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This function f = x*Log[y] is defined for all x and for y>0

f = x*Log[y];
fdomain = FunctionDomain[f, {x, y}]

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so I expected StreamPlot to only show streams for y>0 only, even if the range given in the command itself includes negative values. (may be one did not notice the y range includes something outside the domain).

But the stream plots are all missing from y=0 to y=1 and then start above that.

Why are stream lines missing from y=0..1?

f = x*Log[y];
p = StreamPlot[{1, f}, {x, 0, 3}, {y, -1, 3},
        Axes -> True, Frame -> False, AxesOrigin -> {0, 0}
        ]

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They show up, when changing the y range to start from zero:

f=x*Log[y];
p = StreamPlot[{1,f},{x,0,3},{y,0,3},
      Axes -> True,Frame -> False,AxesOrigin->{0,0}
      ]

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Compare to Maple, for same function and same plot range, it shows correctly the streams for 0..1 for y even though the range asked for starts at -1

f:=x*ln(y);
plots:-fieldplot([1,f],x=0..3,y=-1..3,fieldstrength=fixed);

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Mathematica 11.3 on Linux

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  • $\begingroup$ Same behavior in Mathematica 11.3 Win 10. Could make them show up with this. f = x*Log[y]; p = StreamPlot[{1, f}, {x, 0, 3}, {y, -1, 3}, Axes -> True, Frame -> False, AxesOrigin -> {0, 0}, StreamPoints -> Evaluate[ Flatten[Table[{x, y}, {x, 0, 3, .2}, {y, -0.2, 3, 0.2}], 1]]] $\endgroup$
    – Zviovich
    Jul 31 '18 at 11:56
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    $\begingroup$ Use {y,0,3} and set PlotRange to whatever you want. That's for a workaround, if you need to know why, I'd ask WRI Support. $\endgroup$
    – Kuba
    Jul 31 '18 at 12:11
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Why are stream lines missing from y=0..1?

Fixed in 12.3

ClearAll[x, y];
f = x*Log[y];
p = StreamPlot[{1, f}, {x, 0, 3}, {y, -1, 3}, Axes -> True, 
  Frame -> False, AxesOrigin -> {0, 0}]

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