Maxima Function
some (f, a)
some(f,L_1,...,L_n)
Returns true if the predicate f is true for one or more given arguments.
Given one set as the second argument,
some(f, s) returns true
if is(f(a_i)) returns true for one or more a_i in s.
some may or may not evaluate f for all a_i in s.
Since sets are unordered,
some may evaluate f(a_i) in any order.
Given one or more lists as arguments,
some(f, L_1, ..., L_n) returns true
if is(f(x_1, ..., x_n)) returns true
for one or more x_1, ..., x_n in L_1, ..., L_n, respectively.
some may or may not evaluate
f for some combinations x_1, ..., x_n.
some evaluates lists in the order of increasing index.
Given an empty set {} or empty lists [] as arguments,
some returns false.
When the global flag maperror is true, all lists
L_1, ..., L_n must have equal lengths.
When maperror is false, list arguments are
effectively truncated to the length of the shortest list.
Return values of the predicate f which evaluate (via is)
to something other than true or false
are governed by the global flag prederror.
When prederror is true,
such values are treated as false.
When prederror is false,
such values are treated as unknown.
Examples:
some applied to a single set.
The predicate is a function of one argument.
(%i1) some (integerp, {1, 2, 3, 4, 5, 6}); (%o1) true (%i2) some (atom, {1, 2, sin(3), 4, 5 + y, 6}); (%o2) true
some applied to two lists.
The predicate is a function of two arguments.
(%i1) some ("=", [a, b, c], [a, b, c]); (%o1) true (%i2) some ("#", [a, b, c], [a, b, c]); (%o2) false
Return values of the predicate f which evaluate
to something other than true or false
are governed by the global flag prederror.
(%i1) prederror : false; (%o1) false (%i2) map (lambda ([a, b], is (a < b)), [x, y, z], [x^2, y^2, z^2]); (%o2) [unknown, unknown, unknown] (%i3) some ("<", [x, y, z], [x^2, y^2, z^2]); (%o3) unknown (%i4) some ("<", [x, y, z], [x^2, y^2, z + 1]); (%o4) true (%i5) prederror : true; (%o5) true (%i6) some ("<", [x, y, z], [x^2, y^2, z^2]); (%o6) false (%i7) some ("<", [x, y, z], [x^2, y^2, z + 1]); (%o7) true