Package maths

Class PolyBasic

  • Direct Known Subclasses:
    GeoPoly
    public class PolyBasic
extends java.lang.Object
    This class provides basic polynomial operations.

    • Constructor Summary

      Constructors 
      Constructor Description
      PolyBasic()  

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      TMono b_reduce​(TMono m1, java.util.Vector vlist)
      Reduces the polynomial by dividing it by the leading term of another polynomial.
      java.util.Vector bb_reduce​(java.util.Vector vlist, long t)
      Reduces the polynomial by dividing it by the leading term of another polynomial.
      java.util.Vector bb_reduce​(java.util.Vector vlist, long t, boolean s)
      Reduces the polynomial by dividing it by the leading term of another polynomial.
      double[] calculate_oncr​(TMono mm, Param[] p, int dx, int dy)
      Calculates the values of the polynomial `mm` given the parameters `p` for two variables.
      double[] calculate_online​(TMono mm, Param[] p, int dx, int dy)
      Calculates the values of the polynomial `mm` given the parameters `p` for two variables.
      double[] calculv​(TMono mm, Param[] p)
      Calculates the values of the polynomial `mm` given the parameters `p`.
      double[] calculv_2v​(TMono mm, Param[] p)
      Calculates the values of the polynomial `mm` given the parameters `p` for two variables.
      double[] calculv2poly​(TMono mm1, TMono mm2, Param[] p)
      Calculates the values of two polynomials `mm1` and `mm2` given the parameters `p`.
      boolean check_zero​(TMono m)
      Checks if the given polynomial is zero.
      boolean ck_eq​(TMono m1, TMono m2)
      Checks if two monomials are equal.
      java.math.BigInteger coefgcd​(TMono p)
      Returns the greatest common divisor of the coefficients of the polynomial.
      TMono cp_times​(long c, TMono p1)
      Multiplies a polynomial by a constant.
      boolean ctLessdx​(TMono m, int dx)
      Checks if the polynomial is less than a given value.
      boolean ctLessdx1​(TMono m, int dx)
      Checks if the polynomial is less than a given value.
      int deg​(TMono p)
      Returns the degree of the given polynomial.
      int deg​(TMono p, int x)
      Returns the degree of the given polynomial `p` with respect to the variable `x`.
      void div_factor1​(TMono m, int x, int n)
      Divides the degree of the polynomial `m` by `n` for the variable `x`.
      void eraseCommonDono​(java.util.Vector v)
      Erases common Dono objects from the given vector of polynomials.
      TMono factor_remove​(TMono p1, TMono p2)
      Removes the common factors of the polynomial `p1` using the polynomial `p2`.
      void factor1​(TMono m1)
      Factors the polynomial `m1` by dividing it by its common factors.
      java.util.Vector g_basis​(java.util.Vector v)
      Computes the Groebner basis for the given vector of polynomials.
      boolean gb_finished​(java.util.Vector v)
      Checks if the polynomial is finished.
      TMono get_factor1​(TMono m)
      Gets the common factors of the polynomial `m`.
      java.lang.String getAllPrinted​(TMono p)
      Returns a string representation of all printed monomials in the polynomial.
      java.lang.String getAllPrinted​(TMono p, boolean b)
      Returns a string representation of all printed monomials in the polynomial.
      java.util.Vector getcnds​(java.util.Vector v, int dx)
      Gets the conditions for the given vector of polynomials.
      TDono getDo​(java.util.Vector v, int n)
      Gets the Dono object from the given vector of polynomials.
      java.lang.String getExpandedPrint​(TMono p)
      Returns a string representation of the polynomial with expanded format.
      static PolyBasic getInstance()
      Returns the singleton instance of the PolyBasic class.
      int getMaxX​(java.util.Vector v)
      Gets the maximum value of x in a vector of polynomials.
      TMono getxm1​(int x, int d, TMono m)
      Gets the leading coefficient of a polynomial.
      TMono ll_delta​(int x, TMono m1, TMono m2)
      Computes the delta of two polynomials.
      int lv​(TMono p)
      Returns the leading variable of the given polynomial.
      void ndg_reduce​(java.util.Vector v)
      Reduces the polynomial by removing terms with degree 0.
      TMono p_copy​(TMono p)
      Creates a copy of the polynomial `p`.
      TMono padd​(TMono p1, TMono p2)
      Adds two polynomials.
      java.util.Vector parseCommonDono​(java.util.Vector v, int dx)
      Parses common Dono objects from the given vector of polynomials.
      TMono pcopy​(TMono p)
      Creates a copy of the given polynomial.
      TMono pctimes​(TMono p, long c)
      Multiplies a polynomial by a constant.
      TMono pdif​(TMono p1, TMono p2)
      Subtracts the second polynomial from the first polynomial.
      int plength​(TMono m)
      Returns the length of the given polynomial.
      void ppush​(TMono m, java.util.Vector v)
      Pushes a polynomial into a sorted vector.
      TPoly ppush​(TMono t, TPoly pp)
      Pushes a polynomial into a sorted linked list.
      TMono prem​(TMono p1, TMono p2)
      Computes the pseudo-remainder of two polynomials.
      void print​(TMono p)
      Prints the given polynomial.
      java.lang.String printHead​(TMono m)
      Returns the head of the polynomial as a string.
      java.lang.String printMaxstrPoly​(TMono m)
      Returns a string representation of the polynomial with a maximum length.
      java.lang.String printNPoly​(TMono m)
      Returns a string representation of the polynomial with a maximum length.
      java.lang.String printNPoly​(TMono m1, TMono m2)
      Returns a string representation of two polynomials with a maximum length.
      void printpoly​(TMono m)
      Prints the given polynomial.
      java.lang.String printSPoly​(TMono m)
      Returns a simplified string representation of the polynomial.
      java.lang.String printSPoly​(TMono m, int n)
      Returns a simplified string representation of the polynomial with a specified maximum length.
      void printVpoly​(java.util.Vector v)
      Prints the given vector of polynomials.
      TMono pRtimes​(TMono p1, TMono p2)
      Multiplies two polynomials.
      TMono pth​(int x, int c, int d)
      Creates a new monomial with the specified variable, coefficient, and degree.
      TMono pth​(int x, java.math.BigInteger c, int d)
      Creates a new monomial with the specified variable, BigInteger coefficient, and degree.
      TMono ptimes​(TMono p1, TMono p2)
      Multiplies two polynomials.
      TMono pzero()
      Returns a zero polynomial.
      boolean pzerop​(TMono m)
      Checks if the given polynomial is zero.
      TMono reduce​(TMono m, Param[] p)
      Reduces the given polynomial `m` using the provided parameters `p`.
      TMono reduceMDono​(TMono mm, java.util.Vector v, int dx)
      Reduces the polynomial by dividing it by the leading term of another polynomial.
      java.util.Vector s_polys​(java.util.Vector vlist)
      Computes the S-polynomials for the given vector of polynomials.
      static void setbbStop​(boolean t)
      Sets the BB\_STOP flag.
      static void setRMCOEF​(boolean s)
      Sets the RM\_SCOEF flag.
      TMono simplify​(TMono m, Param[] p)
      Simplifies a polynomial to a lower degree without removing coefficients.
      TDono splitDono​(TMono m, int dx)
      Splits the given monomial into a Dono object.
      void sprint​(TMono p)
      Prints the polynomial in a simplified format.
      java.lang.String String_p_print​(TMono p, boolean ce, boolean first, boolean nn)
      Returns a string representation of the polynomial.
      void upValueDM​(java.util.Vector v, int dx)
      Updates the value of a polynomial by adding a given value to its coefficients.
      void upValueTM​(java.util.Vector v, int dx)
      Updates the value of a polynomial by adding a given value to its coefficients.
      void upValueTM​(TMono m, int dx)
      Updates the value of a polynomial by adding a given value to its coefficients.

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Constructor Detail

      • PolyBasic

        public PolyBasic()

    • Method Detail

      • getInstance

        public static PolyBasic getInstance()
        Returns the singleton instance of the PolyBasic class.
        Returns:
        the singleton instance of PolyBasic

      • setbbStop

        public static void setbbStop​(boolean t)
        Sets the BB\_STOP flag.
        Parameters:
        t - the new value for the BB\_STOP flag

      • setRMCOEF

        public static void setRMCOEF​(boolean s)
        Sets the RM\_SCOEF flag.
        Parameters:
        s - the new value for the RM\_SCOEF flag

      • cp_times

        public TMono cp_times​(long c,
                      TMono p1)
        Multiplies a polynomial by a constant.
        Parameters:
        c - the constant to multiply by
        p1 - the polynomial to be multiplied
        Returns:
        the resulting polynomial after multiplication

      • check_zero

        public boolean check_zero​(TMono m)
        Checks if the given polynomial is zero.
        Parameters:
        m - the polynomial to check
        Returns:
        true if the polynomial is zero, false otherwise

      • deg

        public int deg​(TMono p,
               int x)
        Returns the degree of the given polynomial `p` with respect to the variable `x`.
        Parameters:
        p - the polynomial to check
        x - the variable to check the degree against
        Returns:
        the degree of the polynomial with respect to `x`

      • reduce

        public TMono reduce​(TMono m,
                    Param[] p)
        Reduces the given polynomial `m` using the provided parameters `p`.
        Parameters:
        m - the polynomial to be reduced
        p - the array of parameters used for reduction
        Returns:
        the reduced polynomial

      • simplify

        public TMono simplify​(TMono m,
                      Param[] p)
        Simplifies a polynomial to a lower degree without removing coefficients.
        Parameters:
        m - the polynomial to simplify
        p - the array of parameters used for simplification
        Returns:
        the simplified polynomial

      • prem

        public TMono prem​(TMono p1,
                  TMono p2)
        Computes the pseudo-remainder of two polynomials.
        Parameters:
        p1 - the first polynomial
        p2 - the second polynomial
        Returns:
        the pseudo-remainder of the two polynomials

      • div_factor1

        public void div_factor1​(TMono m,
                        int x,
                        int n)
        Divides the degree of the polynomial `m` by `n` for the variable `x`.
        Parameters:
        m - the polynomial to be modified
        x - the variable whose degree is to be divided
        n - the divisor for the degree

      • factor1

        public void factor1​(TMono m1)
        Factors the polynomial `m1` by dividing it by its common factors.
        Parameters:
        m1 - the polynomial to be factored

      • get_factor1

        public TMono get_factor1​(TMono m)
        Gets the common factors of the polynomial `m`.
        Parameters:
        m - the polynomial to get factors from
        Returns:
        the common factors of the polynomial

      • factor_remove

        public TMono factor_remove​(TMono p1,
                           TMono p2)
        Removes the common factors of the polynomial `p1` using the polynomial `p2`.
        Parameters:
        p1 - the polynomial to be factored
        p2 - the polynomial used for factoring
        Returns:
        the factored polynomial

      • p_copy

        public TMono p_copy​(TMono p)
        Creates a copy of the polynomial `p`.
        Parameters:
        p - the polynomial to copy
        Returns:
        the copied polynomial

      • ppush

        public void ppush​(TMono m,
                  java.util.Vector v)
        Pushes a polynomial into a sorted vector.
        Parameters:
        m - the polynomial to push
        v - the vector to push into

      • print

        public void print​(TMono p)
        Prints the given polynomial.
        Parameters:
        p - the polynomial to print

      • sprint

        public void sprint​(TMono p)
        Prints the polynomial in a simplified format.
        Parameters:
        p - the polynomial to print

      • pth

        public TMono pth​(int x,
                 int c,
                 int d)
        Creates a new monomial with the specified variable, coefficient, and degree.
        Parameters:
        x - the variable of the monomial
        c - the coefficient of the monomial
        d - the degree of the monomial
        Returns:
        the created monomial

      • pth

        public TMono pth​(int x,
                 java.math.BigInteger c,
                 int d)
        Creates a new monomial with the specified variable, BigInteger coefficient, and degree.
        Parameters:
        x - the variable of the monomial
        c - the BigInteger coefficient of the monomial
        d - the degree of the monomial
        Returns:
        the created monomial

      • deg

        public int deg​(TMono p)
        Returns the degree of the given polynomial.
        Parameters:
        p - the polynomial
        Returns:
        the degree of the polynomial

      • lv

        public int lv​(TMono p)
        Returns the leading variable of the given polynomial.
        Parameters:
        p - the polynomial
        Returns:
        the leading variable of the polynomial

      • pzero

        public TMono pzero()
        Returns a zero polynomial.
        Returns:
        a zero polynomial

      • plength

        public int plength​(TMono m)
        Returns the length of the given polynomial.
        Parameters:
        m - the polynomial
        Returns:
        the length of the polynomial

      • pzerop

        public boolean pzerop​(TMono m)
        Checks if the given polynomial is zero.
        Parameters:
        m - the polynomial to check
        Returns:
        true if the polynomial is zero, false otherwise

      • ppush

        public TPoly ppush​(TMono t,
                   TPoly pp)
        Pushes a polynomial into a sorted linked list.
        Parameters:
        t - the polynomial to push
        pp - the linked list to push into
        Returns:
        the updated linked list with the polynomial added

      • calculv

        public double[] calculv​(TMono mm,
                        Param[] p)
        Calculates the values of the polynomial `mm` given the parameters `p`.
        Parameters:
        mm - the polynomial to calculate
        p - the array of parameters used in the calculation
        Returns:
        an array of calculated values of the polynomial

      • calculv_2v

        public double[] calculv_2v​(TMono mm,
                           Param[] p)
        Calculates the values of the polynomial `mm` given the parameters `p` for two variables.
        Parameters:
        mm - the polynomial to calculate
        p - the array of parameters used in the calculation
        Returns:
        an array of calculated values of the polynomial

      • calculate_online

        public double[] calculate_online​(TMono mm,
                                 Param[] p,
                                 int dx,
                                 int dy)
        Calculates the values of the polynomial `mm` given the parameters `p` for two variables.
        Parameters:
        mm - the polynomial to calculate
        p - the array of parameters used in the calculation
        dx - the first variable index
        dy - the second variable index
        Returns:
        an array of calculated values of the polynomial

      • calculate_oncr

        public double[] calculate_oncr​(TMono mm,
                               Param[] p,
                               int dx,
                               int dy)
        Calculates the values of the polynomial `mm` given the parameters `p` for two variables.
        Parameters:
        mm - the polynomial to calculate
        p - the array of parameters used in the calculation
        dx - the first variable index
        dy - the second variable index
        Returns:
        an array of calculated values of the polynomial

      • calculv2poly

        public double[] calculv2poly​(TMono mm1,
                             TMono mm2,
                             Param[] p)
        Calculates the values of two polynomials `mm1` and `mm2` given the parameters `p`.
        Parameters:
        mm1 - the first polynomial to calculate
        mm2 - the second polynomial to calculate
        p - the array of parameters used in the calculation
        Returns:
        an array of calculated values of the polynomials

      • pRtimes

        public TMono pRtimes​(TMono p1,
                     TMono p2)
        Multiplies two polynomials.
        Parameters:
        p1 - the first polynomial
        p2 - the second polynomial
        Returns:
        the product of the two polynomials

      • padd

        public TMono padd​(TMono p1,
                  TMono p2)
        Adds two polynomials.
        Parameters:
        p1 - the first polynomial
        p2 - the second polynomial
        Returns:
        the sum of the two polynomials

      • pdif

        public TMono pdif​(TMono p1,
                  TMono p2)
        Subtracts the second polynomial from the first polynomial.
        Parameters:
        p1 - the first polynomial
        p2 - the second polynomial
        Returns:
        the difference of the two polynomials

      • pcopy

        public TMono pcopy​(TMono p)
        Creates a copy of the given polynomial.
        Parameters:
        p - the polynomial to copy
        Returns:
        the copied polynomial

      • ptimes

        public TMono ptimes​(TMono p1,
                    TMono p2)
        Multiplies two polynomials.
        Parameters:
        p1 - the first polynomial
        p2 - the second polynomial
        Returns:
        the product of the two polynomials

      • pctimes

        public TMono pctimes​(TMono p,
                     long c)
        Multiplies a polynomial by a constant.
        Parameters:
        p - the polynomial
        c - the constant
        Returns:
        the product of the polynomial and the constant

      • printpoly

        public void printpoly​(TMono m)
        Prints the given polynomial.
        Parameters:
        m - the polynomial to print

      • printHead

        public java.lang.String printHead​(TMono m)
        Returns the head of the polynomial as a string.
        Parameters:
        m - the polynomial
        Returns:
        the head of the polynomial as a string

      • printSPoly

        public java.lang.String printSPoly​(TMono m)
        Returns a simplified string representation of the polynomial.
        Parameters:
        m - the polynomial
        Returns:
        the simplified string representation of the polynomial

      • printNPoly

        public java.lang.String printNPoly​(TMono m)
        Returns a string representation of the polynomial with a maximum length.
        Parameters:
        m - the polynomial
        Returns:
        the string representation of the polynomial with a maximum length

      • printNPoly

        public java.lang.String printNPoly​(TMono m1,
                                   TMono m2)
        Returns a string representation of two polynomials with a maximum length.
        Parameters:
        m1 - the first polynomial
        m2 - the second polynomial
        Returns:
        the string representation of the two polynomials with a maximum length

      • printSPoly

        public java.lang.String printSPoly​(TMono m,
                                   int n)
        Returns a simplified string representation of the polynomial with a specified maximum length.
        Parameters:
        m - the polynomial
        n - the maximum length of the string representation
        Returns:
        the simplified string representation of the polynomial with a specified maximum length

      • printMaxstrPoly

        public java.lang.String printMaxstrPoly​(TMono m)
        Returns a string representation of the polynomial with a maximum length.
        Parameters:
        m - the polynomial
        Returns:
        the string representation of the polynomial with a maximum length

      • String_p_print

        public java.lang.String String_p_print​(TMono p,
                                       boolean ce,
                                       boolean first,
                                       boolean nn)
        Returns a string representation of the polynomial.
        Parameters:
        p - the polynomial
        ce - a flag indicating whether to enclose the polynomial in parentheses
        first - a flag indicating whether this is the first polynomial in a sequence
        nn - a flag indicating whether to include the leading coefficient
        Returns:
        the string representation of the polynomial

      • getExpandedPrint

        public java.lang.String getExpandedPrint​(TMono p)
        Returns a string representation of the polynomial with expanded format.
        Parameters:
        p - the polynomial
        Returns:
        the string representation of the polynomial with expanded format

      • getAllPrinted

        public java.lang.String getAllPrinted​(TMono p,
                                      boolean b)
        Returns a string representation of all printed monomials in the polynomial.
        Parameters:
        p - the polynomial
        b - a flag indicating whether to include the leading coefficient
        Returns:
        the string representation of all printed monomials in the polynomial

      • getAllPrinted

        public java.lang.String getAllPrinted​(TMono p)
        Returns a string representation of all printed monomials in the polynomial.
        Parameters:
        p - the polynomial
        Returns:
        the string representation of all printed monomials in the polynomial

      • coefgcd

        public java.math.BigInteger coefgcd​(TMono p)
        Returns the greatest common divisor of the coefficients of the polynomial.
        Parameters:
        p - the polynomial
        Returns:
        the greatest common divisor of the coefficients of the polynomial

      • bb_reduce

        public java.util.Vector bb_reduce​(java.util.Vector vlist,
                                  long t)
        Reduces the polynomial by dividing it by the leading term of another polynomial.
        Parameters:
        vlist - the list of polynomials to reduce
        t - the time limit for reduction
        Returns:
        the reduced polynomial

      • bb_reduce

        public java.util.Vector bb_reduce​(java.util.Vector vlist,
                                  long t,
                                  boolean s)
        Reduces the polynomial by dividing it by the leading term of another polynomial.
        Parameters:
        vlist - the list of polynomials to reduce
        t - the time limit for reduction
        s - a flag indicating whether to use a special reduction method
        Returns:
        the reduced polynomial

      • b_reduce

        public TMono b_reduce​(TMono m1,
                      java.util.Vector vlist)
        Reduces the polynomial by dividing it by the leading term of another polynomial.
        Parameters:
        m1 - the first polynomial
        vlist - the list of polynomials to reduce
        Returns:
        the reduced polynomial

      • printVpoly

        public void printVpoly​(java.util.Vector v)
        Prints the given vector of polynomials.
        Parameters:
        v - the vector of polynomials to print

      • g_basis

        public java.util.Vector g_basis​(java.util.Vector v)
        Computes the Groebner basis for the given vector of polynomials.
        Parameters:
        v - the vector of polynomials
        Returns:
        the Groebner basis as a vector of polynomials

      • s_polys

        public java.util.Vector s_polys​(java.util.Vector vlist)
        Computes the S-polynomials for the given vector of polynomials.
        Parameters:
        vlist - the vector of polynomials
        Returns:
        the S-polynomials as a vector of polynomials

      • ll_delta

        public TMono ll_delta​(int x,
                      TMono m1,
                      TMono m2)
        Computes the delta of two polynomials.
        Parameters:
        x - the variable
        m1 - the first polynomial
        m2 - the second polynomial
        Returns:
        the delta of the two polynomials

      • getxm1

        public TMono getxm1​(int x,
                    int d,
                    TMono m)
        Gets the leading coefficient of a polynomial.
        Parameters:
        x - the variable
        d - the degree
        m - the polynomial
        Returns:
        the leading coefficient

      • upValueTM

        public void upValueTM​(java.util.Vector v,
                      int dx)
        Updates the value of a polynomial by adding a given value to its coefficients.
        Parameters:
        v - the polynomial
        dx - the value to add

      • upValueDM

        public void upValueDM​(java.util.Vector v,
                      int dx)
        Updates the value of a polynomial by adding a given value to its coefficients.
        Parameters:
        v - the polynomial
        dx - the value to add

      • getMaxX

        public int getMaxX​(java.util.Vector v)
        Gets the maximum value of x in a vector of polynomials.
        Parameters:
        v - the vector of polynomials
        Returns:
        the maximum value of x

      • upValueTM

        public void upValueTM​(TMono m,
                      int dx)
        Updates the value of a polynomial by adding a given value to its coefficients.
        Parameters:
        m - the polynomial
        dx - the value to add

      • gb_finished

        public boolean gb_finished​(java.util.Vector v)
        Checks if the polynomial is finished.
        Parameters:
        v - the vector of polynomials
        Returns:
        true if the polynomial is finished, false otherwise

      • ndg_reduce

        public void ndg_reduce​(java.util.Vector v)
        Reduces the polynomial by removing terms with degree 0.
        Parameters:
        v - the vector of polynomials

      • getcnds

        public java.util.Vector getcnds​(java.util.Vector v,
                                int dx)
        Gets the conditions for the given vector of polynomials.
        Parameters:
        v - the vector of polynomials
        dx - the value to add
        Returns:
        the conditions as a vector of polynomials

      • parseCommonDono

        public java.util.Vector parseCommonDono​(java.util.Vector v,
                                        int dx)
        Parses common Dono objects from the given vector of polynomials.
        Parameters:
        v - the vector of polynomials
        dx - the value to add
        Returns:
        a vector of parsed Dono objects

      • eraseCommonDono

        public void eraseCommonDono​(java.util.Vector v)
        Erases common Dono objects from the given vector of polynomials.
        Parameters:
        v - the vector of polynomials

      • ck_eq

        public boolean ck_eq​(TMono m1,
                     TMono m2)
        Checks if two monomials are equal.
        Parameters:
        m1 - the first monomial
        m2 - the second monomial
        Returns:
        true if the monomials are equal, false otherwise

      • ctLessdx1

        public boolean ctLessdx1​(TMono m,
                         int dx)
        Checks if the polynomial is less than a given value. This method only traverses the `coef` chain of the polynomial.
        Parameters:
        m - the polynomial
        dx - the value to compare with
        Returns:
        true if the polynomial is less than the given value, false otherwise

      • ctLessdx

        public boolean ctLessdx​(TMono m,
                        int dx)
        Checks if the polynomial is less than a given value. This method traverses both the `coef` and `next` chains of the polynomial and uses recursion.
        Parameters:
        m - the polynomial
        dx - the value to compare with
        Returns:
        true if the polynomial is less than the given value, false otherwise

      • reduceMDono

        public TMono reduceMDono​(TMono mm,
                         java.util.Vector v,
                         int dx)
        Reduces the polynomial by dividing it by the leading term of another polynomial.
        Parameters:
        mm - the polynomial to reduce
        v - the vector of polynomials
        dx - the value to add
        Returns:
        the reduced polynomial

      • getDo

        public TDono getDo​(java.util.Vector v,
                   int n)
        Gets the Dono object from the given vector of polynomials.
        Parameters:
        v - the vector of polynomials
        n - the value to compare with
        Returns:
        the Dono object, or null if not found

      • splitDono

        public TDono splitDono​(TMono m,
                       int dx)
        Splits the given monomial into a Dono object.
        Parameters:
        m - the monomial
        dx - the value to add
        Returns:
        the Dono object