Package edu.jas.poly

Class ExpVector

java.lang.Object
edu.jas.poly.ExpVector
All Implemented Interfaces:
AbelianGroupElem<ExpVector>, Element<ExpVector>, Serializable, Comparable<ExpVector>
Direct Known Subclasses:
ExpVectorByte, ExpVectorInteger, ExpVectorLong, ExpVectorShort
public abstract class ExpVector extends Object implements AbelianGroupElem<ExpVector>
ExpVector implements exponent vectors for polynomials. Exponent vectors are implemented as arrays of Java elementary types, like long, int, short and byte. ExpVector provides also the familiar MAS static method names. The implementation is only tested for nonnegative exponents but should work also for negative exponents. Objects of this class are intended to be immutable, but exponents can be set (during construction); also the hash code is only computed once, when needed. The different storage unit implementations are ExpVectorLong ExpVectorInteger, ExpVectorShort and ExpVectorByte. The static factory methods create() of ExpVector select the respective storage unit. The selection of the desired storage unit is internally done via the static variable storunit. This variable should not be changed dynamically.
See Also:

  • Field Details

    • hash

      protected transient int hash
      Stored hash code.

    • blen

      protected transient long blen
      Stored bitLength.

    • random

      private static final Random random
      Random number generator.

    • storunit

      public static final ExpVector.StorUnit storunit
      Used storage representation of exponent arrays. Note: Set this only statically and not dynamically.

  • Constructor Details

    • ExpVector

      public ExpVector()
      Constructor for ExpVector.

  • Method Details

    • create

      public static final ExpVector create(int n)
      Factory constructor for ExpVector.
      Parameters:
      n - length of exponent vector.

    • create

      public static final ExpVector create(int n, int i, long e)
      Factory constructor for ExpVector. Sets exponent i to e.
      Parameters:
      n - length of exponent vector.
      i - index of exponent to be set.
      e - exponent to be set.

    • create

      public static final ExpVector create(long[] v)
      Internal factory constructor for ExpVector. Sets val.
      Parameters:
      v - internal representation array.

    • create

      public static final ExpVector create(String s)
      Factory constructor for ExpVector. Converts a String representation to an ExpVector. Accepted format = (1,2,3,4,5,6,7).
      Parameters:
      s - String representation.

    • create

      public static final ExpVector create(Collection<Long> v)
      Factory constructor for ExpVector. Sets val.
      Parameters:
      v - collection of exponents.

    • factory

      public AbelianGroupFactory<ExpVector> factory()
      Get the corresponding element factory.
      Specified by:
      factory in interface Element<ExpVector>
      Returns:
      factory for this Element.
      See Also:

    • isFinite

      public boolean isFinite()
      Is this structure finite or infinite.
      Returns:
      true if this structure is finite, else false.
      See Also:

    • valueOf

      public static ExpVector valueOf(ExpVector e)
      Value of other.
      Parameters:
      e - other ExpVector.
      Returns:
      value in sub class of ExpVector.

    • copy

      public abstract ExpVector copy()
      Clone this.
      Specified by:
      copy in interface Element<ExpVector>
      Returns:
      Creates and returns a copy of this Element.
      See Also:

    • getVal

      public abstract long[] getVal()
      Get the exponent vector.
      Returns:
      val.

    • getVal

      public abstract long getVal(int i)
      Get the exponent at position i.
      Parameters:
      i - position.
      Returns:
      val[i].

    • setVal

      protected abstract long setVal(int i, long e)
      Set the exponent at position i to e.
      Parameters:
      i -
      e -
      Returns:
      old val[i].

    • length

      public abstract int length()
      Get the length of this exponent vector.
      Returns:
      val.length.

    • extend

      public abstract ExpVector extend(int i, int j, long e)
      Extend variables. Used e.g. in module embedding. Extend this by i elements and set val[j] to e.
      Parameters:
      i - number of elements to extend.
      j - index of element to be set.
      e - new exponent for val[j].
      Returns:
      extended exponent vector.

    • extendLower

      public abstract ExpVector extendLower(int i, int j, long e)
      Extend lower variables. Extend this by i lower elements and set val[j] to e.
      Parameters:
      i - number of elements to extend.
      j - index of element to be set.
      e - new exponent for val[j].
      Returns:
      extended exponent vector.

    • contract

      public abstract ExpVector contract(int i, int len)
      Contract variables. Used e.g. in module embedding. Contract this to len elements.
      Parameters:
      i - position of first element to be copied.
      len - new length.
      Returns:
      contracted exponent vector.

    • reverse

      public abstract ExpVector reverse()
      Reverse variables. Used e.g. in opposite rings.
      Returns:
      reversed exponent vector.

    • reverse

      public abstract ExpVector reverse(int j)
      Reverse lower j variables. Used e.g. in opposite rings. Reverses the first j-1 variables, the rest is unchanged.
      Parameters:
      j - index of first variable reversed.
      Returns:
      reversed exponent vector.

    • combine

      public abstract ExpVector combine(ExpVector V)
      Combine with ExpVector. Combine this with the other ExpVector V.
      Parameters:
      V - the other exponent vector.
      Returns:
      combined exponent vector.

    • permutation

      public abstract ExpVector permutation(List<Integer> P)
      Permutation of exponent vector.
      Parameters:
      P - permutation.
      Returns:
      P(e).

    • toString

      public String toString()
      Get the string representation.
      Overrides:
      toString in class Object
      See Also:

    • toString

      public String toString(String[] vars)
      Get the string representation with variable names.
      Parameters:
      vars - names of variables.
      See Also:

    • varsToString

      public static final String varsToString(String[] vars)
      Get the string representation of the variables.
      Parameters:
      vars - names of variables.
      Returns:
      string representation of the variables.
      See Also:

    • toScript

      public String toScript()
      Get a scripting compatible string representation.
      Specified by:
      toScript in interface Element<ExpVector>
      Returns:
      script compatible representation for this Element.
      See Also:

    • toScript

      public String toScript(String[] vars)
      Get a scripting compatible string representation.
      Returns:
      script compatible representation for this Element.
      See Also:

    • toScriptFactory

      public String toScriptFactory()
      Get a scripting compatible string representation of the factory.
      Specified by:
      toScriptFactory in interface Element<ExpVector>
      Returns:
      script compatible representation for this ElemFactory.
      See Also:

    • indexVarName

      public String indexVarName(int idx, String... vars)
      Get the variable name at index.
      Parameters:
      idx - index of the variable
      vars - array of names of variables
      Returns:
      name of variable at the given index.

    • varIndex

      public int varIndex(int idx)
      Get the array index of a variable at index.
      Parameters:
      idx - index of the variable
      Returns:
      array index of the variable.

    • indexVar

      public int indexVar(String x, String... vars)
      Get the index of a variable.
      Parameters:
      x - variable name to be searched.
      vars - array of names of variables
      Returns:
      index of x in vars.

    • evaluate

      public <C extends RingElem<C>> C evaluate(RingFactory<C> cf, List<C> a)
      Evaluate.
      Parameters:
      cf - ring factory for elements of a.
      a - list of values.
      Returns:
      a_1^{e_1} * ... * a_n^{e_n}.

    • equals

      public boolean equals(Object B)
      Comparison with any other object.
      Specified by:
      equals in interface Element<ExpVector>
      Overrides:
      equals in class Object
      Parameters:
      B -
      Returns:
      true if this is equal to b, else false.
      See Also:

    • hashCode

      public int hashCode()
      hashCode. Optimized for small exponents, i.e. ≤ 24 and small number of variables, i.e. ≤ 8.
      Specified by:
      hashCode in interface Element<ExpVector>
      Overrides:
      hashCode in class Object
      Returns:
      the hashCode.
      See Also:

    • bitLength

      public long bitLength()
      Returns the number of bits in the representation of this exponent vector.
      Returns:
      number of bits in the representation of this ExpVector, including sign bits.

    • isZERO

      public boolean isZERO()
      Is ExpVector zero.
      Specified by:
      isZERO in interface AbelianGroupElem<ExpVector>
      Returns:
      If this has all elements 0 then true is returned, else false.

    • stdVars

      public String[] stdVars()
      Standard variable names. Generate standard names for variables, i.e. x0 to x(n-1).
      Returns:
      standard names.

    • stdVars

      public String[] stdVars(String prefix)
      Generate variable names. Generate names for variables, i.e. prefix0 to prefix(n-1).
      Parameters:
      prefix - name prefix.
      Returns:
      standard names.

    • STDVARS

      public static final String[] STDVARS(int n)
      Standard variable names. Generate standard names for variables, i.e. x0 to x(n-1).
      Parameters:
      n - size of names array
      Returns:
      standard names.

    • STDVARS

      public static final String[] STDVARS(String prefix, int n)
      Generate variable names. Generate names for variables from given prefix. i.e. prefix0 to prefix(n-1).
      Parameters:
      prefix - name prefix.
      n - size of names array.
      Returns:
      vatiable names.

    • EVABS

      public static final ExpVector EVABS(ExpVector U)
      ExpVector absolute value.
      Parameters:
      U -
      Returns:
      abs(U).

    • abs

      public abstract ExpVector abs()
      ExpVector absolute value.
      Specified by:
      abs in interface AbelianGroupElem<ExpVector>
      Returns:
      abs(this).

    • EVNEG

      public static final ExpVector EVNEG(ExpVector U)
      ExpVector negate.
      Parameters:
      U -
      Returns:
      -U.

    • negate

      public abstract ExpVector negate()
      ExpVector negate.
      Specified by:
      negate in interface AbelianGroupElem<ExpVector>
      Returns:
      -this.

    • EVSUM

      public static final ExpVector EVSUM(ExpVector U, ExpVector V)
      ExpVector summation.
      Parameters:
      U -
      V -
      Returns:
      U+V.

    • sum

      public abstract ExpVector sum(ExpVector V)
      ExpVector summation.
      Specified by:
      sum in interface AbelianGroupElem<ExpVector>
      Parameters:
      V -
      Returns:
      this+V.

    • EVDIF

      public static final ExpVector EVDIF(ExpVector U, ExpVector V)
      ExpVector difference. Result may have negative entries.
      Parameters:
      U -
      V -
      Returns:
      U-V.

    • subtract

      public abstract ExpVector subtract(ExpVector V)
      ExpVector subtract. Result may have negative entries.
      Specified by:
      subtract in interface AbelianGroupElem<ExpVector>
      Parameters:
      V -
      Returns:
      this-V.

    • scalarMultiply

      public abstract ExpVector scalarMultiply(long s)
      ExpVector multiply by scalar.
      Parameters:
      s - scalar
      Returns:
      s*this.

    • EVSU

      public static final ExpVector EVSU(ExpVector U, int i, long d)
      ExpVector substitution. Clone and set exponent to d at position i.
      Parameters:
      U -
      i - position.
      d - new exponent.
      Returns:
      substituted ExpVector.

    • subst

      public ExpVector subst(int i, long d)
      ExpVector substitution. Clone and set exponent to d at position i.
      Parameters:
      i - position.
      d - new exponent.
      Returns:
      substituted ExpVector.

    • EVRAND

      public static final ExpVector EVRAND(int r, long k, float q)
      Generate a random ExpVector.
      Parameters:
      r - length of new ExpVector.
      k - maximal degree in each exponent.
      q - density of nozero exponents.
      Returns:
      random ExpVector.

    • EVRAND

      public static final ExpVector EVRAND(int r, long k, float q, Random rnd)
      Generate a random ExpVector.
      Parameters:
      r - length of new ExpVector.
      k - maximal degree in each exponent.
      q - density of nozero exponents.
      rnd - is a source for random bits.
      Returns:
      random ExpVector.

    • random

      public static final ExpVector random(int r, long k, float q)
      Generate a random ExpVector.
      Parameters:
      r - length of new ExpVector.
      k - maximal degree in each exponent.
      q - density of nozero exponents.
      Returns:
      random ExpVector.

    • random

      public static final ExpVector random(int r, long k, float q, Random rnd)
      Generate a random ExpVector.
      Parameters:
      r - length of new ExpVector.
      k - maximal degree in each exponent.
      q - density of nozero exponents.
      rnd - is a source for random bits.
      Returns:
      random ExpVector.

    • EVSIGN

      public static final int EVSIGN(ExpVector U)
      ExpVector sign.
      Parameters:
      U -
      Returns:
      0 if U is zero, -1 if some entry is negative, 1 if no entry is negative and at least one entry is positive.

    • signum

      public abstract int signum()
      ExpVector signum.
      Specified by:
      signum in interface AbelianGroupElem<ExpVector>
      Returns:
      0 if this is zero, -1 if some entry is negative, 1 if no entry is negative and at least one entry is positive.

    • EVTDEG

      public static final long EVTDEG(ExpVector U)
      ExpVector total degree.
      Parameters:
      U -
      Returns:
      sum of all exponents.

    • degree

      public long degree()
      ExpVector degree.
      Returns:
      total degree of all exponents.

    • totalDeg

      public abstract long totalDeg()
      ExpVector total degree.
      Returns:
      sum of all exponents.

    • EVMDEG

      public static final long EVMDEG(ExpVector U)
      ExpVector maximal degree.
      Parameters:
      U -
      Returns:
      maximal exponent.

    • maxDeg

      public abstract long maxDeg()
      ExpVector maximal degree.
      Returns:
      maximal exponent.

    • EVMINDEG

      public static final long EVMINDEG(ExpVector U)
      ExpVector minimal degree.
      Parameters:
      U -
      Returns:
      minimal exponent.

    • minDeg

      public abstract long minDeg()
      ExpVector minimal degree.
      Returns:
      minimal exponent.

    • EVWDEG

      public static final long EVWDEG(long[][] w, ExpVector U)
      ExpVector weighted degree.
      Parameters:
      w - weights.
      U -
      Returns:
      weighted sum of all exponents.

    • weightDeg

      public abstract long weightDeg(long[][] w)
      ExpVector weighted degree.
      Parameters:
      w - weights.
      Returns:
      weighted sum of all exponents.

    • weightDeg

      public abstract long weightDeg(long[] w)
      ExpVector weighted degree.
      Parameters:
      w - weights.
      Returns:
      weighted sum of all exponents.

    • EVLCM

      public static final ExpVector EVLCM(ExpVector U, ExpVector V)
      ExpVector least common multiple.
      Parameters:
      U -
      V -
      Returns:
      component wise maximum of U and V.

    • lcm

      public abstract ExpVector lcm(ExpVector V)
      ExpVector least common multiple.
      Parameters:
      V -
      Returns:
      component wise maximum of this and V.

    • EVGCD

      public static final ExpVector EVGCD(ExpVector U, ExpVector V)
      ExpVector greatest common divisor.
      Parameters:
      U -
      V -
      Returns:
      component wise minimum of U and V.

    • gcd

      public abstract ExpVector gcd(ExpVector V)
      ExpVector greatest common divisor.
      Parameters:
      V -
      Returns:
      component wise minimum of this and V.

    • EVDOV

      public static final int[] EVDOV(ExpVector U)
      ExpVector dependency on variables.
      Parameters:
      U -
      Returns:
      array of indices where U has positive exponents.

    • dependentVariables

      public abstract int dependentVariables()
      ExpVector dependent variables.
      Returns:
      number of indices where val has positive exponents.

    • dependencyOnVariables

      public abstract int[] dependencyOnVariables()
      ExpVector dependency on variables.
      Returns:
      array of indices where val has positive exponents.

    • EVMT

      public static final boolean EVMT(ExpVector U, ExpVector V)
      ExpVector multiple test. Test if U is component wise greater or equal to V.
      Parameters:
      U -
      V -
      Returns:
      true if U is a multiple of V, else false.

    • multipleOf

      public abstract boolean multipleOf(ExpVector V)
      ExpVector multiple test. Test if this is component wise greater or equal to V.
      Parameters:
      V -
      Returns:
      true if this is a multiple of V, else false.

    • divides

      public boolean divides(ExpVector V)
      ExpVector divides test. Test if V is component wise greater or equal to this.
      Parameters:
      V -
      Returns:
      true if this divides V, else false.

    • compareTo

      public int compareTo(ExpVector V)
      ExpVector compareTo.
      Specified by:
      compareTo in interface Comparable<ExpVector>
      Specified by:
      compareTo in interface Element<ExpVector>
      Parameters:
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVILCP

      public static final int EVILCP(ExpVector U, ExpVector V)
      Inverse lexicographical compare.
      Parameters:
      U -
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • invLexCompareTo

      public abstract int invLexCompareTo(ExpVector V)
      ExpVector inverse lexicographical compareTo.
      Parameters:
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVILCP

      public static final int EVILCP(ExpVector U, ExpVector V, int begin, int end)
      Inverse lexicographical compare part. Compare entries between begin and end (-1).
      Parameters:
      U -
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • invLexCompareTo

      public abstract int invLexCompareTo(ExpVector V, int begin, int end)
      ExpVector inverse lexicographical compareTo.
      Parameters:
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVIGLC

      public static final int EVIGLC(ExpVector U, ExpVector V)
      Inverse graded lexicographical compare.
      Parameters:
      U -
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • invGradCompareTo

      public abstract int invGradCompareTo(ExpVector V)
      ExpVector inverse graded lexicographical compareTo.
      Parameters:
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVIGLC

      public static final int EVIGLC(ExpVector U, ExpVector V, int begin, int end)
      Inverse graded lexicographical compare part. Compare entries between begin and end (-1).
      Parameters:
      U -
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • invGradCompareTo

      public abstract int invGradCompareTo(ExpVector V, int begin, int end)
      ExpVector inverse graded lexicographical compareTo.
      Parameters:
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVRILCP

      public static final int EVRILCP(ExpVector U, ExpVector V)
      Reverse inverse lexicographical compare.
      Parameters:
      U -
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • revInvLexCompareTo

      public abstract int revInvLexCompareTo(ExpVector V)
      ExpVector reverse inverse lexicographical compareTo.
      Parameters:
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVRILCP

      public static final int EVRILCP(ExpVector U, ExpVector V, int begin, int end)
      Reverse inverse lexicographical compare part. Compare entries between begin and end (-1).
      Parameters:
      U -
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • revInvLexCompareTo

      public abstract int revInvLexCompareTo(ExpVector V, int begin, int end)
      ExpVector reverse inverse lexicographical compareTo.
      Parameters:
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVRIGLC

      public static final int EVRIGLC(ExpVector U, ExpVector V)
      Reverse inverse graded lexicographical compare.
      Parameters:
      U -
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • revInvGradCompareTo

      public abstract int revInvGradCompareTo(ExpVector V)
      ExpVector reverse inverse graded compareTo.
      Parameters:
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVRIGLC

      public static final int EVRIGLC(ExpVector U, ExpVector V, int begin, int end)
      Reverse inverse graded lexicographical compare part. Compare entries between begin and end (-1).
      Parameters:
      U -
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • revInvGradCompareTo

      public abstract int revInvGradCompareTo(ExpVector V, int begin, int end)
      ExpVector reverse inverse graded compareTo.
      Parameters:
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVITDEGLC

      public static final int EVITDEGLC(ExpVector U, ExpVector V)
      Inverse total degree lexicographical compare.
      Parameters:
      U -
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • invTdegCompareTo

      public abstract int invTdegCompareTo(ExpVector V)
      ExpVector inverse total degree lexicographical compareTo.
      Parameters:
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVRLITDEGC

      public static final int EVRLITDEGC(ExpVector U, ExpVector V)
      Reverse lexicographical inverse total degree compare.
      Parameters:
      U -
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • revLexInvTdegCompareTo

      public abstract int revLexInvTdegCompareTo(ExpVector V)
      ExpVector reverse lexicographical inverse total degree compareTo.
      Parameters:
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVIWLC

      public static final int EVIWLC(long[][] w, ExpVector U, ExpVector V)
      Inverse weighted lexicographical compare.
      Parameters:
      w - weight array.
      U -
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • invWeightCompareTo

      public abstract int invWeightCompareTo(long[][] w, ExpVector V)
      ExpVector inverse weighted lexicographical compareTo.
      Parameters:
      w - weight array.
      V -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • EVIWLC

      public static final int EVIWLC(long[][] w, ExpVector U, ExpVector V, int begin, int end)
      Inverse weighted lexicographical compare part. Compare entries between begin and end (-1).
      Parameters:
      w - weight array.
      U -
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.

    • invWeightCompareTo

      public abstract int invWeightCompareTo(long[][] w, ExpVector V, int begin, int end)
      ExpVector inverse weighted lexicographical compareTo.
      Parameters:
      w - weight array.
      V -
      begin -
      end -
      Returns:
      0 if U == V, -1 if U < V, 1 if U > V.