/= (DataType)
 
BPASUnivariatePolynomialoperator<< (int)
 
BPASUnivariatePolynomialoperator<<= (int)
 
BPASUnivariatePolynomialoperator>> (int)
 
BPASUnivariatePolynomialoperator>>= (int)
 
BPASUnivariatePolynomialmonicDivide (BPASUnivariatePolynomial &)
 
BPASUnivariatePolynomialmonicDivide (BPASUnivariatePolynomial &, BPASUnivariatePolynomial *)
 
BPASUnivariatePolynomiallazyPseudoDivide (BPASUnivariatePolynomial &, DataType *, DataType *)
 
BPASUnivariatePolynomiallazyPseudoDivide (BPASUnivariatePolynomial &, BPASUnivariatePolynomial *, DataType *, DataType *)
 
BPASUnivariatePolynomialpseudoDivide (BPASUnivariatePolynomial &, DataType *)
 
BPASUnivariatePolynomialpseudoDivide (BPASUnivariatePolynomial &, BPASUnivariatePolynomial *, DataType *)
 
DataType content ()
 
BPASUnivariatePolynomialgcd (BPASUnivariatePolynomial &)
 
std::vector
< BPASUnivariatePolynomial & > 
squareFree ()
 
DataType leadingCoefficient ()
 
DataType coefficient (int)
 
void setCoefficient (int, DataType)
 
DataType evaluate (DataType)
 
- Public Member Functions inherited from BPASPolynomial
BPASPolynomialoperator= (BPASPolynomial &)
 
BPASPolynomialoperator+ (BPASPolynomial &)
 
BPASPolynomialoperator+= (BPASPolynomial &)
 
BPASPolynomialoperator- (BPASPolynomial &)
 
BPASPolynomialoperator- ()
 
BPASPolynomialoperator-= (BPASPolynomial &)
 
BPASPolynomialoperator* (BPASPolynomial &)
 
BPASPolynomialoperator*= (BPASPolynomial &)
 
BPASPolynomialoperator/ (BPASPolynomial &)
 
BPASPolynomialoperator/= (BPASPolynomial &)
 
BPASPolynomialoperator^ (int)
 
bool operator== (BPASPolynomial &)
 
bool operator!= (BPASPolynomial &)
 

Static Public Attributes

static int characteristic
 
static bool isPrimeField
 
static bool isComplexField
 
- Static Public Attributes inherited from BPASRing
static int characteristic
 
static bool isPrimeField
 
static bool isComplexField
 

Friends

DenseUnivariateRationalPolynomial operator+ (mpq_class c, DenseUnivariateRationalPolynomial p)
 
DenseUnivariateRationalPolynomial operator- (mpq_class c, DenseUnivariateRationalPolynomial p)
 
DenseUnivariateRationalPolynomial operator* (mpq_class c, DenseUnivariateRationalPolynomial p)
 
DenseUnivariateRationalPolynomial operator* (sfixn c, DenseUnivariateRationalPolynomial p)
 
DenseUnivariateRationalPolynomial operator/ (mpq_class c, DenseUnivariateRationalPolynomial p)
 
std::ostream & operator<< (std::ostream &out, DenseUnivariateRationalPolynomial b)
 

Constructor & Destructor Documentation

DenseUnivariateRationalPolynomial::DenseUnivariateRationalPolynomial ( )
inline

Construct a polynomial

Parameters
d
DenseUnivariateRationalPolynomial::DenseUnivariateRationalPolynomial ( int  s)
inline

Construct a polynomial with degree

Parameters
d,:Size of the polynomial
DenseUnivariateRationalPolynomial::DenseUnivariateRationalPolynomial ( Integer  e)
inline

Construct a polynomial with a coefficient

Parameters
e,:The coefficient
DenseUnivariateRationalPolynomial::DenseUnivariateRationalPolynomial ( const DenseUnivariateRationalPolynomial b)
inline

Copy constructor

Parameters
b,:A densed univariate rationl polynomial
DenseUnivariateRationalPolynomial::~DenseUnivariateRationalPolynomial ( )
inline

Destroy the polynomial

Parameters

Member Function Documentation

void DenseUnivariateRationalPolynomial::add ( DenseUnivariateRationalPolynomial  b)

Add another polynomial to itself

Parameters
b,:A univariate rational polynomial
mpq_class DenseUnivariateRationalPolynomial::coefficient ( int  k)
inline

Get a coefficient of the polynomial

Parameters
k,:Offset
mpq_class* DenseUnivariateRationalPolynomial::coefficients ( int  k = 0)
inline

Get coefficients of the polynomial, given start offset

Parameters
k,:Offset
int DenseUnivariateRationalPolynomial::content ( )
inline

Content of the polynomial

Parameters
int DenseUnivariateRationalPolynomial::degree ( )
inlinevirtual

Get degree of the polynomial

Parameters

Implements BPASUnivariatePolynomial.

void DenseUnivariateRationalPolynomial::differentiate ( int  k)
virtual

Compute k-th differentiate

Parameters
k,:k-th differentiate, k > 0

Implements BPASUnivariatePolynomial.

void DenseUnivariateRationalPolynomial::diophantinEquationSolve ( DenseUnivariateRationalPolynomial  a,
DenseUnivariateRationalPolynomial  b,
DenseUnivariateRationalPolynomial s,
DenseUnivariateRationalPolynomial t 
)

s*a + t*b = c, where c in the ideal (a,b)

Parameters
a,:A univariate polynomial b: A univariate polynomial
s,:Either s = 0 or degree(s) < degree(b)
t
bool DenseUnivariateRationalPolynomial::divideByVariableIfCan ( )

Divide by variable if it is zero

Parameters
mpq_class DenseUnivariateRationalPolynomial::evaluate ( mpq_class  x)

Evaluate f(x)

Parameters
x,:Evaluation point
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::gcd ( DenseUnivariateRationalPolynomial  q,
int  type = 0 
)

GCD(p, q)

Parameters
q,:The other polynomial
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::halfExtendedEuclidean ( DenseUnivariateRationalPolynomial  b,
DenseUnivariateRationalPolynomial g 
)

s * a g (mod b), where g = gcd(a, b)

Parameters
b,:A univariate polynomial
g,:The GCD of a and b
void DenseUnivariateRationalPolynomial::homothetic ( int  k = 1)

Homothetic operation

Parameters
k> 0: 2^(k*d) * f(2^(-k)*x);
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::integrate ( )

Compute the integral with constant of integration 0

Parameters
int DenseUnivariateRationalPolynomial::isConstant ( )
inlinevirtual

Is a constant

Parameters

Implements BPASRing.

bool DenseUnivariateRationalPolynomial::isNegativeOne ( )
inlinevirtual

Is polynomial a constatn -1

Parameters

Implements BPASRing.

bool DenseUnivariateRationalPolynomial::isOne ( )
inlinevirtual

Is polynomial a constatn 1

Parameters

Implements BPASRing.

bool DenseUnivariateRationalPolynomial::isTrailingCoefficientZero ( )
virtual

Is the least signficant coefficient zero

Parameters

Implements BPASUnivariatePolynomial.

bool DenseUnivariateRationalPolynomial::isZero ( )
inlinevirtual

Is zero polynomial

Parameters

Implements BPASRing.

DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::lazyPseudoDivide ( DenseUnivariateRationalPolynomial b,
mpq_class *  c,
mpq_class *  d = NULL 
)

Lazy pseudo dividsion Return the quotient and itself becomes remainder e is the exact number of division steps

Parameters
b,:The dividend polynomial
c,:The leading coefficient of b to the power e
d,:That to the power deg(a) - deg(b) + 1 - e
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::lazyPseudoDivide ( DenseUnivariateRationalPolynomial b,
DenseUnivariateRationalPolynomial rem,
mpq_class *  c,
mpq_class *  d 
)

Lazy pseudo dividsion Return the quotient e is the exact number of division steps

Parameters
b,:The divident polynomial
rem,:The remainder polynomial
c,:The leading coefficient of b to the power e
d,:That to the power deg(a) - deg(b) + 1 - e
mpq_class DenseUnivariateRationalPolynomial::leadingCoefficient ( )
inline

Get the leading coefficient

Parameters
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::monicDivide ( DenseUnivariateRationalPolynomial b)

Monic division Return quotient and itself become the remainder

Parameters
b,:The dividend polynomial
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::monicDivide ( DenseUnivariateRationalPolynomial b,
DenseUnivariateRationalPolynomial rem 
)

Monic division Return quotient

Parameters
b,:The dividend polynomial
rem,:The remainder polynomial
void DenseUnivariateRationalPolynomial::negate ( )

Compute -f(x)

@param
void DenseUnivariateRationalPolynomial::negativeOne ( )
inlinevirtual

Set polynomial to -1

Parameters

Implements BPASRing.

void DenseUnivariateRationalPolynomial::negativeVariable ( )

Compute f(-x)

Parameters
int DenseUnivariateRationalPolynomial::numberOfSignChanges ( )

Number of coefficient sign variation

Parameters
void DenseUnivariateRationalPolynomial::one ( )
inlinevirtual

Set polynomial to 1

Parameters

Implements BPASRing.

bool DenseUnivariateRationalPolynomial::operator!= ( DenseUnivariateRationalPolynomial b)
inline

Overload operator !=

Parameters
b,:A univariate rational polynoial
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator* ( DenseUnivariateRationalPolynomial  b)

Multiply to another polynomial

Parameters
b,:A univariate rational polynomial
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator* ( RationalNumber  e)
inline

Overload operator *

Parameters
e,:A rational number
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator*= ( DenseUnivariateRationalPolynomial  b)
inline

Overload operator *=

Parameters
b,:A univariate rational polynomial
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator*= ( RationalNumber  e)

Overload operator *=

Parameters
e,:A rational number
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator*= ( sfixn  e)

Overload operator *=

Parameters
e,:A constant
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator+ ( DenseUnivariateRationalPolynomial  b)

Overload operator +

Parameters
b,:A univariate rational polynomial
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator+ ( RationalNumber  c)
inline

Overload Operator +

Parameters
c,:A rational number
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator+= ( DenseUnivariateRationalPolynomial  b)
inline

Overload Operator +=

Parameters
b,:A univariate rational polynomial
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator+= ( RationalNumber  c)
inline

Overload Operator +=

Parameters
c,:A rational number
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator- ( DenseUnivariateRationalPolynomial  b)

Subtract another polynomial

Parameters
b,:A univariate rational polynomial
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator- ( )

Overload operator -, negate

Parameters
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator- ( RationalNumber  c)
inline

Overload operator -

Parameters
c,:A rational number
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator-= ( DenseUnivariateRationalPolynomial  b)
inline

Overload operator -=

Parameters
b,:A univariate rational polynomial
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator-= ( RationalNumber  c)
inline

Overload operator -=

Parameters
c,:A rational number
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator/ ( DenseUnivariateRationalPolynomial  b)
inline

Overload operator / ExactDivision

Parameters
b,:A univariate rational polynomial
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator/ ( RationalNumber  e)
inline

Overload operator /

Parameters
e,:A rational number
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator/= ( DenseUnivariateRationalPolynomial  b)

Overload operator /= ExactDivision

Parameters
b,:A univariate rational polynomial
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator/= ( RationalNumber  e)

Overload operator /=

Parameters
e,:A rational number
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator<< ( int  k)

Overload operator << replace by muplitying x^k

Parameters
k,:The exponent of variable, k > 0
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator<<= ( int  k)
inline

Overload operator <<= replace by muplitying x^k

Parameters
k,:The exponent of variable, k > 0
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator= ( DenseUnivariateRationalPolynomial  b)
inline

Overload operator =

Parameters
b,:A univariate rational polynoial
bool DenseUnivariateRationalPolynomial::operator== ( DenseUnivariateRationalPolynomial b)
inline

Overload operator ==

Parameters
b,:A univariate rational polynoial
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator>> ( int  k)

Overload operator >> replace by dividing x^k, and return the quotient

Parameters
k,:The exponent of variable, k > 0
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator>>= ( int  k)
inline

Overload operator >>= replace by dividing x^k, and return the quotient

Parameters
k,:The exponent of variable, k > 0
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::operator^ ( int  e)

Overload operator ^ replace xor operation by exponentiation

Parameters
e,:The exponentiation, e > 0
DenseUnivariateRationalPolynomial& DenseUnivariateRationalPolynomial::operator^= ( int  e)
inline

Overload operator ^= replace xor operation by exponentiation

Parameters
e,:The exponentiation, e > 0
Intervals DenseUnivariateRationalPolynomial::positiveRealRootIsolate ( mpq_class  width,
int  ts = -1 
)
inline

Positive real root isolation for square-free polynomials

Parameters
width,:Interval's right - left < width : Taylor Shift option: 0 - CMY; -1 - optimized
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::pseudoDivide ( DenseUnivariateRationalPolynomial b,
mpq_class *  d = NULL 
)

Pseudo dividsion Return the quotient and itself becomes remainder

Parameters
b,:The divident polynomial
d,:The leading coefficient of b to the power deg(a) - deg(b) + 1
DenseUnivariateRationalPolynomial DenseUnivariateRationalPolynomial::pseudoDivide ( DenseUnivariateRationalPolynomial b,
DenseUnivariateRationalPolynomial rem,
mpq_class *  d 
)

Pseudo dividsion Return the quotient

Parameters
b,:The divident polynomial
rem,:The remainder polynomial
d,:The leading coefficient of b to the power deg(a) - deg(b) + 1
Intervals DenseUnivariateRationalPolynomial::realRootIsolate ( mpq_class  width,
int  ts = -1 
)
inline

Real root isolation for square-free polynomials

Parameters
width,:Interval's right - left < width : Taylor Shift option: 0 - CMY; -1 - optimized
void DenseUnivariateRationalPolynomial::reciprocal ( )

Revert coefficients

Parameters
void DenseUnivariateRationalPolynomial::refineRoot ( Interval a,
mpq_class  width 
)
inline

Refine a root

Parameters
a,:The root
width,:Interval's right - left < width
Intervals DenseUnivariateRationalPolynomial::refineRoots ( Intervals a,
mpq_class  width 
)
inline

Refine the roots

a: The roots

Parameters
width,:Interval's right - left < width
mpz_class DenseUnivariateRationalPolynomial::rootBound ( )

Return an integer k such that any positive root alpha of the polynomial satisfies alpha < 2^k

Parameters
void DenseUnivariateRationalPolynomial::scaleTransform ( int  k)

Scale transform operation

Parameters
k> 0: f(2^k*x)
void DenseUnivariateRationalPolynomial::setCoefficient ( int  k,
mpq_class  value 
)
inline

Set a coefficient of the polynomial

Parameters
k,:Offset
val,:Coefficient
void DenseUnivariateRationalPolynomial::setVariableName ( std::string  x)
inlinevirtual

Set variable's name

Parameters
x,:Varable's name

Implements BPASUnivariatePolynomial.

std::vector<DenseUnivariateRationalPolynomial> DenseUnivariateRationalPolynomial::squareFree ( )

Square free

Parameters
void DenseUnivariateRationalPolynomial::subtract ( DenseUnivariateRationalPolynomial  b)

Subtract another polynomial from itself

Parameters
b,:A univariate rational polynomial
void DenseUnivariateRationalPolynomial::taylorShift ( int  ts = -1)

Taylor Shift operation by 1

Parameters
ts,:Algorithm id
std::string DenseUnivariateRationalPolynomial::variable ( )
inlinevirtual

Get variable's name

Parameters

Implements BPASUnivariatePolynomial.

void DenseUnivariateRationalPolynomial::zero ( )
inlinevirtual

Zero polynomial

Parameters

Implements BPASRing.

Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream &  out,
DenseUnivariateRationalPolynomial  b 
)
friend

Overload stream operator <<

Parameters
out,:Stream object
b,:A univariate rational polynoial

The documentation for this class was generated from the following file: