public class OctonionicLeechLattice extends HypercomplexLattice
CANONICAL
Constructor and Description |
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OctonionicLeechLattice()
Constructor
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Modifier and Type | Method and Description |
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Octonion[] |
getAllUnitElements() |
Octonion |
getBrandtTransformer(int nr)
// TODO explain //
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Octonion[] |
getE7Roots() |
java.util.TreeMap<java.lang.String,java.lang.String> |
getMutliplicativeOrderDistribution() |
Octonion[] |
getOctavianUnits(int from,
int to) |
Octonion[] |
getSO16Roots() |
SevenPointsSTS |
getSTS7() |
Octonion |
getUnitElement(int nr) |
boolean |
isUnitElement(Octonion o) |
void |
set128And112BasisHardCoded() |
void |
setCanoniclalBasis() |
void |
setOctavianUnits_Canonical()
This construction of the unit integral octonions servers as a reference.
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void |
setOctavianUnits_D8Representation()
Set 128 elements +/-l0+/-l1+/-l2+/-l3+/-l4+/-l5+/-l6+/-l7 with an odd number of "-"-signs
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void |
setOctavianUnits_FanoPlaneRepresentation(int class_nr,
int nr)
Representation based on one of the 30 different Fano planes (= STS(7)).
112 basis vectors are constructed from the seven lines of the Fano plane considering all 16
sign combinations.
112 basis vectors are constructed from the dual vectors.
16 basis vectors are +/- one element base vectors.
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void |
setOctavianUnits_SubalgebrasRepresentation()
The basis is constructed from a STS(7) defined by the 7 (quaternionic) subalgebras of order 4.
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getAllUnitsAsString, getBasis, getElements, getNumberOfUnitElement, isIntegralUnitElement, isUnitElement
public OctonionicLeechLattice() throws java.lang.Exception
java.lang.Exception
public void setOctavianUnits_Canonical() throws java.lang.Exception
java.lang.Exception
public void setOctavianUnits_SubalgebrasRepresentation() throws java.lang.Exception
java.lang.Exception
public void setOctavianUnits_FanoPlaneRepresentation(int class_nr, int nr) throws java.lang.Exception
class_nr
- Class number of the Fano planee (1 or 2).nr
- Number of Fano plane within a class (1,...15).java.lang.Exception
public void setOctavianUnits_D8Representation() throws java.lang.Exception
java.lang.Exception
public void setCanoniclalBasis() throws java.lang.Exception
java.lang.Exception
public void set128And112BasisHardCoded() throws java.lang.Exception
java.lang.Exception
public Octonion[] getOctavianUnits(int from, int to) throws java.lang.Exception
java.lang.Exception
public java.util.TreeMap<java.lang.String,java.lang.String> getMutliplicativeOrderDistribution() throws java.lang.Exception
getMutliplicativeOrderDistribution
in class HypercomplexLattice
java.lang.Exception
public Octonion[] getSO16Roots() throws java.lang.Exception
java.lang.Exception
public Octonion[] getE7Roots() throws java.lang.Exception
java.lang.Exception
public SevenPointsSTS getSTS7()
public Octonion getBrandtTransformer(int nr) throws java.lang.Exception
nr
- Number of Brand transformerjava.lang.Exception
public Octonion[] getAllUnitElements()
getAllUnitElements
in class HypercomplexLattice
public Octonion getUnitElement(int nr) throws java.lang.Exception
getUnitElement
in class HypercomplexLattice
nr
- Number of the unit integral elements, counting starts with "1".java.lang.Exception
public boolean isUnitElement(Octonion o) throws java.lang.Exception
o
- Octonion.java.lang.Exception