different between holomorphic vs homomorphic

English

Etymology

holo- +? -morphic

Adjective

holomorphic (not comparable)

1. (complex analysis, of a complex function) Complex-differentiable on an open set around every point in its domain.
   • 1998, Stefan-M. Heinemann, Julia Sets in Cⁿ, Hartje Kriete, Progress in Holomorphic Dynamics, Addison Wesley Longman, page 159,

     The iteration of holomorphic maps of one variable is one of the most lively fields of current mathematical research. Since its beginning in the twenties of this century, the theory of holomorphic endomorphisms of the Riemann sphere (= rational functions) has become well developed.

   • 1998, Robert Friedman, Algebraic Surfaces and Holomorphic Vector Bundles, Springer, page 303,

     A holomorphic 1-form on X is closed, and so

     ${\displaystyle 0=d\eta _{1}=df\land \eta _{2}}$.

   • 2010, Graziano Gentili, Jacques Guenot, Giorgio Patrizio, Holomorphic Dynamical Systems: Lectures given at the C.I.M.E. Summer School, Springer, page v,

     The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector field) acting on it.

2. Having holohedral symmetry.

Derived terms

Translations

English

Etymology

homo- +? -morphic

Adjective

homomorphic (comparative more homomorphic, superlative most homomorphic)

1. Of or pertaining to homomorphism; having a homomorphism.
   • 2014, Xun Yi, Russell Paulet, Elisa Bertino, Homomorphic Encryption and Applications, Springer (?ISBN), page 50:

     In 2010, Nigel P. Smart and Frederik Vercauteren presented a fully homomorphic encryption scheme with smaller key and ciphertext sizes.

   • 2014, Miroslaw Kutylowski, Jaideep Vaidya, Verifiable Computation on Outsourced Encrypted Data, in Computer Security – ESORICS 2014, Springer (?ISBN), page 273:

     On one hand, homomorphic encryption allows a cloud server to perform computation on outsourced encrypted data but provides no verifiability that the computation is correct.

Usage notes

• In mathematics, this adjective can be used in phrases like "A and B are homomorphic", "A is homomorphic to B", and, less commonly, "A is homomorphic with B".

Derived terms

• homomorphic encryption

Translations