#4080 ?mgrp(0,infinity) is true

[Barton Willis]

This is wrong--it says that zero is greater than complex infinity

(%i16) ?mgrp(0,infinity);
(%o16)                               true

These are OK

(%i17) ?mgrp(0,minf);
(%o17)                               true
(%i18) ?mgrp(0,inf);
(%o18)                               false

This one is maybe not wrong, but it's not optimal

(%i19) ?mgrp(0,ind);

sign: sign of ind is undefined.

And maybe this should be true

(%i20) ?mgrp(0,zeroa);
(%o20)                            - zeroa > 0

[Stavros Macrakis]

Not sure what would be a better result for ?mgrp(0,ind). ?mgrp(0,x) returns -x>0 but it doesn't make sense to return -ind>0, since we don't know where the ind came from.

Remember that ind, zeroa, zerob are really only "understood" by the limit package, and that the general simplifier does not handle them and other non-finite quantities correctly. Should it be true that zeroa > 0 > zerob? Yes, sure (sign needs to be updated).

But if there's more than on non-finite quantity in an expression, all bets are off....

[Stavros Macrakis]

Maxima bug reports should be in terms of the normal user interface.
Otherwise I wonder: "maybe the callers of ?mgrp never invoke it in this case, so it doesn't matter".
But in fact, is(0>infinity) => true, and trace shows that comes from ?mgrp.

Nothing wrong with mentioning ?mgrp in the body of the bug report to help the next person to work on it, but the main bug report should be about user-visible behavior if at all possible, not about internals.

[Robert Dodier]

This is related to bug #4120, which is about trying to compare items which are incomparable (strings and numbers) -- I think 0 and infinity are incomparable too, since infinity is supposed to be complex infinity.

Dunno if it's MGRP or sign which needs to get fixed up here.