By Michel Léonard (auth.)
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For a number of years now i've been instructing classes in laptop algebra on the Universitat Linz, the collage of Delaware, and the Universidad de Alcala de Henares. within the summers of 1990 and 1992 i've got prepared and taught summer time colleges in laptop algebra on the Universitat Linz. progressively a collection in fact notes has emerged from those actions.
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N n * iR[~+] is an instance of R because R = * R[~+]. iR' = j=l j=l According to the base property iR~ iR'. iR' is a complete instance of R forD because it verifies the jd (R 1... ~). We describe as associated a decomposition D of R and a jd of R which are formed on the same relations. Corollary A valid system of inferences for the jds is also valid for associated decompositions. Proof Take a relation R which decomposes to Dl D2 ... Dp. Its closure verifies the associated join dependencies d 1 d 2 ...
IRk.. i~ are mutually compatible if n (* (iRk) )[Rt] = i~ (V j e (l,n)). k=l COMPLETENESS PROPERTY If the relations R1... Rk···~ form a decomposition D of relation R, then for every entity ri, there is a set of mutually compatible entities (r 1 r2 ... rk ... r0 ) that contains it, and for every clear instance iRk, there is a mutually compatible set of instances (iR 1 iR2 .. i~) that contains it. Proof Since Rk is a projection of R, there is for every instance iRk an instance iR of R such that iR[R~] =iRk.
A key to the relation MACHINE-AVAIL is a minimum set of its attributes such that if two entities of MACHINE-AVAIL take the same values for these attributes in the same instance, these two entities are identical. If NMH is a key then it will not be possible to consider the availability of a machine during the course of several hours in the same instance! This is of course unacceptable. If NH is a key to MACHINE-AVAIL then the availability of a single machine for a given hour could be stored in an instance!