Isomorphism vs. Polymorphism

Isomorphismnoun

Similarity of form

Isomorphismnoun

(biology) the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology.

Isomorphismnoun

(chemistry) the similarity in the crystal structures of similar chemical compounds

Isomorphismnoun

(sociology) the similarity in the structure or processes of different organizations

Isomorphismnoun

A one-to-one correspondence

Isomorphismnoun

(group algebra) A bijection f such that both f and its inverse f −1 are homomorphisms, that is, structure-preserving mappings.

Isomorphismnoun

(computer science) a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets

Isomorphismnoun

(category theory) A morphism which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).

Isomorphismnoun

A similarity of crystalline form between substances of similar composition, as between the sulphates of barium (BaSO4) and strontium (SrSO4). It is sometimes extended to include similarity of form between substances of unlike composition, which is more properly called homœomorphism.

Isomorphismnoun

A one-to-one mapping of one set onto another set which preserves the relations between the elements of the domains of the sets.

Isomorphismnoun

(biology) similarity or identity of form or shape or structure

Isomorphism

In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them.

Polymorphismnoun

The ability to assume different forms or shapes.

Polymorphismnoun

(biology) The coexistence, in the same locality, of two or more distinct forms independent of sex, not connected by intermediate gradations, but produced from common parents.

Polymorphismnoun

(object-oriented programming) The feature pertaining to the dynamic treatment of data elements based on their type, allowing for an instance of a method to have several definitions. en

Polymorphismnoun

The property of certain typed formal systems of allowing for the use of type variables and binders/quantifiers over those type variables; likewise, the property of certain expressions (within such typed formal systems) of making use of at least one such typed variable.

Polymorphismnoun

(crystallography) The ability of a solid material to exist in more than one form or crystal structure; pleomorphism.

Polymorphismnoun

(genetics) The regular existence of two or more different genotypes within a given species or population; also, variability of amino acid sequences within a gene's protein.

Polymorphismnoun

Same as Pleomorphism.

Polymorphismnoun

The capability of assuming different forms; the capability of widely varying in form.

Polymorphismnoun

(chemistry) the existence of different kinds of crystal of the same chemical compound

Polymorphismnoun

(biology) the existence of two or more forms of individuals within the same animal species (independent of sex differences)