As nearly as I can remember here are the steps to add a vent to the Tecma toilet. I did this almost a year ago so I may have not remembered exactly. It has worked perfectly since this mod.
Basically I just placed a wye in the drain line and added an air admittance (one way vent) to the drain. I think I attached pictures of the parts used. I was just having so much fun that I forgot to take pictures as I did it.
Parts list:
1 PVC DWV 1 1/2" wye
1 PVC DWV Street Elbow 45 Degrees
1 piece of PVC pipe 1 1/2" about 3' long
1 Oatey 39016 Sure-Vent Air Admittance Valve with 1-1/2-Inch by 2-Inch PVC Adapter, 2-Inch
1 Flexible PVC Coupling Fitting 1 1/2"
PVC Glue
Remove the 4 screws holding the toilet to the floor and slide the toilet away to gain access.
Pry the wood top off in order to have better access to the area.
Loosen the clamp screw holding the toilet rubber drain to the black PVC drain pipe and disconnect the rubber drain.
Hold the existing drain up against the floor as far as possible and cut the verticle part of the pipe just below the floor (I used a Sawzal). You want to be sure to have enough pipe sticking up to slide a PVC flexible rubber coupling onto the pipe. Before you slide the coupling onto the drain pipe, cut a pvc pipe to fit into the coupling and the wye fitting. This pipe should be just long enough to provide a solid fit into the 2 mating fittings with just maybe 1/2" of extra pipe. You want to be sure it is firmly attached but not sticking up any higher than needed. Once this is cut, slide it into the coupling and then slide the coupling onto the existing drain pipe. Now tighten the screws on the coupling (which probably are facing the wrong way to reach).
Slide the wye fitting onto the pipe sticking up (do not glue yet). Cut a piece of pipe long enough to fit onto the straight through part of the wye and hold the vent just below the wood top. The vent should be as high as possible but not hitting the wood top when you remount the wood.
Place a 45 degree street elbow into the remaining wye opening and turn it so it is pointing so you can attach the toilet rubber drain. Cut a piece of PVC pipe to fit the elbow and allow a surface to connect the rubber toilet drain to.
Once you are sure everything fits glue all of the fittings together and allow to dry for a few minutes. Do a couple of test flushes and look for any leaks.
Slide the toilet back into position and replace the 4 screws.
I did not reattach the wooden cover but just set it in place. It has never come off and I can check that everything is OK.