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Symbol | Definition | | |
---|---|---|

\lceil\; \rceil | CEIL, next higher integer. | | |

\lfloor\;\rfloor | FLOOR, next lower integer. | | |

\approx | approximately equal. | | |

>> | much greater than. | | |

! | factorial. | | |

# | number of. | | |

\log\sb{y}x | logarithm base y of x. | | |

\log{x} | natural logarithm of x, base e = 2.71828182846. | | |

\sum\sb{k}f(k) | sum of all f(k) for the integer k's specified}. | | |

xMODy | modulo function, x reduced by y until x< y. | | |

\jop | one of the comparison operators >\ge;=;\ne\;\le\;<. | | |

\and | and, true if both sides are true. | | |

\or | or, true if either side is true. | | |

| | where, precedes a conditional clause. | | |

\dbinter | set intersection. | | |

\dbunion | set union. | | |

\dbsetdif | set difference. | | |

\dbcross | cartesian product. | | |

\dbselect | select tuples from a relation. | | |

\dbproject | project attributes from a relation. | | |

\dbthetajoin{a = b} | join two relations based on equality of the attributes a, b. | | |

\refto | reference connection. | | |

\ownto | ownership connection. | | |

\subto | subset connection. | | |

\subset | subset of. | | |

\in | member of. | | |

\All | for all. | | |

\becomes | becomes. | | |

{ . . . } | enclose a set. | | |

[ . . . ] | enclose a reference. | | |

\propersubset | proper subset. | | |

Operation | Function | | |
---|---|---|

a + b | addition. | | |

a - b | subtraction. | | |

a * b | multiplication. | | |

a / b | division. | | |

MOD(a,b) | modulo, integer remainder of division. | | |

a ** b | exponentiation, a to the power b. | | |

a = b | depending on context in PL/1, assignment or equality comparison. | | |

a < b | greater than comparison, true if a greater than b. | | |

a> L{b} | greater or equal comparison, true if a greater or equal to b. | | |

a \AND b | and, true if both a, b true, (& in PL/1). | | |

a \OR b | or, true if either a, b true, (| in PL/1). | | |

\NT c | not, true if c false and vice versa. | | |

s \CAT w | catenation, string s connected to string w
to form a single new string. | | |

s | c | where, do s if the predicate (conditional) clause c is true. | | |

R \DBUNION S | union of relations R and S. | | |

R \DBINTER S | intersection of relations R and S. | | |

R \DBCROSS S | cross product of relations R and S. | | |

R \DBSETDIF S | difference, remove tuples matching S from R. | | |

\DBSELECT R.ex | select tuples of R according to expression ex. | | |

\DBPROJECT R.a | projection of attributes a of R. | | |

R.a\DBJOIN S.b | Join R and S, on equality of attribute values in a and b. | | |

R.a\DBOUTERJOIN S.b | Outerjoin including all tuples . | | |

, | field separator. | | |

\kg | key and goal fields separator. | | |

; | statement separator. | | |

. | termination of computational section. | | |

ss, ... | section ss may be repeated. | | |

[ ss ] | section ss is optional. | | |

{ ss|tt} | sections ss, tt are alternatives. | | |

::= | is defined by. | | |

/* Note */ | explanatory comments. | | |

a.b | qualification of variable b by a higher-level
variable a,\ie, employee.name. | | |

'Word' | character string constant. | | |

_ | (underline) pseudo-alphabetic character without syntactic meaning used for legibility within variable names, | | |

| In COBOL - is used for this function. | | |

Symbol | Brief definition | Text definition | | |
---|---|---|---|

A | average space required for attribute name | Sec. 3-1-3. | | |

a | number of different attributes in a file | Sec. 3-1-1. | | |

a\toprime | average number of attributes in a record | Sec. 3-1-1, 3-6-3. | | |

B | blocksize | Sec. 2-2. | | |

b | blockcount | Sec. 2-2-2. | | |

btt | block transfer time = B/t | Eq. 2-13. | | |

\Bfr | blocking factor \approx B/R | Eqs. 2-5, 2-6, 2-7, 2-20. | | |

C | Cost factors | Sec. 5-4-6, 5-5-2. | | |

c | computational overhead per record, when not negligible | Sec. 2-3-4. | | |

D | space required for data | Eq. 5-1, Sec 5-3-3. | | |

d | number of records that have been invalidated | Sec. 3-1-3. | | % |

e | = 2.718281828459. | | | |

\sbscr{F} | subscript denoting a fetch for a specific record | Sec. 3-0-2. | | |

G | space required for an interblock gap | Sec. 2-2-3. | | |

h | classification variable | Sec. 5-4-3. | | |

\sbscr{I} | subscript denoting insertion of a record | Sec. 3-0-2. | | |

j | number of cylinders | Sec. 2-2-1. | | |

K | projection list | Sec. 7-3-2. | | |

{\tbf K } | Kilo or thousand (1024) times. | | | |

k | number of tracks per cylinder | Sec. 2-2-5, Table 2-1. | | |

L | load frequency factors; selection list | Sec. 5-1; 7-3-3. | | |

M | multiprogramming factor | Eq. 5-19. | | |

{\tbf M } | Mega or million (1\,048\,576) times. | | | |

m | number of available slots for records | Sec. 3-5-1. | | |

\sbscr{N} | subscript denoting getting the next serial record | Sec. 3-0-2. | | |

n | number of records in a file | Sec. 3-1-3. | | |

o | number of records that overflow | Secs. 3-1-3, 3-2-3, 3-3-3, 3-5-3. | | |

P | space required for a pointer | Sec. 2-3-3. | | |

p | collision cost, also probability | Eqs. 3-73, 3-74, 3-79, Fig. 3-23. | | |

q | production demand by a file application | Eq. 5-2, 5-4 to 5-6. | | |

R | space required for a complete record; relation | Sec. 3-0-2; 7-1-1. | | |

\sbscr{RW} | subscript indicating rewriting | Sec. 2-3-6. | | |

r | rotational latency time | Eq. 2-3. | | |

SI | storage space for index | Eq. 3-52. | | |

s | average seek time | Eq. 2-2. | | |

s\toprime | effective seek time | Eqs. 2-15, 2-16. | | |

T | the time required for various operations; set of tuples | Sec. 3-0-2; 7-3. | | |

T\sb{sort} | the time required to sort a file | Eq. 3-11} . | | |

t | transfer rate from a storage unit to processing memory | Sec. 2-2-5. | | |

t\toprime | bulk transfer rate | Eqs. 2-17, 2-18, 2-19. | | |

\sbscr{U} | subscript denoting an update of a record | Sec. 3-0-2. | | |

u | utilization | Eqs. 5-3, 5-7 to 5-18, 5-20. | | |

uf | utilization factor | Eqs. 6-25, 6-29. | | |

V | average space for value part of an attribute | Sec. 3-1-3. | | |

v | number of records updated | Sec. 3-2-3. | | |

w | wait time in queues | Eq. 6-26. | | |

W | wasted space due to gaps per record | Eqs. 2-9, 2-10, 2-11, 2-21. | | |

\sbscr{X} | subscript denoting an exhaustive search | Sec. 3-0-2. | | |

x | number of levels in an index structure, master level | Eq. 3-27, 3-49, 3-97. | | |

\sbscr{Y} | subscript denoting a reorganization of a file | Sec. 3-0-2. | | |

y | fanout ratio | Eq. 3-26, 3-48. | | |

\sbscr{Z} | subscript denoting an update by replacement with a larger record | Sec. 3-0-2. | | |