As stated Bloch the categories of the noun-substitute should reflect the categories of the noun and not vice versa. Finally there is also a semantico-syntactic approach to case where a case is treated as semantic relationship. Different semantic relations of the noun and the verb are treated as "deep semantic cases" which have different forms of expression in the surface (or syntactic) structure. Thus, sentences: John opened the door with the key The door was opened with the key by John. The key opened the door, express the same semantic relations between doer, instrument, object and action. She is eager to please. She is easy to please. Syntactic structure is the same but meaning is different. Possessive case is narrower in meaning than genitive case. In Qld English genitive case could be used with living beings but not with inanimate nouns. Today possessive case may express not only the idea of possession but the idea of subject, object, material, measure, part of the whole. There is a very old theory that 's is a kind of abbreviation of pronoun "his".
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Division common proper; common concrete and abstract; countable uncountable; uncountable mass. animate, inanimate; personal non-personal; human non-human. Lexico-semantic variants of nouns may belong to different subclasses (e. paper - a paper). The class of nouns can be described as a lexico-grammatical field. Nouns denoting things constitute the center or nucleus of the field and nouns denoting processes, qualities, abstract notions are marginal or peripheral elements of the field. Morphological Characteristics. Number is proper to countable nouns only. Usually words that lack a certain category have only one form that of the weak member of the opposition. Non-counts may be singular or plural. So, subclasses of noncount nouns constitute a lexico-grammatical opposition: singular only (joy, snow) vs plural only (cattle). The general meaning revealed through the opposition is number or quantity or "oneness/more than oneness". The general meaning revealed through the lexico-grammatical opposition is "discreteness/non-discreteness".
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"On polynomial selection for the general number field sieve" (PDF). Mathematics of Computation. 75 (256): 2037–2047. doi: 10. 1090/S0025-5718-06-01870-9. Retrieved 2007-12-13. ^ Paul Leyland (December 12, 2003). "NFSNET: the first year". Presentation at EIDMA-CWI Workshop on Factoring Large Numbers. Retrieved August 9, 2011. ^ "Welcome to NFSNET". April 23, 2007. Archived from the original on October 22, 2007. Retrieved August 9, 2011. ^ "About NFSNET". Archived from the original on May 9, 2008. Retrieved August 9, 2011. References [ edit] Arjen K. Lenstra and H. W. Lenstra, Jr. (eds. ). "The development of the number field sieve". Lecture Notes in Math. (1993) 1554. Springer-Verlag. Richard Crandall and Carl Pomerance. Prime Numbers: A Computational Perspective (2001). 2nd edition, Springer. ISBN 0-387-25282-7. Section 6. 2: Number field sieve, pp. 278–301. Matthew E. Briggs: An Introduction to the General Number Field Sieve, 1998
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