[CAS] Problems with increased powers of polynomials (coeffn*x^n±c2*x^2±c1*x^1±c0*x^0)
07-03-2016, 05:06 PM (This post was last modified: 07-06-2016 03:15 AM by compsystems.)
Post: #1 compsystems Senior Member Posts: 1,184 Joined: Dec 2013
[CAS] Problems with increased powers of polynomials (coeffn*x^n±c2*x^2±c1*x^1±c0*x^0)
Examples:
1:

[FLags] Output Simplify: None. Increasing: Off
entry line: x^2+x^1-x^0 [Enter] returns x^2+x-1 (OK)

1a: [FLags] Output Simplify: None. Increasing: On
entry line: x^2+x^1-x^0 [Enter] returns x^2+x-1 (Why?)

the system (CAS) does not consider the increase flag, which must be made at the end of process, you agree with this?

1b: [FLags] Output Simplify: Minimun. Increasing: On
entry line: x^2+x^1-x^0 [Enter] returns -1+x+x^2 (OK)

1c: [FLags] Output Simplify: Maximun. Increasing: On
entry line: x^2+x^1-x^0 [Enter] returns x^2+x-1 (Why?)

now with reorder function

1aa: [FLags] Output Simplify: indifferent (None or Minimun or Maximun). Increasing: On
entry line: reorder(x^2+x^1-x^0,[x]) [Enter] returns -1+x+x^2 (OK)

1bb: [FLags] Output Simplify: indifferent (None or Minimun or Maximun). Increasing: OFF
entry line: reorder(x^2+x^1-x^0,[x]) [Enter] returns x^2+x-1 (OK)

2:
2a: [FLags] Output Simplify: None. Increasing: On
entry line: x^2*y^0+x^1*y^1-x^0*2*y^2 [Enter] returns x^2+x*y-2*y^2(Why?)

2b: [FLags] Output Simplify: Minimun. Increasing: On
entry line: x^2*y^0+x^1*y^1-x^0*2*y^2 [Enter] returns x*y+x^2-2*y^2 (OK)
but [For next firmware] Default X increases, it should be able to specify the variable work or main var or increasing var: X or Y, Z ...
PLEASE INCLUDE THIS NEW ITEM, IN CAS CONFIGURATION
This option is available in the CAS of HP50G and HP49G +
Independent varible name: X, Y ...

2c: [FLags] Output Simplify: Maximun. Increasing: On
entry line: x^2*y^0+x^1*y^1-x^0*2*y^2 [Enter] returns x^2+x*y-2*y^2(Why?)

now with reorder function

2aa: [FLags] Output Simplify: indifferent (None or Minimun or Maximun). Increasing: On
entry line: reorder(x^2*y^0+x^1*y^1-x^0*2*y^2,[x]) [Enter] returns -2*y^2+x*y+x^2 (OK)

2bb: [FLags] Output Simplify: indifferent (None or Minimun or Maximun). Increasing: OFF
entry line: reorder(x^2*y^0+x^1*y^1-x^0*2*y^2,[x]) [Enter] returns x^2+x*y-2*y^2 (OK)

3:
3a: [FLags] Output Simplify: Maximun. Increasing: On

(x^2+x*y-2*y^2)*(x^2-2*x*y+3*y^2) =>

x^4-x^3*y-x^2*y^2+7*x*y^3-6*y^4 =(

Attached File(s) Thumbnail(s) 07-03-2016, 07:57 PM (This post was last modified: 07-06-2016 03:25 AM by compsystems.)
Post: #2 compsystems Senior Member Posts: 1,184 Joined: Dec 2013
RE: [HP-PRIME CAS]
in this case if it works.

4:

4a: [FLags] Output Simplify: None. Increasing: OFF (coeffn*x^n ±c2*x^2 ±c1*x^1 ±c0*x^0)
factor(a^3-b^3) => (a^0-b)*(a^2+a^1*b+a^0*b^2) OK

4b: [FLags] Output Simplify: None. Increasing: ON (±c0*x^0 ±c1*x^1 ±c2*x^2 ±coeffn*x^n)
factor(a^3-b^3) => (-b+a^0)*(a^0*b^2+a^1*b+a^2) ~OK

I think or considering, that the factor (a-b) agree to variable increment.

factor(a^3-b^3) => (a^0-b)*(a^0*b^2+a^1*b+a^2) OK
07-04-2016, 11:04 AM (This post was last modified: 07-04-2016 11:11 AM by parisse.)
Post: #3
 parisse Senior Member Posts: 1,036 Joined: Dec 2013
RE: [CAS] Problems with increased powers of polynomials (coeffn*x^n±c2*x^2±c1*x^1±c0*x^0)
Increasing flag applies to normal and regroup (and commands calling them). If auto-simplification is set to none, nothing happens of course.
07-06-2016, 03:14 AM (This post was last modified: 07-06-2016 03:30 AM by compsystems.)
Post: #4 compsystems Senior Member Posts: 1,184 Joined: Dec 2013
RE: [CAS]
- In Example 4a/4b setting simplification: NONE, and changing the flag of increasing (ON/OFF), if it works, but in Example 1/1a no.

- In 4b [FLags] Output Simplify: None. Increasing: ON
factor(a^3-b^3) => (-b+a^0)*(a^0*b^2+a^1*b+a^2) ~OK

if the increase variable is A must be first, why not ordered correctly (-b+a) => (a-b)

factor(a^3-b^3) => (a^0-b)*(a^0*b^2+a^1*b+a^2) OK
07-08-2016, 03:58 AM (This post was last modified: 07-08-2016 08:45 PM by compsystems.)
Post: #5 compsystems Senior Member Posts: 1,184 Joined: Dec 2013
RE: [CAS] Problems with increased powers of polynomials (coeffn*x^n±c2*x^2±c1*x^1±c0*x^0)
also, with MAXIMUM=ON flag, the ordering not work, Why?
07-09-2016, 07:51 AM
Post: #6
 parisse Senior Member Posts: 1,036 Joined: Dec 2013
RE: [CAS] Problems with increased powers of polynomials (coeffn*x^n±c2*x^2±c1*x^1±c0*x^0)
simplify calls ratnormal, but ratnormal is currently not context-aware, therefore the change you made in the settings is not reflected. I'm modifying that for Xcas, but it's a large change, don't expect this to change soon on the Prime.
07-09-2016, 06:44 PM (This post was last modified: 07-12-2016 02:19 PM by compsystems.)
Post: #7 compsystems Senior Member Posts: 1,184 Joined: Dec 2013
RE: [CAS] Problems with increased powers of polynomials (coeffn*x^n±c2*x^2±c1*x^1±c0*x^0)
(07-09-2016 07:51 AM)parisse Wrote:  simplify calls ratnormal, but ratnormal is currently not context-aware, therefore the change you made in the settings is not reflected. I'm modifying that for Xcas, but it's a large change, don't expect this to change soon on the Prime.

thanks, BP, for now I want to see in xcas in a future HP-PRIME =)

also the order of the first factor =>

current:
factor(a^3-b^3) => (-b+a^0)*(a^0*b^2+a^1*b+a^2) =(

future:
factor(a^3-b^3) => (a-b)*(a^0*b^2+a^1*b+a^2) =)
07-10-2016, 04:18 AM
Post: #8
 parisse Senior Member Posts: 1,036 Joined: Dec 2013
RE: [CAS] Problems with increased powers of polynomials (coeffn*x^n±c2*x^2±c1*x^1±c0*x^0)
You have some control with the optional second parameter of factor:
factor(a^3-b^3,a)
factor(a^3-b^3,b)
07-12-2016, 02:15 PM
Post: #9 compsystems Senior Member Posts: 1,184 Joined: Dec 2013
RE: [CAS] Problems with increased powers of polynomials (coeffn*x^n±c2*x^2±c1*x^1±c0*x^0)
: [FLags] Output Simplify: Minimun. Increasing (a): Off = decreassing 2...1

factor(a^3-b^3, a) => (a^0-b)*(a^2+a^1*b+a^0*b^2) OK the variable a, is first that b

: [FLags] Output Simplify: Minimun. Increasing (b): Off = decreassing 2...1

factor(a^3-b^3, b) => -(b^0-a)*(b^2+b^1*a+a^2*b^0) OK the variable b, is first that a

But, control is lost in the following case

: [FLags] Output Simplify: Minimun. Increasing (a): On

factor(a^3-b^3, a) => (-b+a^0)*(a^0*b^2+a*b+a^2)

The factor (a^0*b^2+a^1*b+a^2) is OK, but no (-b+a)

the output must be

: [FLags] Output Simplify: Minimun. Increasing (a): On

factor(a^3-b^3, a) => (a^0-b)*(a^0*b^2+a*b+a^2)
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