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jhypercomplex.algebra
Class AlgebraicProperties

java.lang.Object
  extended by jhypercomplex.algebra.AlgebraicProperties

public abstract class AlgebraicProperties
extends java.lang.Object

Constructor Summary
AlgebraicProperties()
           
 
Method Summary
static boolean isAdamsIdentitiesForAlternativeAlgebrasSatisfied(java.lang.Class hypernumber, int n_comps)
           
static boolean isAdamsIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
           
 boolean isAlternative(Hypernumber h1, Hypernumber h2)
          Alternativity means that X(XY) = (XX)Y and X(YY) = (XY)Y This is equivalent to the associator properties: [X,X,Y] = [X,Y,Y] = 0
static boolean isAlternativeAlgebraIdentitySatisfied(java.lang.Class hypernumber, int nr_of_identity, int n_comps)
          A collection of identities satisfied by alternative algebras.
static boolean isAssociatorIdentity1Satisfied(java.lang.Class hypernumber, int n_comps)
           
static boolean isBolLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isBrukLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isCLoop(java.lang.Class hypernumber, int n_comps, boolean set_first_comp)
           
static boolean isCommutatorAdamsIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
           
static boolean isCommutatorCLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isCommutatorIdentity1Satisfied(java.lang.Class hypernumber, int n_comps)
           
static boolean isCommutatorMalcevIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
           
static boolean isDerivation(java.lang.Class hypernumber, int n_comps)
           
static boolean isExtraLoop(java.lang.Class hypernumber, int n_comps, boolean set_first_comp)
          A(B(CA)) = ((AB)C)A
static boolean isFirstHentzelPeresiIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
           
static boolean isGroup(java.lang.Class hypernumber, int n_comps)
          A(BC) = (AB)C
static boolean isInLeftNucleus(Hypernumber h)
           
static boolean isInMiddleNucleus(Hypernumber h)
           
static boolean isInNucleus(Hypernumber h)
           
static boolean isInRightNucleus(Hypernumber h)
           
static boolean isInversePropertiesSatisfied(java.lang.Class hypernumber, int n_comps)
          A^–1(AB)=B=(BA)A^–1
static boolean isJordanIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
          (A^2B)A - A^2(BA) = 0 <=> [A^2,B,A] = 0 Equivalent identities are A^2(AB) =A(A^2B) (BA)A^2 = (BA^2)A (AB)A^2 = (A^2B)A which are also checked.
static boolean isJordansTripleIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
          Cycl_Sum_{ ([A, [B, A, C], D] + [B, [A, A, C], D] - [B, A, [C, A, D]]) = 0
static boolean isLCLoop(java.lang.Class hypernumber, int n_comps, boolean set_first_comp)
           
static boolean isLeftBolLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isLeftMoufangLoop(java.lang.Class hypernumber, int n_comps)
          ((AB)A)C=A(B(AC))
static boolean IsLeftNuclearSquareLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isLie3Algebra(java.lang.Class hypernumber, int n_comps)
           
static boolean isMiddleMoufangLoop(java.lang.Class hypernumber, int n_comps)
          (AB)(CA) = (A(BC))A = A((BC)A)
static boolean IsMiddleNuclearSquareLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isMoufangLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isNormMultiplicative(java.lang.Class hypernumber, int n_comps)
           
static boolean isProjectionOperator(java.lang.Class hypernumber, int n_comps)
           
static boolean isRCLoop(java.lang.Class hypernumber, int n_comps, boolean set_first_comp)
           
static boolean isRightBolLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isRightMoufangLoop(java.lang.Class hypernumber, int n_comps)
          A(B(CB))=((AB)C)B
static boolean IsRightNuclearSquareLoop(java.lang.Class hypernumber, int n_comps)
           
static boolean isSagleIdentitiesSatisfied(java.lang.Class hypernumber, int n_comps, boolean COMMUTATOR)
           
static boolean isSecondHentzelPeresiIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
           
static boolean isTakhtajanIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
           
static boolean isWeneIdentitySatisfied(java.lang.Class hypernumber, int n_comps)
           
static void setNumericalMode(boolean is_numerical)
           
static void testFourCommutator(java.lang.Class hypernumber, int n_comps)
           
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

AlgebraicProperties

public AlgebraicProperties()
Method Detail

setNumericalMode

public static void setNumericalMode(boolean is_numerical)
Parameters:
is_numerical - 'true': calculations are carried out numerically. 'false': calculations are carried out numerically.

isGroup

public static boolean isGroup(java.lang.Class hypernumber,
                              int n_comps)
                       throws java.lang.Exception
A(BC) = (AB)C

Throws:
java.lang.Exception

isExtraLoop

public static boolean isExtraLoop(java.lang.Class hypernumber,
                                  int n_comps,
                                  boolean set_first_comp)
                           throws java.lang.Exception
A(B(CA)) = ((AB)C)A

Throws:
java.lang.Exception

isMoufangLoop

public static boolean isMoufangLoop(java.lang.Class hypernumber,
                                    int n_comps)
                             throws java.lang.Exception
Throws:
java.lang.Exception

isLeftMoufangLoop

public static boolean isLeftMoufangLoop(java.lang.Class hypernumber,
                                        int n_comps)
                                 throws java.lang.Exception
((AB)A)C=A(B(AC))

Throws:
java.lang.Exception

isRightMoufangLoop

public static boolean isRightMoufangLoop(java.lang.Class hypernumber,
                                         int n_comps)
                                  throws java.lang.Exception
A(B(CB))=((AB)C)B

Throws:
java.lang.Exception

isMiddleMoufangLoop

public static boolean isMiddleMoufangLoop(java.lang.Class hypernumber,
                                          int n_comps)
                                   throws java.lang.Exception
(AB)(CA) = (A(BC))A = A((BC)A)

Throws:
java.lang.Exception

isCLoop

public static boolean isCLoop(java.lang.Class hypernumber,
                              int n_comps,
                              boolean set_first_comp)
                       throws java.lang.Exception
Throws:
java.lang.Exception

isCommutatorCLoop

public static boolean isCommutatorCLoop(java.lang.Class hypernumber,
                                        int n_comps)
                                 throws java.lang.Exception
Throws:
java.lang.Exception

isLCLoop

public static boolean isLCLoop(java.lang.Class hypernumber,
                               int n_comps,
                               boolean set_first_comp)
                        throws java.lang.Exception
Throws:
java.lang.Exception

isRCLoop

public static boolean isRCLoop(java.lang.Class hypernumber,
                               int n_comps,
                               boolean set_first_comp)
                        throws java.lang.Exception
Throws:
java.lang.Exception

IsLeftNuclearSquareLoop

public static boolean IsLeftNuclearSquareLoop(java.lang.Class hypernumber,
                                              int n_comps)
                                       throws java.lang.Exception
Throws:
java.lang.Exception

IsMiddleNuclearSquareLoop

public static boolean IsMiddleNuclearSquareLoop(java.lang.Class hypernumber,
                                                int n_comps)
                                         throws java.lang.Exception
Throws:
java.lang.Exception

IsRightNuclearSquareLoop

public static boolean IsRightNuclearSquareLoop(java.lang.Class hypernumber,
                                               int n_comps)
                                        throws java.lang.Exception
Throws:
java.lang.Exception

isLeftBolLoop

public static boolean isLeftBolLoop(java.lang.Class hypernumber,
                                    int n_comps)
                             throws java.lang.Exception
Throws:
java.lang.Exception

isRightBolLoop

public static boolean isRightBolLoop(java.lang.Class hypernumber,
                                     int n_comps)
                              throws java.lang.Exception
Throws:
java.lang.Exception

isBolLoop

public static boolean isBolLoop(java.lang.Class hypernumber,
                                int n_comps)
                         throws java.lang.Exception
Throws:
java.lang.Exception

isBrukLoop

public static boolean isBrukLoop(java.lang.Class hypernumber,
                                 int n_comps)
                          throws java.lang.Exception
Throws:
java.lang.Exception

isProjectionOperator

public static boolean isProjectionOperator(java.lang.Class hypernumber,
                                           int n_comps)
                                    throws java.lang.Exception
Throws:
java.lang.Exception

isAlternativeAlgebraIdentitySatisfied

public static boolean isAlternativeAlgebraIdentitySatisfied(java.lang.Class hypernumber,
                                                            int nr_of_identity,
                                                            int n_comps)
                                                     throws java.lang.Exception
A collection of identities satisfied by alternative algebras.

Throws:
java.lang.Exception

isAlternative

public boolean isAlternative(Hypernumber h1,
                             Hypernumber h2)
                      throws java.lang.Exception
Alternativity means that X(XY) = (XX)Y and X(YY) = (XY)Y This is equivalent to the associator properties: [X,X,Y] = [X,Y,Y] = 0

Parameters:
h1 - Hypermummer 1.
h2 - Hypernummer 2.
Returns:
true if alternative, false otherwise.
Throws:
java.lang.Exception

isInLeftNucleus

public static boolean isInLeftNucleus(Hypernumber h)
                               throws java.lang.Exception
Parameters:
h - Hyperumber
Returns:
'tue' if [h,A,B]] = 0 for any A,B 'false else
Throws:
java.lang.Exception

isInRightNucleus

public static boolean isInRightNucleus(Hypernumber h)
                                throws java.lang.Exception
Parameters:
h - Hyperumber
Returns:
'tue' if [A,h,B]] = 0 for any A,B 'false else
Throws:
java.lang.Exception

isNormMultiplicative

public static boolean isNormMultiplicative(java.lang.Class hypernumber,
                                           int n_comps)
                                    throws java.lang.Exception
Parameters:
hypernumber -
n_comps -
Returns:
'true' if the norm N satisfies N(A)N(B) = N(AB), 'false' else.
Throws:
java.lang.Exception

isInMiddleNucleus

public static boolean isInMiddleNucleus(Hypernumber h)
                                 throws java.lang.Exception
Parameters:
h - Hyperumber
Returns:
'tue' if [A,B,h]] = 0 for any A,B 'false else
Throws:
java.lang.Exception

isInNucleus

public static boolean isInNucleus(Hypernumber h)
                           throws java.lang.Exception
Parameters:
h - Hypernumber.
Returns:
'true' if h is in the left-, middle and right-nucleus. 'false' else.
Throws:
java.lang.Exception

isInversePropertiesSatisfied

public static boolean isInversePropertiesSatisfied(java.lang.Class hypernumber,
                                                   int n_comps)
                                            throws java.lang.Exception
A^–1(AB)=B=(BA)A^–1

Throws:
java.lang.Exception

isSagleIdentitiesSatisfied

public static boolean isSagleIdentitiesSatisfied(java.lang.Class hypernumber,
                                                 int n_comps,
                                                 boolean COMMUTATOR)
                                          throws java.lang.Exception
Throws:
java.lang.Exception

testFourCommutator

public static void testFourCommutator(java.lang.Class hypernumber,
                                      int n_comps)
                               throws java.lang.Exception
Throws:
java.lang.Exception

isTakhtajanIdentitySatisfied

public static boolean isTakhtajanIdentitySatisfied(java.lang.Class hypernumber,
                                                   int n_comps)
                                            throws java.lang.Exception
Throws:
java.lang.Exception

isDerivation

public static boolean isDerivation(java.lang.Class hypernumber,
                                   int n_comps)
                            throws java.lang.Exception
Throws:
java.lang.Exception

isLie3Algebra

public static boolean isLie3Algebra(java.lang.Class hypernumber,
                                    int n_comps)
                             throws java.lang.Exception
Throws:
java.lang.Exception

isAdamsIdentitySatisfied

public static boolean isAdamsIdentitySatisfied(java.lang.Class hypernumber,
                                               int n_comps)
                                        throws java.lang.Exception
Throws:
java.lang.Exception

isCommutatorAdamsIdentitySatisfied

public static boolean isCommutatorAdamsIdentitySatisfied(java.lang.Class hypernumber,
                                                         int n_comps)
                                                  throws java.lang.Exception
Throws:
java.lang.Exception

isAdamsIdentitiesForAlternativeAlgebrasSatisfied

public static boolean isAdamsIdentitiesForAlternativeAlgebrasSatisfied(java.lang.Class hypernumber,
                                                                       int n_comps)
                                                                throws java.lang.Exception
Throws:
java.lang.Exception

isFirstHentzelPeresiIdentitySatisfied

public static boolean isFirstHentzelPeresiIdentitySatisfied(java.lang.Class hypernumber,
                                                            int n_comps)
                                                     throws java.lang.Exception
Throws:
java.lang.Exception

isSecondHentzelPeresiIdentitySatisfied

public static boolean isSecondHentzelPeresiIdentitySatisfied(java.lang.Class hypernumber,
                                                             int n_comps)
                                                      throws java.lang.Exception
Throws:
java.lang.Exception

isCommutatorMalcevIdentitySatisfied

public static boolean isCommutatorMalcevIdentitySatisfied(java.lang.Class hypernumber,
                                                          int n_comps)
                                                   throws java.lang.Exception
Throws:
java.lang.Exception

isWeneIdentitySatisfied

public static boolean isWeneIdentitySatisfied(java.lang.Class hypernumber,
                                              int n_comps)
                                       throws java.lang.Exception
Throws:
java.lang.Exception

isJordanIdentitySatisfied

public static boolean isJordanIdentitySatisfied(java.lang.Class hypernumber,
                                                int n_comps)
                                         throws java.lang.Exception
(A^2B)A - A^2(BA) = 0 <=> [A^2,B,A] = 0 Equivalent identities are A^2(AB) =A(A^2B) (BA)A^2 = (BA^2)A (AB)A^2 = (A^2B)A which are also checked.

Throws:
java.lang.Exception

isJordansTripleIdentitySatisfied

public static boolean isJordansTripleIdentitySatisfied(java.lang.Class hypernumber,
                                                       int n_comps)
                                                throws java.lang.Exception
Cycl_Sum_{ ([A, [B, A, C], D] + [B, [A, A, C], D] - [B, A, [C, A, D]]) = 0

Throws:
java.lang.Exception

isCommutatorIdentity1Satisfied

public static boolean isCommutatorIdentity1Satisfied(java.lang.Class hypernumber,
                                                     int n_comps)
                                              throws java.lang.Exception
Throws:
java.lang.Exception

isAssociatorIdentity1Satisfied

public static boolean isAssociatorIdentity1Satisfied(java.lang.Class hypernumber,
                                                     int n_comps)
                                              throws java.lang.Exception
Throws:
java.lang.Exception
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