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When gcd : 'spmod, this bug goes away:
(%i7) limit(x*(sqrt(1+x^2)-x),x,inf), algebraic : true, gcd : 'spmod;
(%o7) 1/2
(%i1) x*(sqrt(1+x^2)-x);
(%o1) x*(sqrt(x^2+1)-x)
(%i2) limit(%,x,inf), algebraic : true;
Quotient by a polynomial of higher degree
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When gcd : 'spmod, this bug goes away:
(%i7) limit(x*(sqrt(1+x^2)-x),x,inf), algebraic : true, gcd : 'spmod;
(%o7) 1/2
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Assign category & increase priority.
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Seems to be caused by subresgcd being called with a cre that is not really a
polynomial: the coeffecients contain the top-level variable. Possible solution
would be to test for this condition, then call another gcd algorithm, or just
return 1 as gcd. Any suggestions on how to do the test?
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fixed in rat3c.lisp rev 1.18
add checks to subresgcd and redgcd for cases where the coefficients
of the CRE contain the main variable.
(%i2) limit(x*(sqrt(1+x^2)-x),x,inf), algebraic : true, gcd : subres;
(%o2) 1/2