Mathcad Toolbox - Contains analogs of functions from Mathcad - Messaggi
#201 Pubblicato: 21/08/2025 20:59:20
Interesting things are going on, I am really excited!
I think that the explanation by Gemini is not entirely correct. Yet, he hint on circularity is helpful.
If that was true, we would not have that circularity problem. Also we would not see the entire find command with it's arguments if we display the stored expression from the find block in the dynamic assistant.
Actually I believe that the find function (like any other function in any assignment does nothing (except for substituting existing definitions from the context) unless a result display is requested. I call this delayed evaluation.
Also, assignment to a variable should not affect anything above the current definition. Backfiring should be limited to absolute variables as sometimes used for iterations with on-the-fly animation.
If Gemini was right here, the simp() function in my above example would not help. simp() actually triggers evaluation because num2str() does so. BTW, in the given case S: eval(S) also does the job.
I think that the explanation by Gemini is not entirely correct. Yet, he hint on circularity is helpful.
If that was true, we would not have that circularity problem. Also we would not see the entire find command with it's arguments if we display the stored expression from the find block in the dynamic assistant.
Actually I believe that the find function (like any other function in any assignment does nothing (except for substituting existing definitions from the context) unless a result display is requested. I call this delayed evaluation.
Also, assignment to a variable should not affect anything above the current definition. Backfiring should be limited to absolute variables as sometimes used for iterations with on-the-fly animation.
If Gemini was right here, the simp() function in my above example would not help. simp() actually triggers evaluation because num2str() does so. BTW, in the given case S: eval(S) also does the job.
Modificato 21/08/2025 21:13:21
Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9
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Вячеслав Мезенцев 21/08/2025 22:02:04
#202 Pubblicato: 21/08/2025 21:25:35
Plugin updated.
Changes:
- Draghilev solver added.
This is a very simple implementation.
MathcadToolbox-Draghilev-simple.sm
Modificato 21/08/2025 21:32:28
Russia ☭ forever, Viacheslav N. Mezentsev
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Alvaro 22/08/2025 02:25:04
#203 Pubblicato: 22/08/2025 02:36:02
... The set of variables to be solved is now implicitly determined from all initial guesses (`≈`) provided in the input system. This removes the need to explicitly declare all variables. ...
Hi Viacheslav. Very good job! Instead of sending the equation with the user variables to the solver, and having problems with cyclic recursions, you can send a system of equations based on a single vector variable. This also enables the use of al_nleqsolve, which is the most robust solver available, and is also compatible with the solvers in the nonlinear solvers plugin. This is demonstrated in the code in the attached file, along with combining the x ≈ a notation with the x = a notation.
nsol-handling-equations.sm
Best regards.
Alvaro.
Modificato 22/08/2025 02:45:16
#204 Pubblicato: 22/08/2025 02:43:19
... Draghilev solver added.
Hi Viacheslav. With a matrix non-zero finder, like the one in Matlab, you can simplify the axis crossing detection.
MathcadToolbox-Draghilev-MFind.sm
Best regards.
Alvaro.
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#205 Pubblicato: 22/08/2025 12:42:19
BTW, in the given case S: eval(S) also does the job.
Сan be used as a temporary solution.
Russia ☭ forever, Viacheslav N. Mezentsev
#206 Pubblicato: 22/08/2025 13:37:36
This is demonstrated in the code in the attached file, along with combining the x ≈ a notation with the x = a notation.
You might be interested to know that the find function was written using AI using the nsol function as an example. I have been working with AI for some time and now it can convert almost any description into code.
It understood perfectly what was happening in the nsol code, praised the author and offered the implementation as a find function. Of course, I told it what to do, but basically all the code was written by AI.
All numerical solvers that find() uses are also written by AI in 10 minutes.
The same goes for Draghilev's method, it is also based on your example. It is too complex to understand, but in general I know what is happening there, and for AI there were no difficulties at all.
Now I'm trying to port lsode (odesolve) from C code to c#. It's too huge to be done in one evening and there are many complexities, but the AI said that everything will be fine.
I will later connect all the existing numerical solvers to the find function, and all the numerical differential solvers to odesolve. In particular, it will learn to classify a problem by a set of equations and select an appropriate solver.
Unfortunately, when working with the AI, you need less time, but more knowledge. Not everything it offers corresponds to my level as a programmer.
AI also helped to understand splines. It found an inaccuracy in the Mathcad.
Modificato 22/08/2025 14:01:39
Russia ☭ forever, Viacheslav N. Mezentsev
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Alvaro 22/08/2025 19:26:29
#207 Pubblicato: 22/08/2025 20:05:22
In that case, please also check ndsol , as the way it converts differential equations into systems allows for numerical solutions of hard coupled systems that I can only solve in SMath, but not Maple or Mathematica.... You might be interested to know that the find function was written using AI using the nsol function as an example. I have been working with AI for some time and now it can convert almost any description into code.
The nleqsol solver is the most powerful one you have at hand, it reminds me of the tksolver solver.... All numerical solvers that find() uses are also written by AI in 10 minutes.
Remember to add the option to have the Jacobian as an argument, and the ode solver too.... The same goes for Draghilev's method, it is also based on your example. It is too complex to understand, but in general I know what is happening there, and for AI there were no difficulties at all.
I haven't reviewed the code in the SMath plugin repository, but Adams' algorithm is clearly much faster than the others. Perhaps you could implement the way it evaluates D(t,u) values in rkfixed and RKadapt.... I will later connect all the existing numerical solvers to the find function, and all the numerical differential solvers to odesolve. In particular, it will learn to classify a problem by a set of equations and select an appropriate solver.
... AI also helped to understand splines. It found an inaccuracy in the Mathcad.
You can find the codes in SMath here: https://smath.com/en-US/forum/topic/sKU7o2/CSpline-interpolation#msg129361 . My idea for math software is that advanced functions should be written in their own code, with the exception of those that require a large number of flops (Matlab Word). This should make it easier for developers to discover bugs and optimize the core code. However, there is something very good about SMath's code for the cspline function. Unlike Mathcad, it doesn't require prior calculation of the matrix with splines, yet it still works very quickly.
Finally, as you refine your procedures and add examples, you'll eventually need to consider how to pass arguments to find and specialized ode solvers, as they won't be able to solve all problems with the default parameters. The option I suggest is something similar to the Options(~fname, "pname", pvalue) function you can find in nsol to store "pname" and "pvalue" as strings in the ~fname variable, and Options(~fname,"pname") to obtain pvalue. Remembering that in SMath, every function can modify the value of its arguments globally, and treating ~fname as if it were an object that has the pname parameters as if they were properties of an object.
Best regards.
Alvaro.
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Вячеслав Мезенцев 22/08/2025 21:28:42
#208 Pubblicato: 23/08/2025 23:23:22
Plugin updated.
Changes:
- find() function syntax extended.
Russia ☭ forever, Viacheslav N. Mezentsev
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#209 Pubblicato: 24/08/2025 05:49:38
Hi Viacheslav. You also can ask the IA for matrices with known examples to check the answers. In this case, one variable function, the guess and the root.
check-find.sm
Best regards.
Alvaro.
check-find.sm
Best regards.
Alvaro.
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Вячеслав Мезенцев 24/08/2025 05:51:44, Oscar Campo 24/08/2025 09:54:25, francesco rapuano 24/08/2025 14:41:15
#210 Pubblicato: 24/08/2025 14:52:26
self-check 
Modificato 24/08/2025 14:54:21
Russia ☭ forever, Viacheslav N. Mezentsev
#211 Pubblicato: 24/08/2025 14:55:32
Mathcad block for entering matrices. This allows for inserting and deleting rows and columns using ordinary SMath edit. Each entry is a formula cell.
Problem is that it is easy to get the wrong sequence by slightly misplacing entries.
Also, it is not nice that the procedure can't guess the shape of the matrix from the arrangement of the entries.
collect.sm
Problem is that it is easy to get the wrong sequence by slightly misplacing entries.
Also, it is not nice that the procedure can't guess the shape of the matrix from the arrangement of the entries.
collect.sm
Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9
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#212 Pubblicato: 24/08/2025 15:08:34
You can also try it this way
Russia ☭ forever, Viacheslav N. Mezentsev
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#213 Pubblicato: 25/08/2025 06:45:40
Hi, I see you're using the character at position 8 to find the newline. The text inside the mathcad block uses a different character than the one used in the text inside a description(). One way to get both is this (Carriage Return & Line Feed)
You can then handle text from both the mathcad block and description(), for example, using strrep(text,'CR,'LF)
Best regards.
Alvaro.
You can then handle text from both the mathcad block and description(), for example, using strrep(text,'CR,'LF)
Best regards.
Alvaro.
Modificato 25/08/2025 06:46:29
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Вячеслав Мезенцев 25/08/2025 06:59:03
#214 Pubblicato: 31/08/2025 06:44:52
Smath v1.3.0.9126, MathCad Toolbox v0.6.9367
These equations used to work in the original document, but today they all show red. Then I copy them and paste them to a new blank document, the 1st and 2nd equ works except 3rd one.
These equations used to work in the original document, but today they all show red. Then I copy them and paste them to a new blank document, the 1st and 2nd equ works except 3rd one.
#215 Pubblicato: 31/08/2025 09:46:57
This is the basic form of using the find() function.
All other methods should be used after mastering the basic ones.
All other methods should be used after mastering the basic ones.
Modificato 31/08/2025 09:49:53
Russia ☭ forever, Viacheslav N. Mezentsev
#216 Pubblicato: 31/08/2025 10:01:24
Smath v1.3.0.9126, MathCad Toolbox v0.6.9367
These equations used to work in the original document, but today they all show red. Then I copy them and paste them to a new blank document, the 1st and 2nd equ works except 3rd one.
...
use Clear() function between 2nd and 3rd equations and evaluate:
When this function is evaluated, the value of arguments in the function are cleaned.
Regards,
Oscar
#217 Pubblicato: 01/09/2025 05:34:56
Smath v1.3.0.9126, MathCad Toolbox v0.6.9367
These equations used to work in the original document, but today they all show red. Then I copy them and paste them to a new blank document, the 1st and 2nd equ works except 3rd one.
...
use Clear() function between 2nd and 3rd equations and evaluate:
When this function is evaluated, the value of arguments in the function are cleaned.
Regards,
Oscar
#218 Pubblicato: 01/09/2025 06:25:38
Try this
Russia ☭ forever, Viacheslav N. Mezentsev
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Davide Carpi 01/09/2025 07:40:24
#219 Pubblicato: 01/09/2025 06:35:02
Hi. Usually, isn't easy verify the calculus from a picture, it's better from the source. You use ":=", instead "=", as Oscar suggest.
Best regards.
Alvaro.
Best regards.
Alvaro.
Modificato 01/09/2025 06:41:26
#220 Pubblicato: 01/09/2025 10:39:16
Pay attention to this convention:
When you type ":" in SMath, you are assigneing a value to a variable and SMath renders as: ":=" .
When you type "=", you are asking for the value of a variable, or evaluating a function, and smath renders it as: "="
In your case, Clear() is a function, so, when you type "Clear(z[Ctrl+g]):1" which renders:
Here you must to type "1" and you are assigning the value "1" to "Clear(zeta)" . This is wrong.
The correct syntaxis to evaluate the function Clear() is : "Clear(z[Ctrl+g])=" which renders:
Here you don't type "1". The value "1" is an automatic response to evaluation of the function Clear(). It is the boolean answer of successfully having evaluated the Clear() function
Best,
Oscar
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