4.7.5 boolean expressions
A boolean expression is an int expression used in a logical context:
An int expression <> 0 evaluates to TRUE (represented by 1),
0 evaluates to FALSE (represented by 0).
The following is the list of available comparisons of objects of the same type.
Note: There are no comparisons for ideals and modules, resolutions
and maps.
-
integer comparisons:
| i == j
i != j // or i <> j
i <= j
i >= j
i > j
i < j
|
-
number comparisons:
| m == n
m != n // or m <> n
m < n
m > n
m <= n
m >= n
| For numbers from Z/p or from field extensions not all operations are useful:
- 0 is always the smallest element,
- in Z/p the representatives in the range -(p-1)/2..(p-1)/2 when p>2 resp.
0 and 1 for p=2 are used for comparisons,
- in field extensions the last two operations
(>=,<= ) yield always TRUE (1) and
the < and > are equivalent to != .
-
polynomial or vector comparisons:
| f == g
f != g // or f <> g
f <= g // comparing the leading term w.r.t. the monomial order
f < g
f >= g
f > g
|
-
intmat or matrix comparisons:
| v == w
v != w // or v <> w
|
-
intvec or string comparisons:
| f == g
f != g // or f <> g
f <= g // comparing lexicographically
f >= g // w.r.t. the order specified by ASCII
f > g
f < g
|
-
boolean expressions combined by boolean operations (
and ,
or , not )
Note:
All arguments of a logical expression are first evaluated and
then the value of the logical expression is determined. For example, the
logical expression (a || b) is evaluated by first evaluating
a and b , even though the value of b has no
influence on the value of (a || b) , if a evaluates to
true.
Note that this evaluation is different from the left-to-right, conditional
evaluation of logical expressions (as found in most programming
languages). For example, in these other languages, the value of (1
|| b) is determined without ever evaluating b .
See Major differences to the C programming language.
|