By Kenneth E. Iverson
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Extra resources for A Programming Language.
The catenation of vectors x, y, ... , z is denoted by x y z and is defined by the relation x y EB ... EB z == (Xl' x 2, ... , XJ'(X)' YI' Y2' ... , ZI'(Z))' Catenation is clearly associative and for two vectors x and y it is a special case of the mesh \x, u, y\ in which u is a suffix vector. 9 In nunlerical vectors (for which addition of two vectors is defIned), the effect of the general nlesh operation can be prod uced as the sunl of two nleshes~ each involving one zero vector. Specifically~ \,x~ u~ y\\ == \x~ U~ == \O~ Ii, 0\ + \O~ U~ y\ x\ + \0, U, y\.
3 The language appear. Moreover, in a computer program, numeric symbols (register addresses) are used to represent the variables. In general, then, alphabetic literals, alphabetic variables, numeric literals, and nunleric variables may all appear in a complex process and must be clearly differentiated. The symbols used for literals will be roman letters (enclosed in quotes when appearing in text) and standard numerals. 8. Miscellaneous signs and symbols when used as literals will be enclosed in quotes in both programs and text.
The rOll' cOfnpressiol1 VIA selects clernents of A corresponding to the nonzero elenlents of V. Since the nonzero elenlcnts of V nlay occur in an arbitrary pattern, the result nl ust be construed as a vector rather than a nlatrix. More precisely, VI A denotes the catenation of the vectors V) Ai obtained by row-by-row compression of A by V. 9 The language The colunln conlpressiol1 V II A denotes the catenation of the vectors VJ! A j. ")l, A 12, A 22, A 2a, A:3:3), and VilA == (A]2, A 21, A~2, A 2:3, Aaa, A4 1, A;)l).