affine.mw

> with( LinearAlgebra ):
 

> Rx := <<1,0,0,0>|<0,cos(rx),sin(rx),0>|<0,-sin(rx), cos(rx),0>|<0,0,0,1>>;
 

Rx := Matrix(%id = 6633472) 

> Ry := <<cos(ry),0,-sin(ry),0>|<0,1,0,0>|<sin(ry),0,cos(ry),0>|<0,0,0,1>>;
 

Ry := Matrix(%id = 7411972) 

> Rz := <<cos(rz),sin(rz),0,0>|<-sin(rz),cos(rz),0,0>|<0,0,1,0>|<0,0,0,1>>;
 

Rz := Matrix(%id = 8320192) 

> S := <<sx,0,0,0>|<0,sy,0,0>|<0,0,sz,0>|<0,0,0,1>>;
 

S := Matrix(%id = 6335860) 

> T := <<1,0,0,0>|<0,1,0,0>|<0,0,1,0>|<tx,ty,tz,1>>;
 

T := Matrix(%id = 6741528) 

> composed := simplify( Rz . Ry . Rx . S . T );
 

composed := Matrix(%id = 16892748)
composed := Matrix(%id = 16892748)
composed := Matrix(%id = 16892748)
composed := Matrix(%id = 16892748)
composed := Matrix(%id = 16892748)
composed := Matrix(%id = 16892748)
composed := Matrix(%id = 16892748)
composed := Matrix(%id = 16892748) 

> invComposed := simplify( composed^(-1) );
 

invComposed := Matrix(%id = 17035552)
invComposed := Matrix(%id = 17035552)
invComposed := Matrix(%id = 17035552)
invComposed := Matrix(%id = 17035552) 

> simplify( composed . invComposed );
 

Matrix(%id = 2395324) 

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