Hi everyone,
I run into a very strange problem, that looks like critical to me.
Basically, I plot two functions that I know must be tangent at a given
point, and they are not.
First, the code:
x,y=var('x,y')
utility=y*x^2
budget = 24-x
cp=contour_plot(utility,(x,0,24),(y,
0,24),fill=False,cmap='cool',contours=(100,1000,2048,2700,3500))
bp=plot(budget,(x,0,24),color='red')
cp+bp
Now, the plot that comes after calling 'cp+bp' must have the following
property: the straight red line must be tangent to the contour of the
utility function evaluated at level utility=2048; and they must be
tangent at the point (16,8). In my system (Sage 3.2.3 on OpenSuse11.1)
they are NOT tangent; in fact, the sage plot indicates tangency at a
lower level, ~1820.
I checked the calculations many times, both with pencil and paper and
with Maple and Mathematica (besides, this is a _very_ standard problem
in economics, 101 course): the contourplot is tangent to the budget
line at u=2048 and correctly so displayed in maple and mathematica. I
am fairly sure this is not a miscalculation on my part.
My questions are:
- Is it possible that this is a plotting problem? [i.e. the two curves
are plotted on different scales?] and if so, why would it happen?
- Or else is it a calculation problem on the part of sage? I'd find
this absolutely strange. And critical: I want to trust Sage to do the
calculations correctly.
Can you reproduce it?
Thanks,
Paolo Crosetto
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PhD Student in economics
University of Milan - Italy
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