rotation a quat by a global axis

I want to rotate a quat representing a local rotation
by a global axis rotation

currently I'm extracting the axes from a temp matrix
which works but I think I'm missing a trick

			' AL is the eular pitch yaw roll local rotation angles						
			q.FromEuler(AL)		
			m=q.toMatrix()		' local rotation

			' A is the eular pitch yaw roll world rotation angles
			qz.FromAxisAngle(A.z,m[2], m[6], m[10])		' global Z axis rotation
			qy.FromAxisAngle(A.y,m[1], m[5], m[9])		' global Y axis rotation
			qx.FromAxisAngle(A.x,m[0], m[4], m[8])		' global X axis rotation
			
			qz.multiply(qy)		'quat z=quat z * quat y
			qz.multiply(qx)		'quat z=quat z * quat x
			q.multiply(qz)		'local rotation quat * xyz quat

			m=q.tomatrix()		' the local rotation rotated by the global rotation
			glmultMatrixD(m)

does anyone know a better way of doing this?

I think you want to go the other way. Convert the global axis rotation to the equivalent quaternion.

that would give me 2 local rotations...