Solve with 4 args

#1 Pubblicato: 15/07/2026 07:34:36

Valery Ochkov

67 apprezzamenti in 713 post.

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solve(4).sm (110,53 KiB) scaricato 909 volta(e).

#2 Pubblicato: 15/07/2026 11:14:15

Alvaro

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Hi Valery. It seems that solve doesn't know how to order the interval.

The 6 solutions numerically

And symbolically

solve(4).sm (158,3 KiB) scaricato 924 volta(e).

Best regards.
Alvaro.

#3 Pubblicato: 17/07/2026 07:17:36

Valery Ochkov

67 apprezzamenti in 713 post.

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Thanks, Alvaro

It is one task from the article
https://disk.yandex.ru/i/59sq-AYpKky-3Q

Modificato 17/07/2026 07:28:06

#4 Pubblicato: 25/07/2026 05:40:05

Valery Ochkov

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Do you know the best solution in SMath?

#5 Pubblicato: 25/07/2026 15:50:39

Alvaro

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Hi Valery. Two ways.

heart area.sm (13,36 KiB) scaricato 875 volta(e).

Mathcad 11:

mc11 double int.mcd (4,77 KiB) scaricato 887 volta(e).

Best regards.
Alvaro.

Modificato 25/07/2026 17:52:57

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Valery Ochkov 25/07/2026 18:27:25

#6 Pubblicato: 25/07/2026 19:20:52

Valery Ochkov

67 apprezzamenti in 713 post.

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And what about this. We can create an animation.

Modificato 25/07/2026 19:47:21

#7 Pubblicato: 26/07/2026 02:28:14

Alvaro

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It's possible, although speed isn't one of SMath's main features. And with so few points, there isn't much accuracy.

heart area.sm (26,99 KiB) scaricato 868 volta(e).

Best regards.
Alvaro.

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Valery Ochkov 26/07/2026 13:14:28

#8 Pubblicato: 26/07/2026 13:40:28

Вячеслав Мезенцев

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I can write a function that returns a set of closed isolines. The area can be calculated from the points on the curve. To construct implicit graphs, a function is used that returns the coordinate sets of the found isolines.

Russia ☭ forever, Viacheslav N. Mezentsev

2 utenti hanno apprezzato questo post

Valery Ochkov 26/07/2026 14:32:01, Alvaro 27/07/2026 01:20:46

#9 Pubblicato: 26/07/2026 14:36:05

Valery Ochkov

67 apprezzamenti in 713 post.

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Wrote
I can write a function that returns a set of closed isolines. The area can be calculated from the points on the curve. To construct implicit graphs, a function is used that returns the coordinate sets of the found isolines.

Вячеслав, привет!
Брось все силы на создание инструментов оптимизации с ограничением типа Given... Minimize/Maximize в Mathcad 15. Этого очень не хватает в SMath.
И Андрей на это настроен.

#10 Pubblicato: 27/07/2026 01:25:09

Alvaro

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Using Dragilev Method.

Area and Arc Length of an Implicit Planar Closed Curve - Dragilev Method.sm (16,28 KiB) scaricato 886 volta(e).

Best regards.
Alvaro.

Modificato 27/07/2026 01:33:24

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Valery Ochkov 27/07/2026 06:01:49, Вячеслав Мезенцев 27/07/2026 13:28:37

#11 Pubblicato: 27/07/2026 13:27:20

Вячеслав Мезенцев

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Yes, something like this with the Gaussian area formula.

Russia ☭ forever, Viacheslav N. Mezentsev

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ioan92 28/07/2026 11:13:51

#12 Pubblicato: 28/07/2026 08:24:46

Alvaro

1.139 apprezzamenti in 1.805 post.

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Wrote
Yes, something like this with the Gaussian area formula.

Hi Viacheslav. In that case, I'd like to point out that dividing by the norme (Δ) means the curve is parameterized with respect to arc length, and that if you're going to improve the points using the original function, you must also do so with the parameter variable, which in the program's notation is T. This is because Dragilev's method ultimately obtains the parametric expressions x(t) and y(t) from the implicit function f(x,y) when starting from a point (xo,yo) on the curve.

This is one way to correct the arc length given by T if you choose to improve the curve points, although there must be better methods involving splines for curves in the plane, not just single-valued functions. There are also better approximations for the area enclosed by the curve; the one used here is simply the area defined by a closed polygon.

Area and Arc Length of an Implicit Planar Closed Curve - Dragilev Method.sm (17,78 KiB) scaricato 370 volta(e).

Best regards.
Alvaro.

Modificato 28/07/2026 08:36:40

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Valery Ochkov 28/07/2026 16:17:18

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Solve with 4 args - Is it a bug? - Messaggi