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#162 nested cross products for Vector Polynomial Integer probelm

Edit detail for #162 nested cross products for Vector Polynomial Integer probelm revision 1 of 1

	1
Editor: Time: 2007/11/17 22:00:21 GMT-8
Note:

changed:
-
I'm trying to produce a vector by several cross products
<br>
All variables and elements of the vectors are polynomial integers
<br>
All vectors are Vector Polynomial Integer
<br>
<pre>
X := cross(A0, A1)
Y := cross(A2, A3)
B0 := A0 + a0*X + a0*Y
B1 := A1 + a1*X + a1*Y
B2 := A2 + a2*X + a2*Y
B3 := A3 + a3*X + a3*Y
C0 = cross(B0, B1)
C1 = cross(B2, B3)
D=cross(C0, C1)
</pre>
On the last command Axiom stop working and hang.
Is there any workaround for this problem ?


From BillPage Sat May 28 21:27:25 -0500 2005
From: Bill Page
Date: Sat, 28 May 2005 21:27:25 -0500
Subject: can't reproduce this problem
Message-ID: <20050528212725-0500@page.axiom-developer.org>

Why do you use = in the last 3 lines?

I can't reproduce this problem. The following works for me:
\begin{axiom}
(a0,a1,a2,a3):Polynomial Integer
(a00,a01,a02):Polynomial Integer
A0:=vector [a00,a01,a02]
(a10,a11,a12):Polynomial Integer
A1:=vector [a10,a11,a12]
X:=cross(A0,A1)
(a20,a21,a22):Polynomial Integer
A2:=vector [a20,a21,a22]
(a30,a31,a32):Polynomial Integer
A3:=vector [a30,a31,a32]
Y:=cross(A2,A3)
B0 := A0 + a0*X + a0*Y
B1 := A1 + a1*X + a1*Y
B2 := A2 + a2*X + a2*Y
B3 := A3 + a3*X + a3*Y
C0 := cross(B0,B1)
C1 := cross(B2,B3)
D := cross(C0,C1);
\end{axiom}

But the last expression is very large and is too large
to display on here on MathAction.

Please post the actual Axiom commands that will cause
Axiom to hang.

From unknown Sun May 29 01:50:06 -0500 2005
From: unknown
Date: Sun, 29 May 2005 01:50:06 -0500
Subject: here are actual commands:
Message-ID: <20050529015006-0500@page.axiom-developer.org>

I'm using axiom foe windows with WinTexMAcs -  may be that a problem ?

From unknown Sun May 29 01:58:36 -0500 2005
From: unknown
Date: Sun, 29 May 2005 01:58:36 -0500
Subject: 
Message-ID: <20050529015836-0500@page.axiom-developer.org>

Example code::

  (a0x, a1x, a2x, a3x, a0y, a1y, a2y, a3y) : Polynomial Integer
  (PR0, PR1, PR2, PR3, PRN0, PRN1, PRN2, PRN3, X, Y, Z, XN, YN, ZN): Vector Polynomial  Integer
  PR0 := vector[PR0x, PR0y, PR0z]
  PR1 := vector[PR1x, PR1y, PR1z]
  PR2 := vector[PR2x, PR2y, PR2z]
  PR3 := vector[PR3x, PR3y, PR3z]
  X := cross(PR0, PR3)
  Y := cross(PR1, PR2)
  PRN0 := PR0 + a0x*X + a0y*Y
  PRN3 := PR3 + a3x*X + a3y*Y
  XN := cross(PRN0, PRN3)
  PRN1 := PR1 + a1x*X + a1y*Y
  PRN2 := PR2 + a2x*X + a2y*Y
  YN := cross(PRN1, PRN2)
  ZN := cross(XN, YN)

From unknown Sun May 29 02:10:21 -0500 2005
From: unknown
Date: Sun, 29 May 2005 02:10:21 -0500
Subject: your sample
Message-ID: <20050529021021-0500@page.axiom-developer.org>

You code is not working for me too - hang on the last command

D := cross(C0,C1)

From unknown Sun May 29 02:22:26 -0500 2005
From: unknown
Date: Sun, 29 May 2005 02:22:26 -0500
Subject: update : it's WInTexMAcs problem
Message-ID: <20050529022226-0500@page.axiom-developer.org>

I've launched your test in axiom console without WinTexMacs and it's working.
Any advices how to fix WinTexMacs ?  

From unknown Sun May 29 02:23:37 -0500 2005
From: unknown
Date: Sun, 29 May 2005 02:23:37 -0500
Subject: property change
Message-ID: <20050529022337-0500@page.axiom-developer.org>

Severity: critical => minor 
Status: open => closed

I'm trying to produce a vector by several cross products
All variables and elements of the vectors are polynomial integers
All vectors are Vector Polynomial Integer

X := cross(A0, A1)
Y := cross(A2, A3)
B0 := A0 + a0X + a0Y
B1 := A1 + a1X + a1Y
B2 := A2 + a2X + a2Y
B3 := A3 + a3X + a3Y
C0 = cross(B0, B1)
C1 = cross(B2, B3)
D=cross(C0, C1)

On the last command Axiom stop working and hang. Is there any workaround for this problem ?

can't reproduce this problem --Bill Page, Sat, 28 May 2005 21:27:25 -0500 reply

Why do you use = in the last 3 lines?

I can't reproduce this problem. The following works for me:

fricas

(1) -> (a0,a1,a2,a3):Polynomial Integer

Type: Void

fricas

(a00,a01,a02):Polynomial Integer

Type: Void

fricas

A0:=vector [a00,a01,a02]

$\label{eq1}\left[ a 00, \: a 01, \: a 02 \right]$

(1)

Type: Vector(Polynomial(Integer))

fricas

(a10,a11,a12):Polynomial Integer

Type: Void

fricas

A1:=vector [a10,a11,a12]

$\label{eq2}\left[ a 10, \: a 11, \: a 12 \right]$

(2)

Type: Vector(Polynomial(Integer))

fricas

X:=cross(A0,A1)

$\label{eq3}\begin{array}{@{}l} \displaystyle \left[{{a 01 \ a 12}-{a 02 \ a 11}}, \:{-{a 00 \ a 12}+{a 02 \ a 10}}, \:{{a 00 \ a 11}-{a 01 \ a 10}}\right]$

(3)

Type: Vector(Polynomial(Integer))

fricas

(a20,a21,a22):Polynomial Integer

Type: Void

fricas

A2:=vector [a20,a21,a22]

$\label{eq4}\left[ a 20, \: a 21, \: a 22 \right]$

(4)

Type: Vector(Polynomial(Integer))

fricas

(a30,a31,a32):Polynomial Integer

Type: Void

fricas

A3:=vector [a30,a31,a32]

$\label{eq5}\left[ a 30, \: a 31, \: a 32 \right]$

(5)

Type: Vector(Polynomial(Integer))

fricas

Y:=cross(A2,A3)

$\label{eq6}\begin{array}{@{}l} \displaystyle \left[{{a 21 \ a 32}-{a 22 \ a 31}}, \:{-{a 20 \ a 32}+{a 22 \ a 30}}, \:{{a 20 \ a 31}-{a 21 \ a 30}}\right]$

(6)

Type: Vector(Polynomial(Integer))

fricas

B0 := A0 + a0*X + a0*Y

$\label{eq7}\begin{array}{@{}l} \displaystyle \left[{{a 0 \ a 21 \ a 32}-{a 0 \ a 22 \ a 31}+{a 0 \ a 01 \ a 12}-{a 0 \ a 02 \ a 11}+ a 00}, \: \right. \ \ \displaystyle \left.{-{a 0 \ a 20 \ a 32}+{a 0 \ a 22 \ a 30}-{a 0 \ a 00 \ a 12}+{a 0 \ a 02 \ a 10}+ a 01}, \right. \ \ \displaystyle \left.\:{{a 0 \ a 20 \ a 31}-{a 0 \ a 21 \ a 30}+{a 0 \ a 00 \ a 11}-{a 0 \ a 01 \ a 10}+ a 02}\right]$

(7)

Type: Vector(Polynomial(Integer))

fricas

B1 := A1 + a1*X + a1*Y

$\label{eq8}\begin{array}{@{}l} \displaystyle \left[{{a 1 \ a 21 \ a 32}-{a 1 \ a 22 \ a 31}+{a 01 \ a 1 \ a 12}-{a 02 \ a 1 \ a 11}+ a 10}, \: \right. \ \ \displaystyle \left.{-{a 1 \ a 20 \ a 32}+{a 1 \ a 22 \ a 30}-{a 00 \ a 1 \ a 12}+ a 11 +{a 02 \ a 1 \ a 10}}, \right. \ \ \displaystyle \left.\:{{a 1 \ a 20 \ a 31}-{a 1 \ a 21 \ a 30}+ a 12 +{a 00 \ a 1 \ a 11}-{a 01 \ a 1 \ a 10}}\right]$

(8)

Type: Vector(Polynomial(Integer))

fricas

B2 := A2 + a2*X + a2*Y

$\label{eq9}\begin{array}{@{}l} \displaystyle \left[{{a 2 \ a 21 \ a 32}-{a 2 \ a 22 \ a 31}+ a 20 +{{\left({a 01 \ a 12}-{a 02 \ a 11}\right)}\ a 2}}, \: \right. \ \ \displaystyle \left.{-{a 2 \ a 20 \ a 32}+{a 2 \ a 22 \ a 30}+ a 21 +{{\left(-{a 00 \ a 12}+{a 02 \ a 10}\right)}\ a 2}}, \right. \ \ \displaystyle \left.\:{{a 2 \ a 20 \ a 31}-{a 2 \ a 21 \ a 30}+ a 22 +{{\left({a 00 \ a 11}-{a 01 \ a 10}\right)}\ a 2}}\right]$

(9)

Type: Vector(Polynomial(Integer))

fricas

B3 := A3 + a3*X + a3*Y

$\label{eq10}\begin{array}{@{}l} \displaystyle \left[{{a 21 \ a 3 \ a 32}-{a 22 \ a 3 \ a 31}+ a 30 +{{\left({a 01 \ a 12}-{a 02 \ a 11}\right)}\ a 3}}, \: \right. \ \ \displaystyle \left.{-{a 20 \ a 3 \ a 32}+ a 31 +{a 22 \ a 3 \ a 30}+{{\left(-{a 00 \ a 12}+{a 02 \ a 10}\right)}\ a 3}}, \right. \ \ \displaystyle \left.\:{a 32 +{a 20 \ a 3 \ a 31}-{a 21 \ a 3 \ a 30}+{{\left({a 00 \ a 11}-{a 01 \ a 10}\right)}\ a 3}}\right]$

(10)

Type: Vector(Polynomial(Integer))

fricas

C0 := cross(B0,B1)

$\label{eq11}\begin{array}{@{}l} \displaystyle \left[{ \begin{array}{@{}l} \displaystyle {{\left(-{a 0 \ a 12}+{a 02 \ a 1}\right)}\ a 20 \ a 32}+ \ \ \displaystyle {{\left(-{a 0 \ a 11}+{a 01 \ a 1}\right)}\ a 20 \ a 31}+ \ \ \displaystyle {{\left({{\left({a 0 \ a 12}-{a 02 \ a 1}\right)}\ a 22}+{{\left({a 0 \ a 11}-{a 01 \ a 1}\right)}\ a 21}\right)}\ a 30}- \ \ \displaystyle {a 0 \ a 00 \ {{a 12}^{2}}}+{{\left({a 0 \ a 02 \ a 10}+{a 00 \ a 02 \ a 1}+ a 01 \right)}\ a 12}- \ \ \displaystyle {a 0 \ a 00 \ {{a 11}^{2}}}+{{\left({a 0 \ a 01 \ a 10}+{a 00 \ a 01 \ a 1}- a 02 \right)}\ a 11}+ \ \ \displaystyle {{\left(-{{a 02}^{2}}-{{a 01}^{2}}\right)}\ a 1 \ a 10}$

(11)

Type: Vector(Polynomial(Integer))

fricas

C1 := cross(B2,B3)

$\label{eq12}\begin{array}{@{}l} \displaystyle \left[{ \begin{array}{@{}l} \displaystyle -{a 2 \ a 20 \ {{a 32}^{2}}}+{ \begin{array}{@{}l} \displaystyle {\left({{a 2 \ a 22 \ a 30}+{a 20 \ a 22 \ a 3}+ a 21 +{{\left(-{a 00 \ a 12}+{a 02 \ a 10}\right)}\ a 2}}\right)}\ \cdot \ \ \displaystyle a 32$

(12)

Type: Vector(Polynomial(Integer))

fricas

D := cross(C0,C1);

Type: Vector(Polynomial(Integer))

But the last expression is very large and is too large to display on here on MathAction.

Please post the actual Axiom commands that will cause Axiom to hang.

here are actual commands: --unknown, Sun, 29 May 2005 01:50:06 -0500 reply

I'm using axiom foe windows with WinTexMAcs? - may be that a problem ?

... --unknown, Sun, 29 May 2005 01:58:36 -0500 reply

Example code:

  (a0x, a1x, a2x, a3x, a0y, a1y, a2y, a3y) : Polynomial Integer
  (PR0, PR1, PR2, PR3, PRN0, PRN1, PRN2, PRN3, X, Y, Z, XN, YN, ZN): Vector Polynomial  Integer
  PR0 := vector[PR0x, PR0y, PR0z]
  PR1 := vector[PR1x, PR1y, PR1z]
  PR2 := vector[PR2x, PR2y, PR2z]
  PR3 := vector[PR3x, PR3y, PR3z]
  X := cross(PR0, PR3)
  Y := cross(PR1, PR2)
  PRN0 := PR0 + a0x*X + a0y*Y
  PRN3 := PR3 + a3x*X + a3y*Y
  XN := cross(PRN0, PRN3)
  PRN1 := PR1 + a1x*X + a1y*Y
  PRN2 := PR2 + a2x*X + a2y*Y
  YN := cross(PRN1, PRN2)
  ZN := cross(XN, YN)

your sample --unknown, Sun, 29 May 2005 02:10:21 -0500 reply

You code is not working for me too - hang on the last command

D := cross(C0,C1)

update : it's WInTexMAcs? problem --unknown, Sun, 29 May 2005 02:22:26 -0500 reply

I've launched your test in axiom console without WinTexMacs? and it's working. Any advices how to fix WinTexMacs? ?

property change --unknown, Sun, 29 May 2005 02:23:37 -0500 reply

Severity: critical => minor Status: open => closed