Cadabra Q&A - Recent questions and answers in Feature requests

Answered: make copy expression easier

Mon, 22 Apr 2024 21:42:55 +0000

I would only like to add that a possible variant is

substitute($@[ex]$, $a -> c$)

Using square brackets also creates a copy and does not affect the original expression.

Answered: Instructions on keyboard shortcuts

Mon, 22 Apr 2024 09:11:10 +0000

Hi Eureka.

The answer to your question depends whether you are using the native or the jupyter-notebook user interface.

In the native user interface the help is in the menu bar, shown to the right of the listed actions. There is no CLI to comment code lines, AFAIK.

The jupyter-notebook has many key bindings, and they are not specific to cadabra. See for example https://defkey.com/jupyter-notebook-shortcuts or https://cheatography.com/weidadeyue/cheat-sheets/jupyter-notebook/.

Answered: Other languages support in LaTeX cell

Sat, 13 Apr 2024 13:01:50 +0000

The microtex branch now contains a version of Cadabra which no longer relies on LaTeX for maths typesetting. You can either build that yourself, or try the new (and still experimental) AppImage builds from the download page.

Let me know if this helps with the issue you reported please.

Complex scalar field (Klein-Gordon, Schrodinger, Higgs...)

Fri, 20 Oct 2023 15:56:27 +0000

Hello! One of the simplest (if not the simplest) examples of classical field theory is the complex scalar Klein-Gordon field, the relativistic version of the classical Schrodinger field. Now, Cadabra seems great for General Relativity, the DIrac field, the elecgtromagnetic field... but I see no clear treatment of complex scalars. It would be amazing if the tutorial would include a simple example with the Klein-Gordon field (i.e. how to find the Klein-Gordon equation given the action). This is done in the tutorial for the free classical Maxwell field, having another example would be great.

Answered: Display currently running function

Thu, 02 Feb 2023 19:26:52 +0000

There is some internal functionality for algorithms to send out-of-band progress information to the user interface in v2, but it has mostly been to experiment with it and see what we need. Only the meld algorithm really uses it at the moment. I am not sure we have converged on the right mechanism yet, hence it hasn't been included in other algorithms.

The problem is, as always with logging, that you do not want to log too little, but you also do not want to log too much. However, this distinction is very much a function of the problem you are solving: sometimes you want to see an update for all terms canonicalise acts on, but sometimes that's a very fast part of some inner loop and you are not interested in that. Some nested progress indicator is probably best.

If you have any good ideas, please post.

Answered: Raising and lowering indices with an anti-symmetric tensor

Wed, 16 Nov 2022 18:30:51 +0000

Add the AntiCommuting property to the indices, so e.g.

{A,B}::Indices(position=fixed);
{A,B}::AntiCommuting;
ex:= v^A v_A - v_A v^A;
canonicalise(_);

which produces $2 v^A v_A$.

Answered: New properties: "Normal" and "Orthogonal"

Tue, 11 Oct 2022 21:18:03 +0000

I am not in principle against adding some functionality to make these kind of manipulations easier. However, most of what you want to do can be achieved with some simple substitution rules. I think that the main thing you are looking for is some way to "put vectors or tensors in a labelled set", so that you can apply a rule whenever such an object appears. That makes things more useful in a wider context; your solution is very much tuned to a particular class of problems, and does not generalise well to situations where you may have multiple vector bundles or multiple surfaces to which something can be "orthogonal" or "normal".

Let's think this through a bit. Feel free to continue the discussion here so we get a better idea of what your requirements are.

Answered: Using spherical harmonics in cadabra.

Thu, 02 Jun 2022 18:03:52 +0000

Cadabra currently does not have any functionality for spherical harmonics. There is some support for that in sympy though, which may help. As long as you go from a Cadabra expression to a sympy expression all is fine; getting expressions from sympy back into Cadabra for further computations is not very well supported at the moment.

Answered: question regarding a rule involving partial derivative

Mon, 14 Feb 2022 09:56:47 +0000

Hi, I've got a similar problem before, and it is due (to my understanding) to the fact that cadabra uses the notation

$\partial_{ab}$

to denote

$\partial{a}\partial{b}.$

I solved my problem by adding a dummy symbol that can be then set to one after the simplification (if it is still around), I used the symbol I in the ex2 below

{a,b,c}::Indices.
\partial{#}::PartialDerivative.

ex := \partial_{a}{ A^a } + A_a B^a + \partial_{a}{ \partial_{b}{ A^a }} B^b 
    + \partial_{a}{ A^b } \partial_{b}{ B^a };
ex2 := \partial_{a}{ A^a } + A_a B^a + \partial_{a}{ I \partial_{b}{ A^a }} B^b 
    + \partial_{a}{ A^b } \partial_{b}{ B^a };
rl := \partial_{a}{ A^{b} } -> 0;

substitute(ex, rl);

substitute(ex2, rl);

See the result here

Hope this can be useful.

Update:

Another solution is that you could declare \partial{#}::Derivative. instead of like a partial derivative. The difference is that Derivative does not simplify the notation

$\partial{a}\partial{b}$

$\partial_{ab},$

and the substitution works properly.

See the updated code and result

Answered: Calling a cadabra note book in another one.

Fri, 08 Oct 2021 08:25:46 +0000

Cadabra notebooks are treated as normal python modules when importing them into other notebooks. So you can have one notebook one.cnb and then from another one do

import one

just like you would in Python. The standard rules for importing modules hold, in particular that you need to have the one.cnb somewhere in the PYTHONPATH (or sys.path).

For some more details see https://cadabra.science/notebooks/ref_import.html

Getting list of arguments of functions

Mon, 06 Sep 2021 11:39:31 +0000

Hi,

The "evaluate" function has several arguments, like the parameter rhsonly that appears in different manuals I read. In the official documentation https://cadabra.science/manual/evaluate.html it isn't listed. I also went over the different pdf documents and didn't find a complete list of the arguments and their meaning.

Is there a document with a more thorough description of all the usable functions for Cadabra?

Alternatively, is there a way to get a list of arguments of an arbitrary function (like python's inspect)?

Thanks in advance, Amnon

Answered: Support for plugin `Remote - WSL` in vscode

Thu, 08 Jul 2021 10:00:54 +0000

It's not something I will be implementing myself anytime soon (there simply isn't enough time in the day), but I'm happy to take patches if anyone figures out how to do this.

Split free indices, and not just dummy indices.

Wed, 09 Sep 2020 21:31:14 +0000

It is possible to split sums based on dummy indices:

{M,N,P,Q,R}::Indices(full).
{m,n,p,q,r}::Indices(space1, parent=full).
{a,b,c,d,e}::Indices(space2, parent=full).

ex:=A_{M d Q R} B_{M p Q R};
split_index(_, $M,m,a$);

Can something like this be used for free indices too?

For example, I want:

ex := A_{m p} + A_{a p};

This should split the tensor into two tensors. Graphically, this would split the matrix into two smaller matrices based on their columns, and missing values will be set to zero.

This can be extended for more complicated splits. In this case, one would have to somehow specify splits based on subgroups of indices.

For example, one might want to split a tensor based on an arbitrary set of indices. I.e. given tensor A_{x1 x2 ... xN}, get some specific indices {x1 x2 ... xN} into one tensor, and the rest in another tensor.

Answered: Trace of Gamma Matrices?

Wed, 04 Dec 2019 01:34:04 +0000

You can do it with recent versions of Cadabra but it's a little awkward. For example,

{\mu,\nu,\rho,\sigma}::Indices(vector);
{\mu,\nu,\rho,\sigma}::Integer(0..3);
{a,b,c,d}::Indices(spinor);
Tr{#}::Trace(indices=spinor);
\delta_{\mu \nu}::KroneckerDelta;
\Gamma^{#}::GammaMatrix(metric=\delta);
\Gamma^{\mu}::ImplicitIndex(\Gamma^{\mu}_{a b});
\Gamma^{\mu \nu}::ImplicitIndex(\Gamma^{\mu \nu}_{a b});
\Gamma^{\mu \nu \rho \sigma}::ImplicitIndex(\Gamma^{\mu \nu \rho \sigma}_{a b});
ex:=Tr(\Gamma^{\mu} \Gamma^{\nu \rho} \Gamma^{\sigma});

Then call "join_gamma", "distribute", "untrace" until you only see traces of single gamma matrices. Finally "canonicalise" will kill all of them except Tr(1).

Answered: Collecting scalar terms in expressions with `DifferentialForms`

Sun, 22 Sep 2019 14:18:21 +0000

Current github/master can now do

{f,g}::DifferentialForm(degree=0).
{V, W}::DifferentialForm(degree=1).
foo := f V ^ g W;
unwrap(_);

producing $f g V \wedge W$. Enjoy (and let me know if things don't work properly).

Answered: Providing a `Weight` to a `Derivative`

Thu, 05 Sep 2019 21:59:33 +0000

If you want a derivative to inherit a weight and have a weight of that same type itself, you need to use the self parameter to WeightInherit. So

\nabla{#}::WeightInherit(label=order, self=1, type=multiplicative);

(and drop the Weight property). The type should be multiplicative, which is a confusing way to say that the weights of the child node of the derivative should be combined as if they had been sitting in a product, that is, they should be added up.

(type=additive means that the weights of the children are handled as if the children are sitting in a sum, that is, they should all be equal).

Fierz (Request)

Wed, 04 Sep 2019 14:14:46 +0000

Hi everyone,

Is there a way to perform a Fierz transformation on a product of two spinors?

Thanks.

Edit:

For example, if we have the majonara spinors $\chi^{\sigma} = \bar{\chi} = \bar{\lambda} P_{L}$ and $\varphi_{\alpha} = \varphi = P_{L} \chi$, where $P_{L} = \frac{1}{2} (1 + \gamma_{*}) $, the fierz identity for $\varphi \bar{\chi}$ is $ \varphi \bar{\chi} = -\frac{1}{2} P{L} (\bar{\lambda} P_{L} \chi) + \frac{1}{8} P_{L} (\gamma_{\mu \nu} \bar{\lambda} \gamma^{\mu \nu} P\{L} \chi)$.

Answered: Extending zoom() function

Tue, 03 Sep 2019 14:36:13 +0000

The fact that zoom(smth,$ a Q?? $) does not match a single term a is intended behaviour, but of course that does not help you. This should have been possible by using multiple patterns in the same zoom, but that does not work at the moment. I have opened an issue at https://github.com/kpeeters/cadabra2/issues/161.

Answered: Fierz identities with Majorana fermions in dim=4 and chirality

Fri, 09 Aug 2019 18:30:10 +0000

The chiral matrix $\gamma^5$ can be defined using the epsilon tensor. See my answer to this post

Answered: `eliminate_vielbein` and the `KroneckerDelta`

Thu, 09 May 2019 15:52:53 +0000

The bonus question is already possible, just

\delta{#}::KroneckerDelta;

works.

The other one is more tricky. I usually do

E^{\mu}_{\nu}::KroneckerDelta;
E^{\mu}_{\nu}::LaTeXForm("\delta").

to get the display correct. In order to auto-convert to an actual \delta object, not just something that prints as $\delta$, eliminate_vielbein would need to know that you want to use the \delta^{\mu}_{\nu} as the Kronecker delta for the $\mu, \nu$ indices. That's possible (there is a way for algorithms to look up such properties) but I haven't implemented that yet. Have opened an issue on github to track this ( https://github.com/kpeeters/cadabra2/issues/153 ).

Answered: Vielbein, inverse and their elimination. Documentation

Fri, 03 May 2019 19:26:02 +0000

Have merged your initial docs and the actual algorithm now. There's room for improvement of course.

Answered: Cadabra QA page: functionality

Fri, 26 Apr 2019 12:48:41 +0000

I rely on the Q2A software for all of this; you may be better off making these suggestions on their support forum.

Answered: update Cadabra: reference guide and tutorial to 2.x

Sat, 02 Mar 2019 11:02:16 +0000

See https://cadabra.science/help.html (not entirely complete but better than nothing).

Matrix exponential

Sun, 17 Feb 2019 14:18:29 +0000

It would be nicer if the future Cadabra would be able to deal with calculating the exponentials of (Gamma) matrices.

Answered: Suggestions for tutorial notebooks

Mon, 30 Apr 2018 06:27:05 +0000

Hi Kasper and Leo,

I'd also like to make a contribution.

As a physicist, from my point of view I think that

a tutorial on voice 1. would be an excellent way to combine the experience of using the Cadabra manipulator with the opportunity to discover/learn the basic programming logics (seeing their direct projected application in the context of physics). Thanks to its Open Source nature, Cadabra is predisposed to be a valid tool also from this point of view.
for the other points, I am convinced that the extension of the code/examples provided to the user in a wide range of fields is always a good thing (the user can learn/use/modify according to the specific interests -> new extensions/ideas for the future).

I am therefore in favor of all the points, specific or less than they are :)

Thanks and regards,

Mattia

Answered: Multiple Window in cadabra

Sun, 26 Nov 2017 13:47:43 +0000

Start cadabra again.

Answered: Using anaconda sympy in ubuntu

Sat, 25 Nov 2017 20:39:03 +0000

At the moment, you can't. The Anaconda people have made it seriously difficult to create large packages which are not pure Python (they simply haven't thought through how people want Anaconda to talk to system supplied tools). Your best bet is simply to install sympy for the system-supplied Python, e.g. by doing

sudo apt install python3-sympy

(which may not get you the latest version, unfortunately) or by getting the latest version through a pip install,

sudo pip3 install sympy

importing differential geometry package

Wed, 11 Oct 2017 06:22:51 +0000

any chance of importing the package 1103.1608 I have no idea how such things are done so I can safely say why not....

Answered: usage of Vielbein

Fri, 05 May 2017 10:55:32 +0000

I would be very interested in using cadabra with vielbeins. Will that possibility be available?

Define explicitly dependent objects

Mon, 10 Apr 2017 11:14:03 +0000

Hi everyone, I'm trying to derive the equations of motion of a scalar field with a potential $V(\phi)$, $S:= -\int \sqrt{-g}(\frac{1}{2}g^{\mu \nu} \partial_{\mu}{\phi} \partial_{\nu}{\phi}+V )d^4x$; however when I compute the variational derivative of the action with respect to $\phi$ the potential does not appear (due to property V::Depends::{x}, only allow to make objects implicitly dependent on the coordinates). Is there any property in Cadabra which Makes an object explicitly dependent on other objects, like $V(\phi)$?

Thank you !!

Configure a default folder

Mon, 13 Feb 2017 13:46:14 +0000

I'm not sure if it is my OS configuration (I use debian) , that within cadabra when I hit C-o, it shows me a list of recent documents... however, I would like to set a cadabra2_programs folder.

Is it possible to personalise the default folder?

Answered: Substitute the "absolute" indices

Mon, 17 Oct 2016 12:55:59 +0000

Instead of relying on index names, substitute like this:

substitute(_,$ D_{a}{D_{b}{A_{c}}} -> 1/2 D_{b}{D_{a}{A_{c}}} + 1/2 D_{a}{D_{b}{A_{c}}} + 1/2 R_{a b c d} A^{d} $ );

Or in other words, decompose the double derivative into a symmetric bit and an anti-symmetric bit. The symmetric bits will then cancel in your original expression, leaving the Riemann tensor.