Continued thread
Still trying out SageMath and Jupyter Notebook. Here's the first real-world problem I've solved in it. The general algorithm to transform from S-parameters to T-parameters. #electronics #sagemath
![#### Find the Permutation Matrix
Next, we compute the permutation matrix $ \mathbf{C} $ to transform source variables $ \mathbf{S}_v $ to destination variables $ \mathbf{T}_v $.
Since SageMath's permutation calculation doesn't support symbolic variables, we first assign an indices $ (1, 2, 3, ...) $ to each variable. The ordering should follow their order of appearance in the *destination* matrix $ \mathbf{T}_v $.
```python
var_list = Tv.list()
var_map = {}
for idx, var_name in enumerate(var_list):
# permutations must have positive integers
var_map[var_name] = idx + 1
Sv_list = Sv.subs(var_map).list()
Tv_list = Tv.subs(var_map).list()
display("Sv", Sv_list)
display("Tv", Tv_list)
```
<html>\(\displaystyle \verb|Sv|\)</html>
<html>\(\displaystyle \left[4, 1, 3, 2\right]\)</html>
<html>\(\displaystyle \verb|Tv|\)</html>
<html>\(\displaystyle \left[1, 2, 3, 4\right]\)</html>
Now the permutation matrix $ \mathbf{C} $ can be calculated:
```python
c = Permutation(Sv_list).to_matrix()
display(c)
```
<html>\(\displaystyle \left(\begin{array}{rrrr}
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
1 & 0 & 0 & 0
\end{array}\right)\)</html>](https://misskey-taube.s3.eu-central-1.wasabisys.com/files/e1c113a5-54d1-4162-a489-ab86dd4bebfd.webp "#### Find the Permutation Matrix
Next, we compute the permutation matrix $ \mathbf{C} $ to transform source variables $ \mathbf{S}_v $ to destination variables $ \mathbf{T}_v $.
Since SageMath's permutation calculation doesn't support symbolic variables, we first assign an indices $ (1, 2, 3, ...) $ to each variable. The ordering should follow their order of appearance in the *destination* matrix $ \mathbf{T}_v $.
```python
var_list = Tv.list()
var_map = {}
for idx, var_name in enumerate(var_list):
# permutations must have positive integers
var_map[var_name] = idx + 1
Sv_list = Sv.subs(var_map).list()
Tv_list = Tv.subs(var_map).list()
display(\"Sv\", Sv_list)
display(\"Tv\", Tv_list)
```
<html>\(\displaystyle \verb|Sv|\)</html>
<html>\(\displaystyle \left[4, 1, 3, 2\right]\)</html>
<html>\(\displaystyle \verb|Tv|\)</html>
<html>\(\displaystyle \left[1, 2, 3, 4\right]\)</html>
Now the permutation matrix $ \mathbf{C} $ can be calculated:
```python
c = Permutation(Sv_list).to_matrix()
display(c)
```
<html>\(\displaystyle \left(\begin{array}{rrrr}
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
1 & 0 & 0 & 0
\end{array}\right)\)</html>")
![#### Partition the Permutation Matrix
Then we partition the permutation matrix $ \mathbf{C} $ into 4 quadrants $ \begin{bmatrix} C_{11} & C_{12} \\ C_{21} & C_{22} \end{bmatrix}$, each term is a submatrix.
```python
assert c.nrows() == c.ncols()
terms = c.nrows() / 2
c11 = c.submatrix(0, 0, terms, terms)
c12 = c.submatrix(0, c.ncols() / 2, terms, terms)
c21 = c.submatrix(c.nrows() / 2, 0, terms, terms)
c22 = c.submatrix(c.nrows() / 2, c.ncols() / 2, terms, terms)
display("c11", c11, "c12", c12, "c21", c21, "c22", c22)
```
<html>\(\displaystyle \verb|c11|\)</html>
<html>\(\displaystyle \left(\begin{array}{rr}
0 & 1 \\
0 & 0
\end{array}\right)\)</html>
<html>\(\displaystyle \verb|c12|\)</html>
<html>\(\displaystyle \left(\begin{array}{rr}
0 & 0 \\
0 & 1
\end{array}\right)\)</html>
<html>\(\displaystyle \verb|c21|\)</html>
<html>\(\displaystyle \left(\begin{array}{rr}
0 & 0 \\
1 & 0
\end{array}\right)\)</html>
<html>\(\displaystyle \verb|c22|\)</html>
<html>\(\displaystyle \left(\begin{array}{rr}
1 & 0 \\
0 & 0
\end{array}\right)\)</html>
#### Solve T-Parameters from S-parameters
Convert network parameters using the formula $ \mathbf{T} = (\mathbf{C}_{21} + \mathbf{C}_{22} \cdot \mathbf{S}) \cdot (\mathbf{C}_{11} + \mathbf{C}_{12} \cdot \mathbf{S})^{-1} $.
```python
var("S11, S12, S21, S22")
S = matrix(2, [S11, S12, S21, S22])
display("S-parameters:", S)
T = (c21 + c22 * S) * (c11 + c12 * S)^(-1)
display("T-parameters:", T)
```
<html>\(\displ](https://misskey-taube.s3.eu-central-1.wasabisys.com/files/5ef3c6ad-2ac6-42f1-983b-ac1f103e3dc3.webp "#### Partition the Permutation Matrix
Then we partition the permutation matrix $ \mathbf{C} $ into 4 quadrants $ \begin{bmatrix} C_{11} & C_{12} \\ C_{21} & C_{22} \end{bmatrix}$, each term is a submatrix.
```python
assert c.nrows() == c.ncols()
terms = c.nrows() / 2
c11 = c.submatrix(0, 0, terms, terms)
c12 = c.submatrix(0, c.ncols() / 2, terms, terms)
c21 = c.submatrix(c.nrows() / 2, 0, terms, terms)
c22 = c.submatrix(c.nrows() / 2, c.ncols() / 2, terms, terms)
display(\"c11\", c11, \"c12\", c12, \"c21\", c21, \"c22\", c22)
```
<html>\(\displaystyle \verb|c11|\)</html>
<html>\(\displaystyle \left(\begin{array}{rr}
0 & 1 \\
0 & 0
\end{array}\right)\)</html>
<html>\(\displaystyle \verb|c12|\)</html>
<html>\(\displaystyle \left(\begin{array}{rr}
0 & 0 \\
0 & 1
\end{array}\right)\)</html>
<html>\(\displaystyle \verb|c21|\)</html>
<html>\(\displaystyle \left(\begin{array}{rr}
0 & 0 \\
1 & 0
\end{array}\right)\)</html>
<html>\(\displaystyle \verb|c22|\)</html>
<html>\(\displaystyle \left(\begin{array}{rr}
1 & 0 \\
0 & 0
\end{array}\right)\)</html>
#### Solve T-Parameters from S-parameters
Convert network parameters using the formula $ \mathbf{T} = (\mathbf{C}_{21} + \mathbf{C}_{22} \cdot \mathbf{S}) \cdot (\mathbf{C}_{11} + \mathbf{C}_{12} \cdot \mathbf{S})^{-1} $.
```python
var(\"S11, S12, S21, S22\")
S = matrix(2, [S11, S12, S21, S22])
display(\"S-parameters:\", S)
T = (c21 + c22 * S) * (c11 + c12 * S)^(-1)
display(\"T-parameters:\", T)
```
<html>\(\displ")
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@sagemath 10.6 has been released on April 1, 2025. SageMath now supports RISC-V systems.
A total of 75 people contributed to this release. Of those, 24 made their first contribution to Sage.
More info about this release on https://github.com/sagemath/sage/wiki/Sage-10.6-Release-Tour
The source code can be found on https://github.com/sagemath/sage/releases/tag/10.6
GitHubSage 10.6 Release TourMain repository of SageMath. Contribute to sagemath/sage development by creating an account on GitHub.
I saw today that my CoCalc (https://cocalc.com/) license was about to renew. I've been meaning to move to a more #SelfHosting or #P2P paradigm, so this was good timing for me to cancel. I left this message when doing so:
"I want to support Sage, and I like using CoCalc, but I don't want to put money towards a service that supports Microsoft, Amazon, or OpenAI in any way. I didn't care so much about this before, and I even log in to CoCalc with a GitHub account, but I'm tired of having my work scraped for profit by people who donate to fascists who are destroying my nation. I would consider returning if all ties to these corporations were cut and cloud computing services came from responsible companies, perhaps in the EU."
I'm pretty sure I already have backups of everything I want from GitHub, so I can be done with them too. I should have quit when Microsoft first arrived. My plan is to switch to Radicle (https://radicle.xyz/) rather than another centralized service. I'll be sure to post about how that goes.
cocalc.comCollaborative Calculation and Data ScienceCoCalc landing pages and documentation
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@eugenialoli Just opened #SageMath . For now, I probably still prefer #WxMaxima , but who knows?
@eugenialoli My substitute for Mathematica has been #Maxima , but #SageMath looks to be more powerful (but definitely not lightweight). I'd also suggest, QuickBooks or Sage -> #GnuCash .