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[CAS] listLCM Help - compsystems - 09-22-2016 09:49 PM
Hello Earthlings =)
listLCM is a recursive function to calculate the least common multiple (LCM) of a list of integers numbers, using the internal function of the CAS LCM
/!\ The HP-PRIME CAS is limited to 100 recursions =(
listLCM(arg) Where the function accepts as argument a vector [...] or a list {...}
Code:
#cas
listLCM(lst):=
BEGIN
print(""); print([type(lst),TYPE(lst)]); halt;
if not(TYPE(lst)==6 or type(lst)==DOM_LIST or TYPE(lst)==4) then
return( [ "Error: /!\\ Invalid Data Type", lst ] );
end;
if dim(lst)==0 then
return( [ "Error: Bad Argument type. Empty list", lst ] );
end;
if dim(lst)==1 then
return( lst[1] );
end;
if dim(lst)>100 then
return( [ "/!\\ Maximum recursion: 100 elements" , lst ]);
end;
if dim(lst)==2 then
return( lcm(lst[1],lst[2]) );
end;
if dim(lst)≥3 then
// return( listLCM(concat({lcm(lst[1],lst[2])},right(lst,dim(lst)-2) ) ) );
return( listLCM(concat({lcm(lst[1],lst[2])},tail(tail(lst)) ) ) );
end;
END;
#endlistLCM({}); returns [ "Error: Bad Argument type. Empty list",{} ] OK
listLCM([]); returns [ "Error: Bad Argument type. Empty list",[] ] OK
listLCM("abc"); returns ["Error: /!\ Invalid Data Type","abc"] OK
listLCM({1,2,3}); returns 6 // OK
listLCM({1,2,3,4}); returns 12 // OK
listLCM({x-1,x-2}); returns x^2-3*x+2 // ok
listLCM({x-1,x-2,x-3}) ; returns x^3-6*x^2+11*x-6 // ok
listLCM({x-1,x-2,x-3,x-3,x-3}) ; returns x^3-6*x^2+11*x-6 // ok
listLCM({x-1,x-2,x-3,x-4}) ; returns x^4-10*x^3+35*x^2-50*x+24 // ok
listLCM([1,2,3,4,5]); returns 60 // ok
Now generating vectors, lists, and matrices with commands
lst0:=MAKELIST(I,I,1,100,1) ->{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100}
[type(lst0),TYPE(lst0)]; returns [DOM_LIST,6]
listLCM(lst0); returns 69720375229712477164533808935312303556800 OK
lst1:=(MAKEMAT(abs(I-J)+1,1,100))[1]; returns [1,2,3,...,96,97,98,99,100]
[type(lst1),TYPE(lst1)]; returns [DOM_LIST,4]
listLCM(lst1); returns 69720375229712477164533808935312303556800 OK
lst2:=seq(k,k,1,100); returns [1,2,3,...,96,97,98,99,100]
[type(lst2),TYPE(lst2)]; returns [DOM_LIST,4]
listLCM(lst2); returns 69720375229712477164533808935312303556800 OK
lst2a:=seq(k,k,1,101,1) ; returns [1,2,3,4,5, ..., 101]
listLCM(lst2a); returns "/!\ Maximum recursion: 100" OK
Using the double dot operator (..) on seq cmd
lst3:=seq(k, k = 1 .. 100,1); returns
[ 1,2,3,...,96,97,98,99,100 ]
with conteiners [ ] on the history view
now, goto the entry line
[^](key up) {copy} (menu), disappear the conteiners [] WHY?
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100
type(lst3); returns DOM_LIST
dim(lst3); returns 100 // objet list of 100 elements
RE: [CAS] listLCM Help - zahi48g - 09-22-2016 10:45 PM
Try MAKELIST(K,K,1,99,1), the output will be a list ,not a vector then lcm will work .
RE: [CAS] listLCM Help - toshk - 09-22-2016 10:51 PM
without the container [], {} your are inputting a bunch of arguments into the function call which is intended for a single input argument or (passing max intended arguments) for a function . the arguments will fail your test.
typo in the first input: listLCM(list1)---> shd be lst1.
it works with listLCM(lst1)
RE: [CAS] listLCM Help - compsystems - 09-23-2016 01:53 PM
(09-22-2016 10:45 PM)zahi48g Wrote: Try MAKELIST(K,K,1,99,1), the output will be a list, not a vector then lcm will work .
OK, I have adhered to the code TYPE(lst)==4 for support vectors, please check the code updated above
Now appears the following: Using the double dot operator (..) on SEQ CMD, works to 97 elements, but the maximum number of recursion is 100, therefore, why not operate between 98..100?
lst3:=seq(k,k = (1 .. 101), 1)
listLCM(lst3) -> error // OK
lst4:=seq(k,k = (1 .. 100), 1)
listLCM(lst4) -> error WHY?
lst4a:=seq(k,k = (1 .. 99), 1)
listLCM(lst4a) -> error WHY?
lst4b:=seq(k,k = (1 .. 98), 1)
listLCM(lst4b) -> error WHY?
lst5:=seq(k,k = (1 .. 97), 1) ->
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97
listLCM(lst5) -> 69720375229712477164533808935312303556800
RE: [CAS] listLCM Help - zahi48g - 09-23-2016 04:58 PM
Hi
I'm not an expert !
I am here to learn . I said "Try " !!
To me , as the output of seq uses square-bracket , I would rather use MAKELIST whose output uses curved bracket . But I've checked , and you may be right since lcm uses any type of bracket so I can't be more helpful .