7.16 SELECT Operator
The select operator extracts from a list, or from the arguments of an n–ary
operator, elements corresponding to a boolean predicate. It is used with the
syntax:
select(\(\langle \)fnc:function\(\rangle \), \(\langle \)lst:list\(\rangle \))
fnc can be one of the following forms:
-
1.
- the name of an operator with a single argument: the operator is evaluated
once on each element of lst;
-
2.
- an algebraic expression with exactly one free variable, i.e. a variable
preceded by the tilde symbol. The expression is evaluated for each element
of \(\langle \)lst\(\rangle \), with the element substituted for the free variable;
-
3.
- a replacement rule of the form \(\langle \)var\(\rangle \) =>\(\langle \)rep\(\rangle \) where \(\langle \)var\(\rangle \) is a variable (a kernel
without subscript) and \(\langle \)rep\(\rangle \) is an expression that contains \(\langle \)var\(\rangle \). \(\langle \)rep\(\rangle \) is evaluated
for each element of LST with the element substituted for \(\langle \)var\(\rangle \). \(\langle \)var\(\rangle \) may be
optionally preceded by a tilde.
The rule form for fnc is needed when more than one free variable occurs.
The result of evaluating fnc is interpreted as a boolean value corresponding to the
conventions of REDUCE. These values are composed with the leading operator of the
input expression.
Examples:
select( ~w>0 , {1,-1,2,-3,3}) -> {1,2,3}
select(evenp deg(~w,y),part((x+y)^5,0):=list)
-> {X^5 ,10*X^3*Y^2 ,5*X*Y^4}
select(evenp deg(~w,x),2x^2+3x^3+4x^4)
-> 4X^4 + 2X^2
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