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## Re: [Axiom-developer] Question concerning types...

 From: Ralf Hemmecke Subject: Re: [Axiom-developer] Question concerning types... Date: Sun, 17 Sep 2006 02:33:19 +0200 User-agent: Thunderbird 1.5.0.5 (X11/20060719)

The problem, as described to me, was having three matrices A, B and C. C is known. The goal was to choose the elements of one of A or B then
```look for equations coming from AB-BA = C.  The elements of A and B are
quaternion.
```
```
Maybe you want that... Add the C yourself.
The trick is that you add variables if form of polynomials.

)clear all
R := Fraction Integer
P := Polynomial R
Q := Quaternion P
M := Matrix Q

A1 := quatern(A11, A1i, A1j, A1k)
A2 := quatern(A21, A2i, A2j, A2k)
A3 := quatern(A31, A3i, A3j, A3k)
A4 := quatern(A41, A4i, A4j, A4k)

A: M := matrix [[A1, A2], [A3, A4]]

B1: Q := quatern( 1,  2,  3,  5)
B2: Q := quatern( 7, 11, 13, 17)
B3: Q := quatern(19, 23, 29, 31)
B4: Q := quatern(37, 41, 43, 47)

B: M := matrix [[B1, B2], [B3, B4]]

Z := A*B - B*A

Ralf

```