Basic Examples
Basic Examples
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Get the quaternion :
1+2i+3j+4k
[1,2,3,4]
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Add two quaternions:
[1,2,3,4]+
[2,3,4,5]
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Use () to multiply quaternions:
**
[2,0,-6,3]**
[1,3,-2,2]
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This multiplication is noncommutative:
[1,3,-2,2]**
[2,0,-6,3]
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Properties and Relations
Properties and Relations
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In the conjugate of a quaternion, all the signs of the nonreal components are reversed:
q=Conjugate
[4,-3,1,-2]
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The sign of a quaternion is defined in the same way as the sign of a complex number. It is the "direction" of the quaternion:
Sign[q]
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Get the standard Euclidean length:
Abs[q]
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30
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The exponential of a quaternion can be quite complicated:
[2,3,1,6]
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Just as with complex numbers, it is important to beware of branch cuts:
SinCos
[.3,.1,.5,.5]
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A four-dimensional analog of de Moivre’s theorem is used for calculating powers of quaternions:
[1,2,0,1]
2.5
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Round for quaternions returns a in which either all components are integers, or all components are odd multiples of 1/2:
Quaternion
Round,3,4,
1
2
5
2
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A quaternion is even if its norm is even:
EvenQ
[2,3,4,5]
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True
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EvenQNorm
[2,3,4,5]
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True
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Just as with complex numbers, the quaternion works:
Mod
[-3,4,1,2],3
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You can specify a quaternion as the modulus:
Mod
[1,3,4,1],
[3,4,1,2]
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