Yesterday I was demonstrating to my calculus class Sage's ability to
implement the method of Lagrange multipliers. I used a standard example,
putting the following code into SageMath Cell:
var('x,y,l')
f(x,y)=10*x^(1/3)*y^(2/3)
g(x,y)=5*x-6*y
fx=diff(f,x)
fy=diff(f,y)
gx=diff(g,x)
gy=diff(g,y)
solve((fx(x,y)==l*gx(x,y),fy(x,y)==l*gy(x,y),g(x,y)==120),(x,y,l))
That works beautifully. Then I decided to show off Sage's powers by
making a little change:
var('x,y,l')
f(x,y)=10*x^(1/3)*y^(2/3)
g(x,y)=5*x^2+6*y
fx=diff(f,x)
fy=diff(f,y)
gx=diff(g,x)
gy=diff(g,y)
solve((fx(x,y)==l*gx(x,y),fy(x,y)==l*gy(x,y),g(x,y)==120),(x,y,l))
SageCell now gives me a spinning symbol ("I'm working") for a while,
then seems to exit without any result. On my local installation (Sage
9.2 on Windows) it returns an empty list, [].
What is curious is that the constraint equation 5x^2 + 6y=120 is easily
solved for y...
Questions:
1) Shouldn't SageCell output an empty list here?
2) Is this a known limitation of "solve"?
Fernando
PS: It seems that if I add "algorithm='sympy'" then solutions are found.
--
==================================================================
Fernando Q. Gouvea
Carter Professor of Mathematics
Colby College
Mayflower Hill 5836
Waterville, ME 04901
fqgou...@colby.edu http://www.colby.edu/~fqgouvea
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