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Offline uni  
#21 Posted : 18 July 2018 01:49:21(UTC)
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Updated. al_nleqsolve() refactored. Try now.

2018-07-18_04-04-25.png 2018-07-18_04-30-59.png

You can also specify only names of the systems (f and j).

2018-07-18_08-37-49.png 2018-07-18_07-23-29.png

Edited by user 18 July 2018 06:39:19(UTC)  | Reason: Not specified

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Offline Ber7  
#22 Posted : 18 July 2018 08:35:44(UTC)
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One example of V. Mezentsev (Uni)
Primer Uni.sm (14kb) downloaded 61 time(s).

Edited by user 27 July 2018 16:37:57(UTC)  | Reason: Not specified

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Offline omorr  
#23 Posted : 18 July 2018 11:40:48(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
One example of V. Mezentsev (Uni)
Primer Uni.sm (14kb) downloaded 61 time(s).


Fortunately, I was wrong. We could use it with different number of equations and unknowns.
I just use the Ber7 example and change it with n as a global variable. No need for zeros as non-existing functions.

ber7.GIF

Primer%20Uni-mod.sm (14kb) downloaded 57 time(s).
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
Offline tomtit  
#24 Posted : 18 July 2018 16:15:46(UTC)
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Thanks a lot uni!
The issue listed in my post #18 has been resolved.
But for some reason simple Newton-Raphson with variable step usually
works better than al_nleqsolve.
Offline Jean Giraud  
#25 Posted : 18 July 2018 21:19:47(UTC)
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Originally Posted by: tomtit Go to Quoted Post
But for some reason simple Newton-Raphson with variable step usually
works better than al_nleqsolve.


Can you demonstrate for this application ?

Electfnct.PNG

Solve al_nleqsolve-Electron.sm (19kb) downloaded 44 time(s).

Offline Ber7  
#26 Posted : 21 July 2018 18:45:03(UTC)
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We find several roots at once


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Offline Ber7  
#27 Posted : 22 July 2018 09:50:27(UTC)
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3d.sm (30kb) downloaded 53 time(s).

Edited by user 27 July 2018 16:35:26(UTC)  | Reason: Not specified

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Offline Jean Giraud  
#28 Posted : 23 July 2018 05:29:32(UTC)
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Thanks Ber7 for the 3D, nice.

Jean
Offline Ber7  
#29 Posted : 24 July 2018 19:03:26(UTC)
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Solution of an overdetermined system of equations. The problem is taken from here
https://en.smath.info/forum/yaf_...745_How-to-solve-it.aspx

Overdetermined.sm (16kb) downloaded 47 time(s).
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Offline Ber7  
#30 Posted : 30 July 2018 19:09:38(UTC)
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The process of finding the roots

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Offline Ber7  
#31 Posted : 22 August 2018 10:32:16(UTC)
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The intersection points of two curves

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Primer1b.pdf (213kb) downloaded 36 time(s).
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Offline Ber7  
#32 Posted : 22 August 2018 17:39:31(UTC)
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Fixed. Now you can find all the intersection points.

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Offline Ber7  
#33 Posted : 23 August 2018 11:11:57(UTC)
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Primer3.sm (21kb) downloaded 49 time(s).
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Offline Jean Giraud  
#34 Posted : 23 August 2018 16:57:07(UTC)
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... thanks Ber7

Astroid.PNG

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Offline Ber7  
#35 Posted : 25 August 2018 12:22:47(UTC)
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Primer6.sm (19kb) downloaded 45 time(s).
Offline Ber7  
#36 Posted : 06 October 2018 20:56:58(UTC)
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Simple solutions to two problems
1.The construction of a sphere with respect to four given points
2.The construction of a circle with respect to three given points
To calculate the coordinates of the center and radius using the solver AlgLib
In the first problem, a system of four sphere equations for four given points is solved.
In the second - a system of three equations of a circle and the equation of a plane for three given points.

SphereAlglib.sm (65kb) downloaded 45 time(s).
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Offline Razonar  
#37 Posted : 08 October 2018 09:23:09(UTC)
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Hi. The same, but without plugins.

SphereSMath.sm (76kb) downloaded 46 time(s).

Best regards.
Alvaro.

PD: Do you know the angles for your rotation matrix gamma? I get this, but can't put the matrix elements in the correct order nor sign:

Clipboard1.gif

Actually, as I know, the minus in the last atan is a mistake, but at least give the same absolute values.
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Offline Ber7  
#38 Posted : 09 October 2018 17:42:42(UTC)
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Originally Posted by: Razonar Go to Quoted Post
Hi. The same, but without plugins.

PD: Do you know the angles for your rotation matrix gamma? I get this, but can't put the matrix elements in the correct order nor sign:

Actually, as I know, the minus in the last atan is a mistake, but at least give the same absolute values.


Hi, Alvaro.
Unfortunately, I have never done reverse transformations (gamma-omega).
Your error may be caused by the use of the left coordinate system in Smath- graphs.
I selected the angles for the axial matrices empirically in order to get a good perspective ,using the gamma matrix.perspective.

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Offline Jean Giraud  
#39 Posted : 10 October 2018 06:40:38(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
Unfortunately, I have never done reverse transformations (gamma-omega).

Mathcad solves the Euler angles from a given γ [gamma matrix].
Smath does not immediately, it complains: Try to use a more specific algorithm.
There are 24 [4!] possible ways to define a 3D system [Mathematica].
The most common is Euler though Mathcad Mathcad ≠ Mathematica.
For common use to define some pleasant views, especially in Smath:
1. Euler [ 3 trig angles]
2. Parametric [X,Y,Z,t] very easy to manage.
3. Quaternion only two coefficients that Quaternion solves for the 3D γ matrix

Rotate Horn.sm (16kb) downloaded 50 time(s).
Solve Euler Fails.sm (23kb) downloaded 43 time(s).
Rotate Breather [Euler].sm (38kb) downloaded 42 time(s).
Rotate_0 Euler, xyz(t), Quaternion.sm (276kb) downloaded 46 time(s).
Offline uni  
#40 Posted : 12 December 2018 18:57:19(UTC)
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Updated.

Changes for al_rkckadapt():
- zero point issue fixed;
- added support for the simple D(t,x) definition.

Edited by user 12 December 2018 19:28:27(UTC)  | Reason: Not specified

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