abstract algebra, a bicomplex number is a pair (w, z) of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate ( w...

complex number system, C 2 {\displaystyle \mathbb {C} _{2}} is the bicomplex number system, C 3 {\displaystyle \mathbb {C} _{3}} is the tricomplex number system...

In this construction, a bicomplex number (w, z) has conjugate (w, z)* = (w, – z). The biquaternion is then a pair of bicomplex numbers (a, b), where the...

numbers (considered as algebras over the reals) leads to four-dimensional bicomplex numbers C ⊗ R C {\displaystyle \mathbb {C} \otimes _{\mathbb {R} }\mathbb...

Less common variants include as bicomplex numbers, coquaternions, and biquaternions. p-adic numbers: Various number systems constructed using limits...

projective space C P n {\displaystyle \mathbb {CP} ^{n}} by Takeuchi. Bicomplex number Complex geometry CR manifold Dolbeault cohomology Harmonic maps Harmonic...

trivial involution to begin the Cayley–Dickson constructions leading to bicomplex, biquaternion, and bioctonion composition algebras. On complex numbers...

bicomplex. More precisely, any bicomplex determines two spectral sequences: one of the two spectral sequences determined by the variational bicomplex...

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...

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...

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...

functor, which can be explicitly computed by the means of the (b, B)-bicomplex. If the field k contains the rational numbers, the definition in terms...

split algebras arise in the series bicomplex numbers, biquaternions, and bioctonions, which uses the complex number field C {\displaystyle \mathbb {C}...

cases one finds that Cl0(C) ≅ C, the complex numbers Cl1(C) ≅ C ⊕ C, the bicomplex numbers Cl2(C) ≅ M2(C), the biquaternions where Mn(C) denotes the algebra...

quadratic form z2, then four composition algebras over C are C itself, the bicomplex numbers, the biquaternions (isomorphic to the 2×2 complex matrix ring...

it is well known that[citation needed] jet bundles and the variational bicomplex are the correct domain for such a description. The Hamiltonian variant...

the generation of C by doubling R. When this C is doubled it produces bicomplex numbers, and doubling that produces biquaternions, and doubling again...

variation Isoperimetric inequality Variational principle Variational bicomplex Fermat's principle Principle of least action Infinite-dimensional optimization...

its motivation. In 1892 Corrado Segre recalled the tessarine algebra as bicomplex numbers. Naturally the subalgebra of real tessarines arose and came to...

equation, i.e., for the space of infinite jets) is the so-called variational bicomplex. Furthermore, Vinogradov introduced a new bracket on the graded algebra...