Polynomial with real coefficients —> array w/ real coeff
11-22-2021, 03:09 PM (This post was last modified: 11-24-2021 12:21 AM by Gil.)
Post: #1
 Gil Senior Member Posts: 637 Joined: Oct 2019
Polynomial with real coefficients —> array w/ real coeff
I could not find a suitable program to get the real coefficients of a polynomial in form of an array.

So I prepared one, indeed somewhat "bulky", but working smoothly.

As the variable of the polynomial may already be defined in the current directory, the program changes its original name in the expression into another weird dummy variable X__, to be itself transformed back, at the end, to its original name after adequate string manipulations.

Enter for example
'2*(t+4*(5+10))-7*t^6'

Press P—>ARR

To get
'2*(t+4*(5+10))-7*t^6' (original expression in stack level 2)
'-7*t^6+2*t+120' (simplified expression in stack level 1)
:[ana0]: [ -7 0 0 0 0 2 120 ] (coefficients requested with label).

The program will also detect incorrect similar variable names and give a corresponding message warning (as only 1 variable is allowed).

Regards,
Gil Campart

Attached File(s)
11-22-2021, 05:12 PM
Post: #2
 Albert Chan Senior Member Posts: 2,705 Joined: Jul 2018
RE: Polynomial with real coefficients
Hi, Gil

This may be what you wanted.

(10-26-2020 04:25 PM)Albert Chan Wrote:
(10-24-2020 02:03 PM)John Keith Wrote:  'X^5-19*X^4+79*X^3+146*X^2-1153*X+1222'

Is there a command to convert this symbolic polynomial form to an array

XCas has symy2poly, but I can't find one for HP50G

XCas> symb2poly((x+1)*(x+2)*(x+3)) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → poly1[1, 6, 11, 6]

Code:
≪ 0 OVER DEGREE → D    ≪ 3. DUP D + FOR k HORNER k ROLLD NEXT       + + D 1 + →ARRY    ≫ ≫

Save above to, say, PARRY

hp50g> '(X+1)*(X+2)*(X+3)'
hp50g> PARRY ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → [1 6 11 6]
hp50g> PROOT ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → [-1. -2. -3.]

hp50g> 'X^5-19*X^4+79*X^3+146*X^2-1153*X+1222'
hp50g> PARRY ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → [1 -19 79 146 -1153 1222]
11-22-2021, 05:51 PM (This post was last modified: 11-22-2021 06:56 PM by Gil.)
Post: #3
 Gil Senior Member Posts: 637 Joined: Oct 2019
RE: Polynomial with real coefficients
Your given code : great and most compact.
Incredible!

But it does not work for non integers coefficients an to a0 in a polynomial like

'an × X^n
+...
+a0 × X^0'.

Finally, both methods, now, with the correct coefficients, do give the correct answers, as expected.

Here is my corrected version 2a of P—>ARRAY.

Regards,
Gil

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11-23-2021, 11:23 AM (This post was last modified: 11-23-2021 01:44 PM by Gil.)
Post: #4
 Gil Senior Member Posts: 637 Joined: Oct 2019
RE: Polynomial with real coefficients
Version 2b

As a special "polynomial", now you can introduce such non simplified expressions
'2*x-2*x',
'3*x-x^2+4-x^2-4+-3*x' and alike always equal to zero.

The output will be, for the first one:
'2*x-2*x' (original input expression at stack level 3)
0 (simplified, "cleanest" expression, here always without a dot, at stack level 2)
an...a0: [0] (smallest possible array, here always without a dot, with a tag label, at stack level 1).

This version, as the previous one, accepts, as input, just a variable name (then never evaluated), existing or not in the directory, or only one or several real/integer numbers.

't' P—>ARR returns
't' (original input expression, here the variable t, in stack level 3)
't' (simplified, cleanest" expression, but never evaluated for a single variable, here then the variable name t again)
an...a0: [1 0] (smallest possible array, with a tag label, at stack level 1).

'120-20.' P—>ARR returns
'120-20.' (original input expression in stack level 3)
100 (simplified expression/value, if possible without a dot like here, in stack level 2)
an...a0: [100] (smallest possible array, if possible without dots like here, with a tag label, at stack level 1).

'0.' P—>ARR returns
0. (original input expression/value in stack level 3)
0 (simplified expression/value in stack level 2, if possible without a dot like here)
an...a0: [0] (smallest possible array, if possible without a dot like here, with a tag label).

Just in case, here is the full code:

\<< "\[] Version 2b
2021.11.23

\[] 1 ALG Arg (''):

'(ai*X^i +) *
+
+ (ak*X^k +) *  + '

\[] Order not important
\[] ai, ak : reals
\[] i, k : integers
existing! or not)
\[] By default: Polynom.
degree is n.MAX=15
(to change it: 1st
instruction after
DROP, 6 lines below)

\[] Output:
[an an-1a0], an \=/ 0

" DROP 15 RCLF 0 0 0 0 \-> d.MAX fg s STR p v
\<< DUP d.MAX XQ 'd.MAX' STO LVAR DUP TYPE 5 \=/
IF
THEN DUP OBJ\-> OBJ\-> DROP XQ \-> nv
\<< nv 1 >
IF
THEN nv \->LIST \->STR nv "Here " SWAP + " var
" + SWAP + ":

Use only 1 !" + SWAP ROT DROP2 DOERR
END
\>> SWAP DROP "" + 'v' STO \->STR v "X\175\175" SREPL DROP OBJ\-> -105 SF EXPAND -105 CF \->STR "+-" "-" SREPL DROP "-(" "+" SREPL 0 >
IF
THEN ")" "" SREPL DROP "E-" "E\175" SREPL DROP "-" "\175\|>" SREPL DROP "+" "-" SREPL DROP "\175\|>" "+" SREPL DROP "E\175" "E-" SREPL DROP
END ".+" "+" SREPL DROP ".-" "-" SREPL DROP ".*" "*" SREPL DROP ".'" "'" SREPL DROP "\|>" + ".\|>" "" SREPL DROP "\|>" "" SREPL DROP DUP "X\175\175" v SREPL DROP OBJ\-> SWAP "+X\175\175" "+1*X\175\175" SREPL DROP "-X\175\175" "-1*X\175\175" SREPL DROP "'X\175\175" "'+1*X\175\175" SREPL DROP "'" "" SREPL DROP DUP SIZE 's' STO 'STR' STO { } d.MAX 2 XQ
FOR i STR "^" i + POS 'p' STO p 0 \=/
IF
THEN STR 1 p 5 - SUB OBJ\-> STR p i \->STR SIZE + 1 + s SUB DUP SIZE 's' STO 'STR' STO
ELSE 0
END + -1 XQ
STEP STR DUP "X" POS DUP 'p' STO 2 - 1 SWAP SUB DUP "" \=/
IF
THEN OBJ\->
ELSE DROP 0
END + STR p DUP 0 \=/ 3 1 IFTE + s SUB DUP "" \=/
IF
THEN OBJ\->
ELSE DROP 0
END + DUP SIZE { 0 } \-> l s l0
\<< 1 d.MAX 1 +
FOR i l i GET 0 \=/
IF
THEN l 'l0' STO d.MAX 1 + 'i' STO
END
NEXT l0 l SAME
IF
THEN
REPEAT l0 TAIL 'l0' STO
END
END l0 OBJ\->
\>>
ELSE DROP EVAL \->STR "'" + ".'" "" SREPL DROP OBJ\-> DUP 1
END \->ARRY "[ana0]" \->TAG fg STOF
\>>
\>>

Other format (with non readable characters ):

« " Version 2b
2021.11.23

 1 ALG Arg (''):

'(ai*X^i +) *
+
+ (ak*X^k +) *  + '

 Order not important
 ai, ak : reals
 i, k : integers
existing! or not)
 By default: Polynom.
degree is n.MAX=15
(to change it: 1st
instruction after
DROP, 6 lines below)

 Output:
[an an-1a0], an  0

" DROP 15 RCLF 0 0 0 0  d.MAX fg s STR p v
« DUP d.MAX XQ 'd.MAX' STO LVAR DUP TYPE 5 
IF
THEN DUP OBJ OBJ DROP XQ  nv
« nv 1 >
IF
THEN nv LIST STR nv "Here " SWAP + " var
" + SWAP + ":

Use only 1 !" + SWAP ROT DROP2 DOERR
END
» SWAP DROP "" + 'v' STO STR v "X¯¯" SREPL DROP OBJ -105 SF EXPAND -105 CF STR "+-" "-" SREPL DROP "-(" "+" SREPL 0 >
IF
THEN ")" "" SREPL DROP "E-" "E¯" SREPL DROP "-" "¯" SREPL DROP "+" "-" SREPL DROP "¯" "+" SREPL DROP "E¯" "E-" SREPL DROP
END ".+" "+" SREPL DROP ".-" "-" SREPL DROP ".*" "*" SREPL DROP ".'" "'" SREPL DROP "" + "." "" SREPL DROP "" "" SREPL DROP DUP "X¯¯" v SREPL DROP OBJ SWAP "+X¯¯" "+1*X¯¯" SREPL DROP "-X¯¯" "-1*X¯¯" SREPL DROP "'X¯¯" "'+1*X¯¯" SREPL DROP "'" "" SREPL DROP DUP SIZE 's' STO 'STR' STO { } d.MAX 2 XQ
FOR i STR "^" i + POS 'p' STO p 0 
IF
THEN STR 1 p 5 - SUB OBJ STR p i STR SIZE + 1 + s SUB DUP SIZE 's' STO 'STR' STO
ELSE 0
END + -1 XQ
STEP STR DUP "X" POS DUP 'p' STO 2 - 1 SWAP SUB DUP "" 
IF
THEN OBJ
ELSE DROP 0
END + STR p DUP 0  3 1 IFTE + s SUB DUP "" 
IF
THEN OBJ
ELSE DROP 0
END + DUP SIZE { 0 }  l s l0
« 1 d.MAX 1 +
FOR i l i GET 0 
IF
THEN l 'l0' STO d.MAX 1 + 'i' STO
END
NEXT l0 l SAME
IF
THEN
REPEAT l0 TAIL 'l0' STO
END
END l0 OBJ
»
ELSE DROP EVAL STR "'" + ".'" "" SREPL DROP OBJ DUP 1
END ARRY "[ana0]" TAG fg STOF
»
»

Attached File(s)
11-24-2021, 03:02 PM
Post: #5
 Gil Senior Member Posts: 637 Joined: Oct 2019
RE: Polynomial with real coefficients —> array w/ real coeff
Version 2c

Deletion of some unnecessary instructions.

Attached File(s)
11-27-2021, 03:33 PM (This post was last modified: 11-27-2021 03:42 PM by Gil.)
Post: #6
 Gil Senior Member Posts: 637 Joined: Oct 2019
RE: Polynomial with real coefficients —> array w/ real coeff
Suppose you execute RCLVX
(to get the current variable)

and you get the variable name 't'.

Suppose that somewhere the 't' variable was already defined, then you will be requested, in the previous program version, to delete that variable 't'.

The question/request might be confusing and there is indeed no reason to delete that variable right now.

That's the purpose of changing, provisory, the current working variable VX into Y__. See then, right below, the added part in bold:

\<< "\[] Long Version 2g
(w/ use of strings)

2021.11.27

\[] 1 ALG Arg (''):

'(ai*X^i +) *
+
+ (ak*X^k +) *  + '

\[] Order not important
\[] ai, ak : reals
\[] i, k : integers
existing! or not)
\[] By default: Polynom.
degree is n.MAX=15
(to change it: 1st
instruction after
DROP, 6 lines below)

\[] Output:
[an an-1a0], an \=/ 0

" DROP 15 RCLF 0 0 0 0 \-> d.MAX fg s STR p v
\<< DUP d.MAX XQ 'd.MAX' STO LVAR DUP TYPE 5 \=/
IF
THEN DUP OBJ\-> OBJ\-> DROP XQ \-> nv
\<< nv 1 >
IF
THEN nv \->LIST \->STR nv "Here " SWAP + " var
" + SWAP + ":

Use only 1 !" + SWAP ROT DROP2 DOERR
END
\>> SWAP DROP "" + 'v' STO \->STR v "X\175\175" SREPL DROP OBJ\-> RCLVX DUPDUP \-> vx
\<< EVAL SAME NOT
IF
THEN 'Y\175\175' STOVX
END -105 SF EXPAND vx STOVX
\>>
-105 CF \->STR "+-" "-" SREPL DROP "-(" "+" SREPL 0 >
IF
THEN ")" "" SREPL DROP "E-" "E\175" SREPL DROP "-" "\175\|>" SREPL DROP "+" "-" SREPL DROP "\175\|>" "+" SREPL DROP "E\175" "E-" SREPL DROP
END ".+" "+" SREPL DROP ".-" "-" SREPL DROP ".*" "*" SREPL DROP ".'" "'" SREPL DROP DUP "X\175\175" v SREPL DROP OBJ\-> SWAP "+X\175\175" "+1*X\175\175" SREPL DROP "-X\175\175" "-1*X\175\175" SREPL DROP "'X\175\175" "'+1*X\175\175" SREPL DROP "'" "" SREPL DROP DUP SIZE 's' STO 'STR' STO { } d.MAX 2 XQ
FOR i STR "^" i + POS 'p' STO p 0 \=/
IF
THEN STR 1 p 5 - SUB OBJ\-> STR p i \->STR SIZE + 1 + s SUB DUP SIZE 's' STO 'STR' STO
ELSE 0
END + -1 XQ
STEP STR DUP "X" POS DUP 'p' STO 2 - 1 SWAP SUB DUP "" \=/
IF
THEN OBJ\->
ELSE DROP 0
END + STR p DUP 0 \=/ 3 1 IFTE + s SUB DUP "" \=/
IF
THEN OBJ\->
ELSE DROP 0
END + DUP SIZE { 0 } \-> l s l0
\<< 1 d.MAX 1 +
FOR i l i GET 0 \=/
IF
THEN l 'l0' STO d.MAX 1 + 'i' STO
END
NEXT l0 l SAME
IF
THEN
REPEAT l0 TAIL 'l0' STO
END
END l0 OBJ\->
\>>
ELSE DROP EVAL \->STR "'" + ".'" "" SREPL DROP OBJ\-> DUP 1
END \->ARRY "[ana0]" \->TAG fg STOF
\>>
\>>

As it appears, this version is quite heavy.

A simpler/compacter version 3a is shown below,
with as output the initial argument and the final, resulting array.

\<< "\[] Compact Version 3a
(no use of strings)

2021.11.24

\[] 1 ALG Arg (''):

'(ai*X^i +) *
+
+ (ak*X^k +) *  + '

\[] Order not important
\[] ai, ak : reals
\[] i, k : integers
existing! or not)

\[] Output:
[an an-1a0]

" DROP RCLF 0 \-> fg v
\<< DUP LVAR DUP TYPE 5 \=/
IF
THEN DUP OBJ\-> OBJ\-> DROP XQ \-> nv
\<< nv 1 >
IF
THEN nv \->LIST \->STR nv "Here " SWAP + " var
" + SWAP + ":

Use only 1 !" + SWAP ROT DROP2 DOERR
END
\>> SWAP DROP "" + 'v' STO \->STR v "X\175\175" SREPL DROP OBJ\-> RCLVX DUPDUP \-> vx
\<< EVAL SAME NOT
IF
THEN 'Y\175\175' STOVX
END -105 SF EXPAND -105 CF 'X\175\175' * SIMPLIFY DUP { } \-> f l
\<< DEGREE 1
START f 'X\175\175' / SIMPLIFY DUP 0 'X\175\175' STO \->NUM DUP "\|>" + ".\|>" "" SREPL DROP "\|>" "" SREPL DROP OBJ\-> l + 'l' STO - 'f' STO 'X\175\175' PURGE -1
STEP l OBJ\->
\>> vx STOVX
\>>
ELSE DUP -105 CF DROP2 EVAL "\|>" + ".\|>" "" SREPL DROP "\|>" "" SREPL DROP OBJ\-> 1
END \->ARRY "[ana0]" \->TAG fg STOF
\>>
\>>

Attached File(s)
05-05-2023, 07:57 AM (This post was last modified: 05-05-2023 12:18 PM by gor1060.)
Post: #7
 gor1060 Junior Member Posts: 23 Joined: Mar 2017
RE: Polynomial with real coefficients —> array w/ real coeff

Update:
05-05-2023, 12:03 PM
Post: #8
 rprosperi Super Moderator Posts: 6,492 Joined: Dec 2013
RE: Polynomial with real coefficients —> array w/ real coeff

If the goal is for someone to use your program, please consider sharing it either typed or in a text file, etc. it can't be copied from a screen grab. Showing these is better than nothing at all, but most folks won't copy from an image. Just trying to help you share in a better way.

--Bob Prosperi
05-05-2023, 02:03 PM (This post was last modified: 05-05-2023 11:22 PM by Gil.)
Post: #9
 Gil Senior Member Posts: 637 Joined: Oct 2019
RE: Polynomial with real coefficients —> array w/ real coeff
Very nice indeed.

Thanks.

Perhaps we could simplify your tests by a single one as follows:
« 0 { } —> N L
« DUP DEGREE 'N' STO N 1 <
IF
THEN 1 —>LIST
ELSE 0 N 1 -
START 0 HORNER 'L' STO+ DROP
NEXT L +
END AXL
»
»

And to have your program work without being asked if we want to go to real, add the following 3 instructions
-105 SF for real, PUSH to save the initial flags and POP to restore the initial flags:

« PUSH -105 SF 0 { } —> N L
« DUP DEGREE 'N' STO N 1 <
IF
THEN 1 —>LIST
ELSE 0 N 1 -
START 0 HORNER 'L' STO+ DROP
NEXT L +
END AXL POP
»
»
05-08-2023, 12:07 PM
Post: #10
 gor1060 Junior Member Posts: 23 Joined: Mar 2017
RE: Polynomial with real coefficients —> array w/ real coeff
(05-05-2023 02:03 PM)Gil Wrote:  Very nice indeed.

Thanks.

Perhaps we could simplify your tests by a single one as follows:
« 0 { } —> N L
« DUP DEGREE 'N' STO N 1 <
IF
THEN 1 —>LIST
ELSE 0 N 1 -
START 0 HORNER 'L' STO+ DROP
NEXT L +
END AXL
»
»

And to have your program work without being asked if we want to go to real, add the following 3 instructions
-105 SF for real, PUSH to save the initial flags and POP to restore the initial flags:

« PUSH -105 SF 0 { } —> N L
« DUP DEGREE 'N' STO N 1 <
IF
THEN 1 —>LIST
ELSE 0 N 1 -
START 0 HORNER 'L' STO+ DROP
NEXT L +
END AXL POP
»
»

There is no limit to perfection.

Enabling the PUSH and POP instructions with -105 SF is a questionable idea, because in exact mode you can't get an array with exact polynomial coefficients. My original program gives an approximate result in approximate mode and an exact result in exact mode. With real coefficients of the polynomial in the approximate mode, the program does not ask about changing the mode.

I didn't think about any optimization of my program, but if you want, then let the next iteration be like this: