"Automatic is not a valid StreamPoints specification"

Question

If I run

StreamPlot[{a, b}, {a, 0, 10}, {b, 0, a}]

the kernel hangs, and I have to restart it. I also get the error message

StreamPlot::strmpts: Automatic is not a valid StreamPoints specification.

If I try to manually specify StreamPoints, the kernel still hangs, and the error message changes: e.g., with StreamPoints -> 10, I get

StreamPlot::strmpts: 10 is not a valid StreamPoints specification.

(For the record, I'm using 10.4.1 for Microsoft Windows (64-bit)).

What's going on here? What does this message mean, and how can I fix it?

Answer 1

No idea why it doesn't work as in Plot3D[ a b , {a, 0, 10}, {b, 0, a}]...

Try RegionFunction

StreamPlot[{a, b}, {a, 0, 10}, {b, 0, 10},RegionFunction -> Function[{a, b}, b < a]]

Answer 2

StreamPlot is not designed to work with such domain specs. It ought to give a better message though. Actually it doesn't seem to validate the domain before sending it to the internal routines. (Probably, it used a standard plot validation, but the internal routines assume the limits are numeric, i.e., that it's a rectangle.)

tr = Trace[
   StreamPlot[{a, b}, {a, 0, 10}, {b, 0, a}],
   _Visualization`VectorFields`VectorFieldsDump`StreamPointsParse,
   TraceInternal -> True];

StreamPlot::strmpts: Automatic is not a valid StreamPoints specification.

Cases[
 Flatten@tr, 
 HoldForm[parse_Visualization`VectorFields`VectorFieldsDump`StreamPointsParse] :>
  parse]

StreamPlot::strmpts: Automatic is not a valid StreamPoints specification.

(*  {None}  *)

One can inspect StreamPointsParse and its subroutines with GeneralUtilities`PrintDefinitions, if one's curious. It's fairly short code and easy to follow.