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abstract algebra, a
bicomplex number is a pair (w, z) of
complex numbers constructed by the Cayley–****son
process that
defines the
bicomplex conjugate ( w...
- the
bicomplex have a Z × Z {\displaystyle \mathbb {Z} \times \mathbb {Z} } -grading. The most
general definition of a
double complex, or a
bicomplex, is...
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bundles is
globally formulated in
algebraic terms of the
variational bicomplex,
without appealing to the
calculus of variations. For instance, this is...
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variational bicomplex of the
differential graded algebra O∗∞(Y) of
exterior forms on jet
manifolds of Y → X. The
coboundary operator of this
bicomplex contains...
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dynamic equations such as the Ginzburg–Landau equation, or by use of a
bicomplex variable. A
vortex street forms only at a
certain range of flow velocities...
- Split-quaternions Split-octonions Over C {\displaystyle \mathbb {C} } :
Bicomplex numbers Biquaternions Bioctonions Other hypercomplex Dual
numbers Dual...
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numbers (considered as
algebras over the reals)
leads to four-dimensional
bicomplex numbers C ⊗ R C {\displaystyle \mathbb {C} \otimes _{\mathbb {R} }\mathbb...
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numbers of
dimensions 64 and greater. Less
common variants include as
bicomplex numbers, coquaternions, and biquaternions. p-adic numbers:
Various number...
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trivial involution to
begin the Cayley–****son
constructions leading to
bicomplex, biquaternion, and
bioctonion composition algebras. On
complex numbers...
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possible to
construct Mandelbrot sets in 4
dimensions using quaternions and
bicomplex numbers.
White and Nylander's
formula for the "nth power" of the vector...
