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>1. Your bug #1 is not really a bug. If you start axiom (in the text mode) 
>and say
>)set output tex on
>you will see that
>xy
>produsec the output
>$$
>xy
>$$
>and
>x*y
>produces the output
>$$
>x \ y
>$$
>and this '\ ' does produce a little extra space in the math mode. I agree 
>that this space is too little. But the only way to change this is to 
>re-write TeX generation functions in axiom to produce something other than 
>'\ '. So, this was a design decision of the authors of TeX generation in 
>axiom (maybe, not the best one).

In the meantime I´ve solved this problem (bug)! :-)

I´ve found the right place of this ´\ ´ in the file
...\axiom\mnt\windows\algebra\TEX.o
and changed it to ´* ´ with a hex-editor - and now
WinTeXmacs correctly displays every multiplication
with the wanted ´*´ character! :-)

Now there´s only the other bug (with ´\over´) left -
maybe we can find also such a hexeditor-patch to
one of the Axiom or WinTeXmacs files to fix it!?

Regards,
Franz.