MathAction #162 nested cross products for Vector Polynomial Integer probelm

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  - #162 nested cross products for Vector Polynomial Integer probelm <-- You are here.

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

Subject: (replying) Be Bold !!

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