Add Angular Momentum builtins... #496

rocky · 2022-08-07T16:59:01Z

which starts a Quantum Mechanics section.

~~TODO:~~

Unit tests for errors.

Ensure function attributes are correct

~~Ensure we error on what we are supposed to and not on what we do not~~

mmatera · 2022-08-07T22:20:28Z

mathics/builtin/quantum_mechanics/angular.py

+
+    <dl>
+      <dt>'ClebschGordan[{$j1$, $m1$}, {$j2$, $m2$}, {$j$ $m$}]'
+      <dd>returns the Clebsch-Gordan coefficient for the decomposition of in terms of |$j$, $m$|$j2$, $m2$>.


To be precise, * ... in terms of |$j_1, m_1$>|j_2 m_2$>.*

Maybe $\rangle$ instead of $>$.

The persistent problem we have is that we the homegrown doc system really can't handle symbols reliably. We have seen this time and time again with things like Phi.

Do we use the bra or ket symbols anywhere else? If you know that when we go to print this it will work, then we can use.

OK, let's keep ">", but then the description should say
returns the Clebsch-Gordan coefficient for the decomposition of in terms of $|j_1, m_1>|j_2, m_2>$.

Thanks for finding the mistake. I think it is fixed now in bb73c51

Speaking of >, the ket symbol and our homegrown docsystem fragility: when I was working on the guide section for the process of adding Curl as an example, I wanted to write:

$$ ( \partial f_3 / \partial x_2 - \partial f_2 / \partial x_3, \ \ % \partial f_1 / \partial x_3 - \partial f_3 / \partial x_1, \ \ % \partial f_2 / \partial x_1 - \partial f_1 / \partial x_2 ) $$

in the Sphinx document. and I was pleasantly surprised that I could do this without fuss, and that there was a world of flexibility available rather that this kind of constrained system where we are working around things and getting less-good results in the end.

So there is hope if we can get over the mountain of moving this to sphinx.

mmatera · 2022-08-07T22:22:12Z

mathics/builtin/quantum_mechanics/angular.py

+            sympy_jms += [p.to_sympy() for p in pair.elements]
+        return from_sympy(CG(*sympy_jms).doit())
+
+


At some place, it would be good to implement also KroneckerProduct (https://reference.wolfram.com/language/ref/KroneckerProduct.html)

I have been going by reference guide section. That seems to belong to Matrix or Tensor things even though everything is related. Feel free to add it, but I am not sure where we would add it.

I am not sure where we would add it.

It looks like it goes under "Vector Space Operations" which we already have. See https://reference.wolfram.com/language/guide/OperationsOnVectors.html

As I was doing these, it occurred to me that there was a set not intuitive process I used that makes doing this kind of thing more automatic.

Find a Builtin that hasn't been implemented. This PR comes from the bottom this this issue. See also TODO's at the bottom of newer sections/modules for missing functions.

Decide where in the code/doc to put it. As noted, I first noticed it as a missing Combinatorial Function. However on more recent reflection, those last three are more specifically isolated as Angular Momentum functions (and in Combinatorial Functions it is not split out or noted as such). If this is a new section, then things are harder. If not a new section, then please add class in alphabetic order.

See if it is a SymPy function. And the rest will assume yes. But if not try to SciPy and mpmath. I suppose numpy might be tried too.

Copy one of the newer existing Sympy functions and adapt. Newer existing Sympy functions have Wiki, SyPy, and WMA links. Probably in the WMA link, all you will have to do is change the copied WMA name into the new name.

Use WMA link to adapt the docstring. It might be consulted to get the summary text too.

Go into mathics and see that you can get "info" or "?" on the changed doc.

Adapt the pattern match rule and parameters. This is probably the hardest part. Cases in mathics can help here. If you have put the code with related functions, often that class will be similar to some other class and that can make adapting the pattern match and body of the code easier. Also, similar classes do not follow the most recent conventions, consider updating nearby related builtins so that do follow new conventions.

Adapt the eval method parameters and body.

Make sure the function attributes are correct.

Adapt some doctests and test. Examples from WMA and SymPy are a good source, but try to make the examples meaningful.

Run the tests using python mathics/docpipeline -s <builtin name>

Go over error conditions and error messages

Write unit tests for all of these edge cases and uninteresting cases to try. test using python -m pytest -s test/builtin/.../test-.py`

Run all tests.

Add new builtin entry to CHANGES.rst

Create PR.

The above even though long is still kind of sketchy. So I will go through this process on KroneckerProdect as a detailed example and put this in the developer guide.

Probably,this is something that should go into the developer guide.

I started down this path. See https://github.com/Mathics3/mathics-development-guide/tree/adding-KroneckerProduct and https://mathics-development-guide.readthedocs.io/en/adding-kroneckerproduct/extending/developing-code/extending/adding-new-mathics-function.html.

I stopped however when I see that there is this is not going to make for a simple example, because of the matrix checking, and conversion to Matrix in SymPy that we probably need to do. And this is just for the matrix case, not the vector case.

I will pick a simpler example. As for the KroneckerProduct branch , I don't intend on going further there in case you are interested.

In that case, I would say that this is almost ready.

(I never was my intention to add it here - these are the angular momentum functions.)

Possibly over the weekend I may add pytests.. However redoing how Part works and changes ListExpression is more important.

mathics/builtin/quantum_mechanics/angular.py

mmatera · 2022-08-07T22:30:19Z

Something that I am not sure about this is whether these functions belong to a quantum mechanics section, or to other modules (PauliMatrix to linear algebra, ClebschGordan, ThreeJSymbol and SixJSymbol to "Combinatorial Functions" (https://reference.wolfram.com/language/guide/CombinatorialFunctions.html) , etc. Otherwise, we should put the special polynomials also under this category.

rocky · 2022-08-07T23:08:24Z

Something that I am not sure about this is whether these functions belong to a quantum mechanics section, or to other modules (PauliMatrix to linear algebra, ClebschGordan, ThreeJSymbol and SixJSymbol to "Combinatorial Functions" (https://reference.wolfram.com/language/guide/CombinatorialFunctions.html) , etc. Otherwise, we should put the special polynomials also under this category.

I am following https://reference.wolfram.com/language/guide/FunctionsUsedInQuantumMechanics.html

We will also have to deal with the duplication somehow. But that is yet another battle with autodoc for some other time.

Otherwise, we should put the special polynomials also under this category.

Again I am following the organization cited above and we'll have to figure out how to deal with duplication under sections.

which starts a Quantum Mechanics section. TODO: * Unit tests for errors. * Ensure function attributes are correct * Ensure we error on what we are supposed to and not on what we do not

Show symmetry in doc and add some error handling

rocky · 2022-08-15T10:23:15Z

This weekday's activity will probably be finish the development guide for Curl, and I might also add KroneckerProduct since I now see what is up with sympy Matrices.

rocky requested review from mmatera and TiagoCavalcante August 7, 2022 16:59

rocky marked this pull request as draft August 7, 2022 16:59

rocky force-pushed the add-angular-momentum branch 5 times, most recently from 61a71c6 to e30dff9 Compare August 7, 2022 22:10

mmatera reviewed Aug 7, 2022

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rocky force-pushed the add-angular-momentum branch 3 times, most recently from c71ec83 to f862984 Compare August 8, 2022 06:29

rocky marked this pull request as ready for review August 13, 2022 17:00

rocky force-pushed the add-angular-momentum branch 3 times, most recently from 94a053e to e888eea Compare August 13, 2022 19:32

rocky added 7 commits August 13, 2022 15:36

Add Angular Momentum builtins...

82570b5

which starts a Quantum Mechanics section. TODO: * Unit tests for errors. * Ensure function attributes are correct * Ensure we error on what we are supposed to and not on what we do not

Address some lint wining

7127ef4

Beef up SixJSymbol

8db4571

Remove Listable for PauliMatrix

5db8582

Beef up ThreeJSymbol

ae9fc7e

Show symmetry in doc and add some error handling

Beef up angular momentum examples

b8c3da5

Correct ClebschGordan docstring description

881a11b

rocky force-pushed the add-angular-momentum branch from e888eea to 881a11b Compare August 13, 2022 19:36

rocky merged commit 432e80b into master Aug 15, 2022

rocky deleted the add-angular-momentum branch August 15, 2022 10:21

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Add Angular Momentum builtins... #496

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rocky commented Aug 15, 2022

		sympy_jms += [p.to_sympy() for p in pair.elements]
		return from_sympy(CG(*sympy_jms).doit())

Add Angular Momentum builtins... #496

Add Angular Momentum builtins... #496

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