I need to define some symbolic constants in some expressions, so that the symbolic constant survives differentiation. How can they be defined?
I may not understand your question. As long as you declare the variable whith respect to which you differentiate, there should not be any problem, for example:
sage: f(x,y) = x*y
sage: f
(x, y) |--> x*y
sage: f.differentiate(x)
(x, y) |--> yHere, you differentiate whith respect to x, so y is considered as a constant. Also:
sage: f(x) = pi*x
sage: f
x |--> pi*x
sage: f.differentiate(x)
x |--> piBut Sage also protect you from differentiating whith respect to a constant:
sage: f.differentiate(pi)
TypeError: argument symb must be a symbolPermit me to ask this another way. I want to compute the symbolic gradient of the following:
-mu * x / r^3, where mu is a constant and r = sqrt( x^2 + y^2 + z^2 )
In my sage worksheet I have:
variables = var( 'x, y, z, r, f' )
constants = var( 'm' )
r = sqrt( x^2 + y^2 + z^2 )
f = -m * x / r^3
show(f.gradient([x,y,z]))
Sage does not give me the correct answer. My question is how do I get Sage to treat or declare m as a constant in the calculus sense?
When i do this, i get (3mx2(x2+y2+z2)52−m(x2+y2+z2)32,3mxy(x2+y2+z2)52,3mxz(x2+y2+z2)52) I did the computation by hand and it seems to be the correct result. If you replace `m` by `pi`, you will get the same answer. Which expression did you expect ?
Asked: 11 years ago
Seen: 3,013 times
Last updated: Nov 20 '13
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