[CAS] PART FUNCTION on sum of n terms

[compsystems]

Hello, the part function works fine, but there is a problem. If the expression is a sum of n terms (a+b+c+d+e+f+.... n), returns the number of terms, that make within a program, the expression parser will be dificultier

part( a + b + c + d + e + f +.... n) returns n

the TI68k calculators return in a group of two terms

PHP Code:

part( a + b + c + d + e + f +.... n)  => part( (a) +(b+c+d+e+f+.... n) ) returns 2
part( a + b + c + d + e + f +.... n, 1 )  => part( (a) +(b+c+d+e+f+.... n), 1 ) returns (a)
part( a + b + c + d + e + f +.... n, 2 )  => part( (a) +(b+c+d+e+f+.... n), 2 ) returns (b+c+d+e+f+.... n) 


when nested part (hp-prime), the sums expressions are difficult to control.

Is possible to reprogram the PART function that groups of two terms in a sum? as the ti68k

hp-prime
part( quote( 1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ) )
RETURNS 10

part( quote( 1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ), 2 )
RETURNS -1/2

TI89
part( quote( 1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ) ) =>
part(quote( (1/1) + (-1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10) ))
RETURNS 2


part( quote( 1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ), 1 )
RETURNS 1/1
part( quote( 1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ) , 2 )
RETURNS (-1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10)

Thanks

[parisse]

In short: no.
It's much better to have all arguments of + or * at the same level with a n-ary operator than to embedd some of them sometimes very deeply if + or * are binary, it reflects much better the structure of the expression (for example you can exchange two arguments easily).

[compsystems]

HP48 to HP50 also grouped the terms of addition and multiplication by twos

PHP Code:

« 0 0 { } -> EXPRESSION XPART NPARTS OPERATOR OBJECTS
  « EXPRESSION
    IFERR OBJ->
    THEN ->STR 'OPERATOR' STO 0 'NPARTS' STO OPERATOR 1 ->LIST 'OBJECTS' STO
    ELSE ->STR 'OPERATOR' STO 'NPARTS' STO NPARTS ->LIST 'OBJECTS' STO NPARTS OPERATOR OBJECTS 3 ->LIST DROP
    END
      IF XPART NPARTS <= XPART -1 >= AND NOT
      THEN "EXPRESSION " EXPRESSION + " CONTAINS ONLY " + NPARTS + " PARTS" +
      ELSE
        IF XPART 0 ==
        THEN OPERATOR
        ELSE
          IF XPART -1 ==
          THEN NPARTS
          ELSE OBJECTS XPART GET
          END
        END
      END
  »
»
'PART' STO 


'x^3-6*x^2+11*x-6' -1 PART @ returns 2 (parts)
'x^3-6*x^2+11*x-6' 0 PART @ returns "-"
'x^3-6*x^2+11*x-6' 1 PART @ returns '(x^3-6*x^2+11*x)'
'x^3-6*x^2+11*x-6' 2 PART @ returns 6
'x^3-6*x^2+11*x-6' 3 PART @ returns "EXPRESSION 'x^3-6*x^2+11*x-6' CONTAINS ONLY 2 PARTS"
'x^3-6*x^2+11*x-6' -3 PART @ returns "EXPRESSION 'x^3-6*x^2+11*x-6' CONTAINS ONLY 2 PARTS"

'X' -1 PART @ returns 0 (parts)
'X' OBJ->@ returns "ERROR" =(
'X^1' EVAL OBJ-> @ returns"ERROR" =(
'X^1' EVAL -1 PART @ returns 0 (parts)

'-X' -1 PART @ returns 1
'-X' 0 PART @ returns "NEG"
'-X' 1 PART @ returns 'X'

e -1 PART @ returns 0
e 0 PART @ returns "e"

pi -1 PART @ returns 0
pi 0 PART @ returns "pi"


'1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ' -1 PART @ returns 2
'1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ' 0 PART @ returns "+"
'1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ' 1 PART @ '-1/10 '
'1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9 + -1/10 ' 2 PART @ '1/1 + -1/2 + 1/3 + -1/4 + 1/5 + -1/6 + 1/7 + -1/8 + 1/9'

[parisse]

Correct. That's precisely because I knew the limitations of having binary + and * that I designed Giac with n-ary + and *. One of the limitation (that is perhaps not obvious on a calc) is to be able to handle sums with a very large number of arguments (for example 1 million). With binary + the last argument would be so much embedded that many symbolic operations would segfault because of stack overflow during recursion.

[Claudio L.]

(07-09-2016 08:03 AM)parisse Wrote:  Correct. That's precisely because I knew the limitations of having binary + and * that I designed Giac with n-ary + and *. One of the limitation (that is perhaps not obvious on a calc) is to be able to handle sums with a very large number of arguments (for example 1 million). With binary + the last argument would be so much embedded that many symbolic operations would segfault because of stack overflow during recursion.

I agree. Symbolics in newRPL also have n-ary + and * (there's no CAS yet, but the expression format and compiler/decompiler is finished). Much easier to scan for terms or factors in a flattened tree than a binary tree.