# define symbolic constant

I need to define some symbolic constants in some expressions, so that the symbolic constant survives differentiation. How can they be defined?

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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) |--> y


Here, 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 |--> pi


But Sage also protect you from differentiating whith respect to a constant:

sage: f.differentiate(pi)
TypeError: argument symb must be a symbol

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Permit 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

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?

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When i do this, i get $\left(\frac{3 \, m x^{2}}{{\left(x^{2} + y^{2} + z^{2}\right)}^{\frac{5}{2}}} - \frac{m}{{\left(x^{2} + y^{2} + z^{2}\right)}^{\frac{3}{2}}},\,\frac{3 \, m x y}{{\left(x^{2} + y^{2} + z^{2}\right)}^{\frac{5}{2}}},\,\frac{3 \, m x z}{{\left(x^{2} + y^{2} + z^{2}\right)}^{\frac{5}{2}}}\right)$ 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 ?