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Let $$\mathbf{R} = [x,y,z]$$ be a cartesian vector, $$R_\alpha$$ it's tensor representation with $$\alpha = x,y,z$$ and let $$R=\sqrt{x^2 + y^2 + z^2}$$ be its norm. I want to do tensor derivatives of the Coulomb potential $$1/R$$. The first derivative is $$\frac{\partial}{\partial R_\alpha} \frac{1}{R} = -\frac{R_\alpha}{R^3}$$ and the second derivative is $$\frac{\partial}{\partial R_\beta} \frac{\partial}{\partial R_\alpha} \frac{1}{R}= \frac{\delta_{\alpha\beta}R^2 - R_\alpha R_\beta }{R^5}$$. I want to make further derivatives in Mathematica.

I tried

R = Sqrt[x^2 + y^2 + z^2]


$$\sqrt{x^2 + y^2 + z^2}$$

rR = 1/R


$$\frac{1}{\sqrt{x^2 + y^2 + z^2}}$$

drR = Grad[rR, {x, y, z}, "Cartesian"]


$$\{-\frac{x}{(x^2 + y^2 + z^2)^{3/2}}, -\frac{y}{(x^2 + y^2 + z^2)^{3/2}}, -\frac{z}{(x^2 + y^2 + z^2)^{3/2}} \}$$

So can I make Mathematica identify the denominators as $$R^3$$ and the numerators as $$R_\alpha$$ and get it to the compact form $$-\frac{R_\alpha}{R^3}$$, or is there some other way to do tensor arithmeticscalculus/arithmetics compactly?

Let $$\mathbf{R} = [x,y,z]$$ be a cartesian vector, $$R_\alpha$$ it's tensor representation with $$\alpha = x,y,z$$ and let $$R=\sqrt{x^2 + y^2 + z^2}$$ be its norm. I want to do tensor derivatives of the Coulomb potential $$1/R$$. The first derivative is $$\frac{\partial}{\partial R_\alpha} \frac{1}{R} = -\frac{R_\alpha}{R^3}$$ and the second derivative is $$\frac{\partial}{\partial R_\beta} \frac{\partial}{\partial R_\alpha} \frac{1}{R}= \frac{\delta_{\alpha\beta}R^2 - R_\alpha R_\beta }{R^5}$$. I want to make further derivatives in Mathematica.

I tried

R = Sqrt[x^2 + y^2 + z^2]


$$\sqrt{x^2 + y^2 + z^2}$$

rR = 1/R


$$\frac{1}{\sqrt{x^2 + y^2 + z^2}}$$

drR = Grad[rR, {x, y, z}, "Cartesian"]


$$\{-\frac{x}{(x^2 + y^2 + z^2)^{3/2}}, -\frac{y}{(x^2 + y^2 + z^2)^{3/2}}, -\frac{z}{(x^2 + y^2 + z^2)^{3/2}} \}$$

So can I make Mathematica identify the denominators as $$R^3$$ and the numerators as $$R_\alpha$$ and get it to the compact form $$-\frac{R_\alpha}{R^3}$$, or is there some other way to do tensor arithmetics compactly?

Let $$\mathbf{R} = [x,y,z]$$ be a cartesian vector, $$R_\alpha$$ it's tensor representation with $$\alpha = x,y,z$$ and let $$R=\sqrt{x^2 + y^2 + z^2}$$ be its norm. I want to do tensor derivatives of the Coulomb potential $$1/R$$. The first derivative is $$\frac{\partial}{\partial R_\alpha} \frac{1}{R} = -\frac{R_\alpha}{R^3}$$ and the second derivative is $$\frac{\partial}{\partial R_\beta} \frac{\partial}{\partial R_\alpha} \frac{1}{R}= \frac{\delta_{\alpha\beta}R^2 - R_\alpha R_\beta }{R^5}$$. I want to make further derivatives in Mathematica.

I tried

R = Sqrt[x^2 + y^2 + z^2]


$$\sqrt{x^2 + y^2 + z^2}$$

rR = 1/R


$$\frac{1}{\sqrt{x^2 + y^2 + z^2}}$$

drR = Grad[rR, {x, y, z}, "Cartesian"]


$$\{-\frac{x}{(x^2 + y^2 + z^2)^{3/2}}, -\frac{y}{(x^2 + y^2 + z^2)^{3/2}}, -\frac{z}{(x^2 + y^2 + z^2)^{3/2}} \}$$

So can I make Mathematica identify the denominators as $$R^3$$ and the numerators as $$R_\alpha$$ and get it to the compact form $$-\frac{R_\alpha}{R^3}$$, or is there some other way to do tensor calculus/arithmetics compactly?

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Let $$\mathbf{R} = [x,y,z]$$ be a cartesian vector, $$R_\alpha$$ it's tensor representation with $$\alpha = x,y,z$$ and let $$R=\sqrt{x^2 + y^2 + z^2}$$ be its norm. I want to do tensor derivatives of the Coulomb potential $$1/R$$. The first derivative is $$\frac{\partial}{\partial R_\alpha} \frac{1}{R} = -\frac{R_\alpha}{R^3}$$ and the second derivative is $$\frac{\partial}{\partial R_\beta} \frac{\partial}{\partial R_\alpha} \frac{1}{R}= \frac{\delta_{\alpha\beta}R^2 - R_\alpha R_\beta }{R^5}$$. I want to make further derivatives in Mathematica.

I tried

R = Sqrt[x^2 + y^2 + z^2]


$$\sqrt{x^2 + y^2 + z^2}$$

rR = 1/R


$$\frac{1}{\sqrt{x^2 + y^2 + z^2}}$$

drR = Grad[rR, {x, y, z}, "Cartesian"]


$$\{-\frac{x}{(x^2 + y^2 + z^2)^{3/2}}, -\frac{y}{(x^2 + y^2 + z^2)^{3/2}}, -\frac{z}{(x^2 + y^2 + z^2)^{3/2}} \}$$

So can I make Mathematica identify the denominators as $$R^3$$ and the numerators as $$R_\alpha$$ and get it to the compact form $$-\frac{R_\alpha}{R^3}$$, or is there some other way to do tensor arithmetics compactly?