Converse of object

• construct: In this section we have constructed homomorphisms by specifying images for a set of generators.

• define: This defines a natural homomorphism of C into the symmetric group of degree n.

• return: This function returns the natural homomorphism from C onto L.

• use: The information in this section is mainly relevant for implementing new methods and not for using homomorphisms.

• induce: The next step is to compute the homomorphism induced by inclusion of the circle as the boundary of the respective punctured surface.

• compute: The next step is to compute the homomorphism induced by inclusion of the circle as the boundary of the respective punctured surface.

Preposition: between

• group: No test is performed on whether the functions actually give an homomorphism between both groups because this would require testing the full multiplication table.

Adjective modifier

• natural: This function returns the natural homomorphism from C onto L.

• such: The corresponding decision problem consists of deciding whether or not any such homomorphisms exist.

• unique: Then there exists a unique homomorphism: G * K H F such that i = and j = .

• corresponding: However, it is also possible to explicitly construct factor groups and their corresponding natural homomorphisms.

Modifies a noun

• hom: This function returns the left A -module defined by the homomorphism hom.

• problem: We introduce the minimum cost graph homomorphism problem, provide partial results and pose an open problem.

Noun used with modifier

• action: We will now look at this action homomorphism again to find out on what objects it operates.

• group: The result is a group homomorphism onto a permutation group, in the worst case this is the identity mapping on G.

• cost: We introduce the minimum cost graph homomorphism problem, provide partial results and pose an open problem.

• algebra: Its methods may assume that gens generates A and that the mapping of gens to imgs defines an algebra homomorphism.

• ring: Recall concepts of a ring homomorphism, ideal, right ( left ) ideal, principal ideal in a commutative ring.

• operation: The permutation group arising by the induced action is then the image of this operation homomorphism.

Preposition: of

• graph: We prove that the general LORA problem is NP-hard by using an important result on list homomorphisms of graphs.