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By Kenneth E. Iverson

ISBN-10: 0471430145

ISBN-13: 9780471430148

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Mapping is not, in general, commutative. Mapping is extended to Inatrices as follows: Ji = Mil' J h Bi , MJJII B<=:>Cj = MjJh B j . A ~ M JrII B<=:>Ai C~ Rowand column mappings are associative. A row mapping 1M and a column mapping 2M do not, in general, commute, but do if all rows of 1M agree (that is, 1M = e p), and if all columns of 2M agree (that is, 2M = q ~ e). The generalized matrix product is defined for the cases 0 o J A, and 0 M Ja. , m A ~ B n1 <=:> Ai = B,ni' Permutations A vector k of dimension n is called a j-origin per/nutation rector if k == lj(n).

The four output lists will be denoted by the Illatrices P, Q, R, and S, respectively. 9. 9. Since L 3 is the vector of balances, and 2€ is a conlpatible vector each of whose conlponents equals two, the relational statenlent (L: 3 2€) defIIles a logical vector having unit conlponents corresponding to those accounts to be 1 2 3 4 ~ P +-(L 3 < 2 €)jjL Q R S +++- L kth account. (L 3 < -100 €)jjL L 3k (L 3 > 1000 €)jja 2/L (L 1 = none €)j/€2/L Bank ledger. Balance of kth account. Account number of kth account.

This denotes a branch to statement nunlber Si of the program if the relation The paranleters rand S may themselves be defined and re­ defined in other parts of the prograITI. IJ holds. 3 Structure (~f the language 7 statenlent s. 6. More generalIy~ two or rnore otherwise independent progranls may interact through a statenlent in one progranl specifying a branch in a second. The statenlent nunlber occurring in the branch rllust then be augrnented by the name of the progranl in which the branch is effected.

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A Programming Language. by Kenneth E. Iverson

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