Cadabra Q&A - Recent questions in Feature requests

Instructions on keyboard shortcuts

Sun, 21 Apr 2024 11:55:51 +0000

I have a naive question: Where can I find instructions on keyboard shortcuts? For example, what is keyboard shortcut to comment code?

make copy expression easier

Thu, 18 Apr 2024 14:33:57 +0000

When one wants to copy expression, (s)he needs to do something like

ex:=a b;
ex1:=@(ex).
substitute(_,$a->c$);

but it's not direct, is there a more direct way to do this? For example,

ex:=a b;
substitute(@(ex),$a->c$);

Other languages support in LaTeX cell

Thu, 21 Mar 2024 08:15:23 +0000

At present, Cadabra2 just support English input when cell is LaTeX. If other languages, e.g. Chinese, can be supported, this software should be easier to use for some users. This should be an important feature for people whose native language is not English. Maybe add an option related to it to settings to make this possible.

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.

Display currently running function

Thu, 02 Feb 2023 14:54:13 +0000

Does anyone know a way to display the currently running function?

In Cadabra v1, this was extremely useful when I was doing a long list of substitutions / functions. It would give the function (e.g. "canonicalise") and display numerically how far along it was. If something were to hang, I could see immediately what the issue was.

I would love to be able to replicate that functionality within Cadabra v2. Perhaps there is a way to query the kernel for this information?

Raising and lowering indices with an anti-symmetric tensor

Wed, 16 Nov 2022 18:09:12 +0000

Hi there,

I'm quite enamoured with Cadabra's capabilty.

One thing that would be useful is being able to raise indices with an anti-symmetric objeect \epsilon_AB, \epsilon^AB

Right now if I set index behaviour to 'free', the canonicalise function assumes that

u^{A}v_{A} = u_{A}v^{A}

whereas in my line of work it is customary that:

u^{A}v_{A} = -u_{A}v^{A}.

At the moment the only workaround I can think of is keeping all indices lowered and manually inserting \epsilon^AB everywhere.

I had a look at the source for an easy edit I could make and I also couldn't find one. Any suggestions?

Cheers

New properties: "Normal" and "Orthogonal"

Tue, 11 Oct 2022 19:31:01 +0000

(This is a re-post of a question, now under "feature request")

I suggest adding two new properties for tensors that are not scalars

"Normal" can be applied to a 1D tensor (vector or covector), with two fields
1. 'norm' that can be either +1 or -1
2. 'deriv' that will reference a Derivative symbol (like if you defined \nabla{#}:Derivative earlier)
"Orthogonal" can be applied to any tensor (that is not a scalar)

The properties will be unaffected by raising or lower indices, e.g. if A_{m,n} is orthogonal, then A_{m}^{n} is also orthogonal and if B_{k} is normal then so is B^{k}.

Then there need to be a new method contract_normal(expr), that will scan an expression and look for contractions between tensors

if two tensors are 1D normal vector & 1D covector then their contraction is the value of 'norm'
if one tensor is orthogonal and the other is a normal vector/covector then their contraction is 0
if one tensor is a normal vector and the other is the 'deriv' operator on a normal vector e.g. A^{m} \nabla_{k}{A_{m}} or A_{m} \nabla_{k}{A^{m}}, then the contraction is 0.

Using spherical harmonics in cadabra.

Thu, 02 Jun 2022 04:57:53 +0000

How I can use spherical harmonic in the cadabra?

question regarding a rule involving partial derivative

Mon, 14 Feb 2022 07:48:40 +0000

Hi,

I was looking for a rule involving partial derivative action on a tensor. Suppose I have an expression like

\begin{align} \partial_{a} A^{a}+ A_{a}B^{a} + (\partial_{a b}A_{a}) B^{b} + \partial_{b}A_{a} \partial^{b}B^{a} \end{align}

I wish to define a rule such that I need to set the quadratic terms that involves the derivatives to vanish , i.e, I need to set $\partial_{a b}{A_{a}} B^{b} \rightarrow 0, \partial_{b}A_{a} \partial^{b}B^{a} \rightarrow 0$, I am not abe to get a proper rule to do this.

Also is there any way in which I can also set a partial derivative that involves any no f derivatives to zero, like I need to set \begin{align} \partial_{a} A^{c} =0; \partial_{a b} A^{c}=0; \end{align}

etc

I was thinking of something like

ex:= \partial{#}{A{#}} -> 0;

But didnt seem to work. can you please help me out

Calling a cadabra note book in another one.

Fri, 08 Oct 2021 08:21:02 +0000

I just started using Cadabra software. I want to know is it possible to call a saved Cadabra notebook into a new one? If it is possible, can anyone suggest to me how to call it? particularly how to give a pathway in the new one about the saved notebook location?

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

Support for plugin `Remote - WSL` in vscode

Wed, 07 Jul 2021 19:40:30 +0000

I wonder whether I can run cadabra-kernel in vscode by using plugins Jupyter & Remote - WSL. I have some tries, but never succeed, while python2/3-kernel works fine. If it can be supported, the world will be better for windows users.

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.

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)$.

Providing a `Weight` to a `Derivative`

Mon, 02 Sep 2019 16:34:41 +0000

I tried to isolate terms with a certain order of derivation by defining a Weight property to the derivative.

(x, y)::Coordinate.
(i, j)::Indices(values={x, y}, position=fixed).
\nabla{#}::Derivative.
h_{i j}::Depends(x, y, \nabla{#}).
\delta{#}::KroneckerDelta:
\nabla{#}::Weight(label=order, value=1);
\nabla{#}::WeightInherit(label=order, type=additive);

Then, a test expression

test := A \delta_{i j} + h_{i j} 
+ \nabla_{x}{h_{i j}} 
+ B \nabla_{y}{h_{i j}} 
+ C \nabla_{x}{ \nabla_{y}{ h_{i j} } } 
+ \nabla_{x}{ \nabla_{x}{ h_{i j} } };

Finally, I'd like to define terms with a certain order on derivatives,

term0 := @(test).
keep_weight(_, $order=0$);
term1 := @(test).
keep_weight(_, $order=1$);
term2 := @(test).
keep_weight(_, $order=2$);

It results in the

The zeroth order is Ok, but the first and second yield problems.

Question

What is the right way (if any) of providing Weight to a derivative operator?

P.D.: The same occurs with the PartialDerivative or by changing the WeightInherit type to multiplicative.

Collecting scalar terms in expressions with `DifferentialForms`

Fri, 30 Aug 2019 09:52:06 +0000

It seems that the wedge product does not allow (yet) collecting scalar terms

Example

{f,g}::DifferentialForm(degree=0).
{V, W}::DifferentialForm(degree=1).
foo := f V ^ g W;
canonicalise(foo);
sort_product(foo);
collect_factors(foo);

In the above example all the simplification algorithms return the original foo expression, while the expected result is $f g V \wedge W$.

Extending zoom() function

Thu, 29 Aug 2019 18:12:37 +0000

Hello!

As far as I understood, the zoom() command was introduced to produce manipulations on a subset of the full sum. It might be useful to extend its functionality in two ways.

First, if you have a long expression, you would probably want to examine it by parts. In present form zoom() does not suits this goal. To illustrate this, consider the following code:

test := H = a + b a;

Then by using zoom() in different ways I get:

zoom(test, $ a $); 
H = a + ...
unzoom(test),
zoom(test, $ a Q?? $);
H = ba + ...

The second result is what one needs for the manipulations of the expressions. However, none of them suits for examining all terms including a in a simple way. Or is there an implemented mechanism for getting all terms including a?

Second, having an analogue of zoom for creating new object might be useful. Schematically, something like

H2 := zoom(H1,$ a Q?? $),

will allow to add H2 to other objects, etc. I did not find a way to implement this in the present version of Cadabra.

The things I've described can be implemented by introducing additional steps (like using substitute and setting some of the parameters to zero), but 1) it would not always work and 2) it is nice when it is possible to make complicated things by running only one command.

Kasper, thank you very much for creating and improving Cadabra! It is very useful.

Fierz identities with Majorana fermions in dim=4 and chirality

Tue, 16 Jul 2019 18:46:24 +0000

Is there any function to have Fierz Identities for Majorana fermions in four dimensions?

Moreover, is there any method to split the chirality components of a fermion and implement the \gamma^5 matrix?

Thank you for your help.

`eliminate_vielbein` and the `KroneckerDelta`

Mon, 06 May 2019 09:38:09 +0000

Thank you Kasper. I've build the github version 2.2.7, and soo that you improve my rusty version of the notebooks. Great work!

I'd like to mention that I try the following code:

{M,N,P,Q,J,K,L}::Indices(full, position=independent).
{\mu,\nu,\rho,\sigma,\gamma,\lambda}::Indices(sub,position=independent, parent=full).
e^{M}_{\mu}::Vielbein;
E^{\mu}_{M}::InverseVielbein;
\delta^{\mu?}_{\nu?}::KroneckerDelta;
\delta_{\mu?}^{\nu?}::KroneckerDelta; 
ex := e^{M}_{\mu} E^{\nu}_{M};
eliminate_vielbein(ex);

The result is E^{\nu}_{\mu}, which is correct of course, but I expected that after defining the InverseVielbein the result would be a KroneckerDelta.

Question: Do you think it is possible to change that behaviour?

I know that it is possible that my expectations make not a lot of sense from the coding view point... since it's possible that the user had not defined the KronerckerDelta, or the fact that the delta has to be defined in both spaces, and so on.

BTW,

Bonus question: Instead of defining several KroneckerDelta, Would be possible to define a single \delta{#}::KroneckerDelta; that works on whatever indices type and position?

Vielbein, inverse and their elimination. Documentation

Fri, 03 May 2019 10:27:27 +0000

On an old question (https://cadabra.science/qa/162/usage-of-vielbein?show=162#q162), the implementation of the property Vielbein was requested. While it was implemented, as well as the property InverseVielbein, the implementation of the algorithm eliminate_vielbein is not yet implemented.

Request and questions

Is it possible to implement the related algorithms to the Vielbein and InverseVielbein properties be implemented?
I noticed that the lack of documentation of those properties. I'm interested in contribute documenting algorithms and properties. Can you provide some (minimal) guidelines?

Cadabra QA page: functionality

Fri, 26 Apr 2019 09:48:51 +0000

Perhaps this is not the place to comment about my concerns with the QA page, but there are some features that could be useful:

Possibility of editing other people questions or comments: There are really interesting questions, which can be improved in format with ease, e.g. LaTeX code, cadabra block code, etc. Inspired in stackexchange, one could use the number of points to limit the privileges given to people.
Vote up comments: Some times the discussion derived from a question/answer is as valuable than the question/answer. Those comments deserve recognition! Don't they?

Thank you

update Cadabra: reference guide and tutorial to 2.x

Sat, 02 Mar 2019 11:01:55 +0000

The paper Cadabra: reference guide and tutorial is out of fashion, just 1.x. I wish author could update it to 2.x.

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.

Suggestions for tutorial notebooks

Tue, 24 Apr 2018 18:28:28 +0000

This is a list of tentative topics for tutorial notebooks which have been suggested to me by email or otherwise. If you can think of anything else you would like to see covered, please reply in this thread.

Programming topics, e.g. loading/saving expressions, writing packages, expression traversal.
Differential forms, gauge theories.
Elementary demonstrations in general relativity, e.g. how to derive Einstein equations using vary.
Gravitational waves.
Friedmann equations and related topics.
Advanced pattern matching/substitution (e.g. use of conditionals).

Multiple Window in cadabra

Sun, 26 Nov 2017 12:25:47 +0000

When I try to open a new notebook, the current notebook automatically closes down. I don't know whether this is a problem in my installation. Is there a way to open multiple windows at a time? (this is particularly useful When I try to copy a notebook content to another)

Using anaconda sympy in ubuntu

Sat, 25 Nov 2017 19:29:04 +0000

I am using anaconda python in ubuntu. When I try to use `complete' in cadabra, it says "ImportError: No module named 'sympy' ". It seems that the error is with the anaconda python. How to use Cadabra with anaconda python in Linux? Thanks...

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....

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?

Trace of Gamma Matrices?

Wed, 04 Jan 2017 06:52:41 +0000

Is there any command/package for computing the traces of gamma matrices using Cadabra? Or if it can be calculated in a simple way with existing commands? If not, it would be a really great addition for doing computations. Thanks in advance for either of the cases.

usage of Vielbein

Fri, 23 Dec 2016 20:14:58 +0000

Hello,

When I try to use a Vielbein in cadabra2 I get the following error:

h^{m}_{\mu}::Vielbein.

The error reads:

Traceback (most recent call last):
   File "<string>", line 11, in <module>
NameError: name 'Vielbein' is not defined

Does anybody have experience with this?

Thank you,

Asier

Substitute the "absolute" indices

Mon, 17 Oct 2016 11:18:10 +0000

Example:

{a, b, c, d}::Indices.
D{#}::Derivative.
ex:= D_{a}{D_{b}{A_{c}}} -D_{b}{D_{a}{A_{c}}};
substitute(_,$ D_{a}{D_{b}{A_{c}}} -> D_{b}{D_{a}{A_{c}}} +R_{a b c d} A^{d} $ )

I hope the substitute returns zero directly. So maybe a new feature for substitute like following:

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

Thus, substitute only substitutes the first term with the "absolute" indices, i.e. D_{a}{D_{b}{A_{c}}}, and do nothing to the second term, i.e. D_{b}{D_{a}{A_{c}}}.

In short, I need to be able to suppress automatic recognition for indices.

By the way, some features in Cadabra.1 such as regular expression, ? and ?? etc. are very helpful for my work.