Lists.wxm

/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 22.04.0 ] */
/* [wxMaxima: input   start ] */
/* Date: Sun Oct 18 09:41:19 WEST 2015 */
/* Contributor: Marco Verpelli */
/* Description: Code for retrieving the nth element of a list (the "else last(l)" can be ommitted putting <= instead of <) */
nth(l, n) := if n < length(l) then first(rest(l, n-1)) else last(l);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Mon Feb 17 03:07:15 WET 2003 */
/* Contributor: Stavros Macrakis */
/* Description: applies for all */
forall(func,list) := apply("and",map(func,list))$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Sun Dec 7 18:31:31 WET 2003 */
/* Contributor: Stavros Macrakis */
/* Description: returns the n first terms of the list l */
firstn(l,n):=rest(l,n-length(l))$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Sun Dec 7 18:44:22 WET 2003 */
/* Contributor: Richard Fateman */
/* Description: returns the  terms of the list k between indices r+1 and s */
listheader: ?car([])$
f(k,r,s):=block(
    [simp:off],
    ?cons(listheader,?subseq(?cdr(k),r,s))
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Fri Dec 26 17:44:36 WET 2003 */
/* Contributor: Stavros Macrakis */
/* Description: copies a list */
copyall(l):=if listp(l) then map('copyall,l) else l$
copyallall(l):=block(
    [inflag:true],   /* operate on internal forms */
    if atom(l) or subvarp(l) then l 
    else funmake(copyallall(part(l,0)),map('copyallall,args(l)))
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: 2017-07-10 15:38:43 UTC */
/* Contributor: Stavros Macrakis */
/* Description: returns a set with the duplicated elements of the list l */
dups(l) :=block(
    [res : []],
    while l # [] do (
        if member(first(l), rest(l)) then push(first(l), res),
        l : rest(l)
    ),
    setify(res)
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: 2017-07-10 15:38:43 UTC */
/* Contributor: Stavros Macrakis */
/* Description: returns a list with the duplicated elements of the list l */
dups(l) :=block(
    [dups:[],counts],
    local(counts),
    counts[x]:=0,
    for i in l do counts[i]: counts[i]+1,
    for i in rest(arrayinfo(counts),2) do if counts[first(i)]>1 then push(first(i),dups),
    dups
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Wed May 19 21:12:31 WEST 2010 */
/* Contributor: Piotr Słomski */
/* Description: Intended implementation of Mathematica tuples */
Tuples(S, N):=block(
    K:length(S),
    counter:create_list(1, i, 1, N),
    res:[create_list(S[counter[i]],i,1,N)],
    for i:1 thru K^N-1 do (
        counter[1]:counter[1]+1,
        for j:1 thru N-1 do (
            if counter[j]>K then (
                counter[j]:1,
                counter[j+1]:counter[j+1]+1
            ) else (
                return
            )
        ),
        res:append(res, [create_list(S[counter[i]],i,1,N)])
    ),
    res
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Thu May 20 17:44:38 WEST 2010 */
/* Contributor: Mario Rodriguez */
/* Description: Intended implementation of Mathematica tuples */
tuples(lis, n) :=block(
    [ len_lis, aux_lis, aux_set, cart_prod],
    len_lis : length(lis),
    aux_lis : makelist(?gensym(),k,1,len_lis),
    aux_set : setify(aux_lis),
    cart_prod : apply(cartesian_product, makelist(aux_set,k,1,n)),
    subst(map("=", aux_lis, lis), listify(cart_prod))
) $
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Wed Dec 11 03:57:16 WET 2002 */
/* Contributor: Stavros Macrakis */
/* Description: Filters a list with respect to a predicate (as sublist does) */
filter(f,l):=if l=[] then [] 
elseif f(first(l)) then cons(first(l),filter(f,rest(l))) 
else filter(f,rest(l))$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Tue Dec 9 21:52:46 WET 2003 */
/* Contributor: Richard Fateman */
/* Description: Filters a list with respect to a predicate (as sublist does) */
selectif(pred,set):= if set=[] then set 
else if pred(first(set)) then cons(first(set),selectif(pred,rest(set))) 
else selectif(pred,rest(set))$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Fri Aug 4 17:06:41 WEST 2006 */
/* Contributor: Richard Fateman */
/* Description: Filters a list with respect to a predicate (as sublist does) */
filter(l,pred):= if (l=[]) then [] 
else if pred(first(l)) then cons(first(l),filter(rest(l),pred)) 
else filter(rest(l),pred)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: 20/03/2014 */
/* Contributor: Pankaj Sejwal */
/* Description: Tries to return the entries and the indexes that satisfies a predicate for first and single time */
takewhile(x,p):=block(
    [s:1,temp:[],temp1:[],count:1,xx:create_list([x[i],i],i,makelist(i,i,length(x)))],
    for i in xx do if apply(p,[first(i)])  then temp:cons(i,temp),
    temp:reverse(temp),
    if (length(temp)>=2 and flatten(temp)#[]) then (
        while(last(temp[s])+1=last(temp[s+1]) and count<=length(temp)) do (
            temp1:cons(temp[s],temp1),
            count:count+1,
            s:s+1
        ),
        if (s<length(temp)) then temp1:cons(temp[s],temp1)
    ) 
    else temp1:temp,
    reverse(temp1)
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: 20/03/2014 */
/* Contributor: Pankaj Sejwal */
/* Description: Tries to return the entries and the indexes that satisfies a predicate for first and single time */
takewhile1(x,p):=block(
    [s:1,temp:[],temp1:[],count:1,xx:create_list([x[i],i],i,makelist(i,i,length(x)))],
    for i in xx do (if parse_string(concat(first(i),p))  then temp:cons(i,temp)),
    temp:reverse(temp),
    if(length(temp)>=2 and flatten(temp)#[]) then (
        while (last(temp[s])+1=last(temp[s+1]) and count<=length(temp)) do (
            temp1:cons(temp[s],temp1),
            count:count+1,
            s:s+1
        ),
        if(s<length(temp)) then temp1:cons(temp[s],temp1)
    )
    else temp1:temp,
    reverse(temp1)
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Mon Aug 29 01:28:25 WEST 2005 */
/* Contributor: Richard Fateman  */
/* Description: it is similar to lreduce */
dominate(fun,list,default):=if emptyp(list) then default else dominate(fun,rest(list),fun(first(list),default));
/* [wxMaxima: input   end   ] */



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