[Axiom-math] Axiom: Matrix manipulations

[C. Frangos]

I have tried to read in the file test.input pasted below. However,
I am getting continuously error messages re. the matrix Acon, and have been
unable to make progress.

Any assistance would be appreciated.

Thanks very much.

C. Frangos.


--file test.input

--)read expandsincos.input

Acon := matrix([[1 , 0 , Lo1*sin(phi) , -sin(phi)*a , 0 , 0 , 0 , 0 , 0],_
[0 , 1 , -Lo1*cos(phi) , a*cos(phi) , 0 , 0 , 0 , 0 , 0],_
[1 , 0 , -Lo1*sin(phi) , 0 , -a*sin(phi), 0 , 0 , 0 , 0],-
[0 , 1 , Lo1*cos(phi) , 0 , a*cos(phi) , 0 , 0 , 0 , 0],_
[1,0,-Lc*cos(phi)+Lo1*sin(phi),0,0,0,-a*sin(phi)*cos(delta3)_
-a*cos(phi)*sin(delta3),0,0],_
[0,1,-Lc*sin(phi)-Lo1*cos(phi),0,0,0,a*cos(phi)*cos(delta3)_
-a*sin(phi)*sin(delta3),0,0],_
[1,-Lc*cos(phi)-Lo1*sin(phi),0,0,(-2*sin(phi)*Lo1*sin(delta3)-sin(phi)*_
Lc*cos(delta3)-cos(phi)*Lc*sin(delta3))*a/sqrt(4*Lo1^2*sin(delta3)^2+_
4*Lo1*sin(delta3)*Lc*cos(delta3)+Lc^2*cos(delta3)^2+Lc^2*sin(delta3)^2),0,0,0],_
[0,1,-Lc*sin(phi)+Lo1*cos(phi),0,0,a*(2*cos(phi)*Lo1*sin(delta3)+_
cos(phi)*Lc*cos(delta3)-sin(phi)*Lc*sin(delta3))/sqrt(4*Lo1^2*sin(delta3)^2+_
4*Lo1*sin(delta3)*Lc*cos(delta3)+Lc^2*cos(delta3)^2+Lc^2*sin(delta3)^2),0,0,0],_
[0 , 0 , 0 , 0 , 0 , 1 , 1 , 0 , -k]])

rankAcon := rank(Acon)

nullityAcon := nullity(Acon)

Aconre := rowEchelon(Acon)

Aconnull := nullSpace(Acon)


--end of file.

[Francois Maltey]

Hi C. !

What is your expandsincos.input file.

First you read this file of axiom command. But for me it's a mysterious file.

Post by C. Frangos
--file test.input
--)read expandsincos.input

You might create line after line the matrix :
I can't read all the charecters, it's too complex for me.
Perhaps the a term is missing at L7, its length is 8 and not 9.

Do you know how to study this matrix, I don't know it.
Any cas is more powerfull when the user know the reponse...
So he can suggest the right calculus way.

Have a nice day !

F. in France.

L1 := [1 , 0 , Lo1*sin(phi) , -sin(phi)*a , 0 , 0 , 0 , 0 , 0]
L2 := [0 , 1 , -Lo1*cos(phi) , a*cos(phi) , 0 , 0 , 0 , 0 , 0]
L3 := [1 , 0 , -Lo1*sin(phi) , 0 , -a*sin(phi), 0 , 0 , 0 , 0]
L4 := [0 , 1 , Lo1*cos(phi) , 0 , a*cos(phi) , 0 , 0 , 0 , 0]
L5 := [1,0,-Lc*cos(phi)+Lo1*sin(phi),0,0,0,-a*sin(phi)*cos(delta3)_
-a*cos(phi)*sin(delta3),0,0]
L6 := [0,1,-Lc*sin(phi)-Lo1*cos(phi),0,0,0,a*cos(phi)*cos(delta3)_
-a*sin(phi)*sin(delta3),0,0]
L7 := [1,-Lc*cos(phi)-Lo1*sin(phi),0,0,(-2*sin(phi)*Lo1*sin(delta3)-sin(phi)*_
Lc*cos(delta3)-cos(phi)*Lc*sin(delta3))*a/sqrt(4*Lo1^2*sin(delta3)^2+_
4*Lo1*sin(delta3)*Lc*cos(delta3)+Lc^2*cos(delta3)^2+Lc^2*sin(delta3)^2),_
0,0,0]
L8 := [0,1,-Lc*sin(phi)+Lo1*cos(phi),0,0,a*(2*cos(phi)*Lo1*sin(delta3)+_
cos(phi)*Lc*cos(delta3)-sin(phi)*Lc*sin(delta3))/sqrt(4*Lo1^2*_
sin(delta3)^2+4*Lo1*sin(delta3)*Lc*cos(delta3)+Lc^2*cos(delta3)^2+_
Lc^2*sin(delta3)^2),0,0,0]
L9 := [0 , 0 , 0 , 0 , 0 , 1 , 1 , 0 , -k]

[#L1, #L2, #L3, #L4, #L5, L6, #L7, #L8, #L9]
Acon := matrix [L1,L2,L3,L4,L5,L6,L7,L8,L9]

rankAcon := rank(Acon)

nullityAcon := nullity(Acon)

Aconre := rowEchelon(Acon)

Aconnull := nullSpace(Acon)

[Waldek Hebisch]

Post by C. Frangos
I have tried to read in the file test.input pasted below. However,
I am getting continuously error messages re. the matrix Acon, and have been
unable to make progress.
--file test.input
--)read expandsincos.input
Acon := matrix([[1 , 0 , Lo1*sin(phi) , -sin(phi)*a , 0 , 0 , 0 , 0 , 0],_
[0 , 1 , -Lo1*cos(phi) , a*cos(phi) , 0 , 0 , 0 , 0 , 0],_
[1 , 0 , -Lo1*sin(phi) , 0 , -a*sin(phi), 0 , 0 , 0 , 0],-

^
You need underscore here.

Post by C. Frangos
[0 , 1 , Lo1*cos(phi) , 0 , a*cos(phi) , 0 , 0 , 0 , 0],_
[1,0,-Lc*cos(phi)+Lo1*sin(phi),0,0,0,-a*sin(phi)*cos(delta3)_
-a*cos(phi)*sin(delta3),0,0],_
[0,1,-Lc*sin(phi)-Lo1*cos(phi),0,0,0,a*cos(phi)*cos(delta3)_
-a*sin(phi)*sin(delta3),0,0],_
[1,-Lc*cos(phi)-Lo1*sin(phi),0,0,(-2*sin(phi)*Lo1*sin(delta3)-sin(phi)*_
Lc*cos(delta3)-cos(phi)*Lc*sin(delta3))*a/sqrt(4*Lo1^2*sin(delta3)^2+_
4*Lo1*sin(delta3)*Lc*cos(delta3)+Lc^2*cos(delta3)^2+Lc^2*sin(delta3)^2),0,0,0],_

The row above has only 8 entries.

Post by C. Frangos
[0,1,-Lc*sin(phi)+Lo1*cos(phi),0,0,a*(2*cos(phi)*Lo1*sin(delta3)+_
cos(phi)*Lc*cos(delta3)-sin(phi)*Lc*sin(delta3))/sqrt(4*Lo1^2*sin(delta3)^2+_
4*Lo1*sin(delta3)*Lc*cos(delta3)+Lc^2*cos(delta3)^2+Lc^2*sin(delta3)^2),0,0,0],_
[0 , 0 , 0 , 0 , 0 , 1 , 1 , 0 , -k]])
rankAcon := rank(Acon)
nullityAcon := nullity(Acon)
Aconre := rowEchelon(Acon)
Aconnull := nullSpace(Acon)

After correcting the two problems above (I added leading 0 to
the short row) I get rank 8 and [[0,0,0,0,0,0,0,1,0]] as
nullSpace.