> Hmm, three dots are probably clearer than question mark.  And 
> documentation for degreeSubResultantEuclidean and 
> semiDegreeSubResultantEuclidean still looks wrong 
> (mentions different function).

I'll fix that.

> IIUC they are used in case of finite fields. 

Oh, that makes sense.  Then I'll rename *_naif to *
and put them under 'if R has Finite and R has Field'?

> IIUC SUP uses pseudoDivide from polycat.spad.  The 
> one in prs.spad looks more efficient. 

I noticed that too, so should we implement pseudoDivide
and pseudoQuotient alongside with pseudoRemainder
in poly.spad? (PRS is not the right place for pseudoDivide)

> This one produces some weird error for me. 

Which error? The implementation of Lazard* is exactly the same
between prs.spad and newpoly.spad.

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