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FRACTINT hypercomplex type (191 words) |
 | It is not possible to fully generalize the complex numbers to four dimensions without sacrificing some of the algebraic properties shared by real and complex numbers. |
| Hypercomplex numbers fail the rule that says all non-zero elements have multiplicative inverses - that is, if z is not 0, there should be a number 1/z such that (1/z)*(z) = 1. |
| Hypercomplex numbers were brought to our attention by Clyde Davenport, author of "A Hypercomplex Calculus with Applications to Relativity", ISBN 0-9623837-0-8. |
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Hypercomplex number (104 words) |
| Hypercomplex numbers are extensions of the complex numbers, such as quaternions, octonions and sedenions. |
| Whereas complex numbers can be viewed as points in a plane, hypercomplex numbers can be viewed as points in some higher-dimensional Euclidean space (4 dimensions for the quaternions, 8 for the octonions, 16 for the sedenions). |
| The Clifford algebras are another family of hypercomplex numbers. |
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