This Treasury is huge ! mostly initiatic [Engineering/Scientific]
Inversing/solving a function may come in 3 forms
1. Explicit NASA(h) ... Frechet
2. maple RootOf as single/dual solver
3. LambertW [Gumbel, mostly arithmetic expressions]

This document extends Lambert dual branches [exemplified]
As it looks from recent years it has immense applications
Just schemed in this first brew. If you have more applications ... welcome.

Jean

Solve Inverse Symbolic Suite READ First Copy.sm (282 KiB) downloaded 72 time(s).

Hello Jean,

It seems something was wrong here - "no real roots".



Regards,
Radovan

Wrote

It seems something was wrong here - "no real roots".

"No real roots" SS 7109 is a bug wrt that version.
Surprising it does not complain elsewhere the solve bloc is called ?
The attached is SS 6179.
Salut Radovan, thanks for reporting ... Jean.

RootOf.sm (11 KiB) downloaded 54 time(s).

Wrote

Hello Jean,

It seems something was wrong here - "no real roots".

Thanks Radovan ... no bug: just bad construction.
The main work sheet doctored.
α, β were consumed in the Pt100 thermometer.

Jean

Solve Inverse Symbolic Suite READ First Copy.sm (289 KiB) downloaded 62 time(s).

... Fréchet & Gumbel have been doctored.
Maple failed the two Lambert branches for Gumbel.

Solve Inverse Symbolic Suite READ First Copy.sm (293 KiB) downloaded 80 time(s).

Wrote

... Fréchet & Gumbel have been doctored.
Maple failed the two Lambert branches for Gumbel.

Solve Inverse Symbolic Suite READ First Copy.sm (293 KiB) downloaded 80 time(s).

Hello Jean,

Hmm...I am not sure if it should be this way but this has been working to long.
I just opened the worksheet and it seems that it get stuck at this graph.

The SMath version was 0.99.7109



Regards,
Radovan

Wrote

Hello Jean,

Hmm...I am not sure if it should be this way but this has been working to long.
I just opened the worksheet and it seems that it get stuck at this graph.

The SMath version was 0.99.7109

For sure, it does not make sense.
What about just that created in new sheet ?

Wrote

Wrote

Hello Jean,

Hmm...I am not sure if it should be this way but this has been working to long.
I just opened the worksheet and it seems that it get stuck at this graph.

The SMath version was 0.99.7109

For sure, it does not make sense.
What about just that created in new sheet ?

You are right. It does not make sense.
New worksheet, the same situation. Tried on Win7 and Win10

Could anyone else confirm this please.



Regards,
Radovan

Wrote

You are right. It does not make sense.
New worksheet, the same situation. Tried on Win7 and Win10

Could anyone else confirm this please.

That's for Gurus ... where are you ?
If Lambert fails, it could confirm the bug is "roots"

roots_solve test.sm (9 KiB) downloaded 73 time(s).

The problem is that W(4*exp(4-x)) returns an error "index out of matrix bounds" if x is negative (check it on the canvas). Then this triggers the infinite calculation time in the 2D plot.

Wrote

The problem is that W(4*exp(4-x)) returns an error "index out of matrix bounds" if x is negative (check it on the canvas). Then this triggers the infinite calculation time in the 2D plot.

Solution of this demo DE is wrt Lambert W0(x)
I attempted W1(x) "Division by zero"
On the other hand: Lambert [W0(x0, W1(x)] do not vectorize
but tabulates for loop discrete. Wait and see Radovan next visit.

roots_solve test.sm (18 KiB) downloaded 64 time(s).

Wrote

Wrote

The problem is that W(4*exp(4-x)) returns an error "index out of matrix bounds" if x is negative (check it on the canvas). Then this triggers the infinite calculation time in the 2D plot.

Solution of this demo DE is wrt Lambert W0(x)
I attempted W1(x) "Division by zero"
On the other hand: Lambert [W0(x0, W1(x)] do not vectorize
but tabulates for loop discrete. Wait and see Radovan next visit.

I simply do not understand why is this happening (triggering the infinite calculation time in 2D plot) and think that in 7109 this behavior is wrong regarding the 2D graph.



I think it should be considered a bug. If the x-y point can not be calculated it should be just skipped, nothing else. I also think that in 6179 is applied that behavior. The X-Y plot is doing this just right.



Regards,
Radovan

Wrote

I think it should be considered a bug. If the x-y point can not be calculated it should be just skipped, nothing else. I also think that in 6179 is applied that behavior. The X-Y plot is doing this just right.

A desperate case: Quick plot 6179 just fine
X_Y red does not solve "roots" on its own canvas.
Interesting but does not cut the mustard yet .

I am now more puzzled than before ???

To be honest, I've never liked the roots() function. It makes me troubles so many times.

Wrote

I am now more puzzled than before ???
To be honest, I've never liked the roots() function.
It makes me troubles so many times.

Yes Radovan but so gorgeous solving on the running canvas.
Something like Mathcad 'root', much easier to implement.
Cheers ... Jean

Inst_Mach Number Pitot.sm (187 KiB) downloaded 66 time(s).

Wrote

Wrote

I am now more puzzled than before ???
To be honest, I've never liked the roots() function.
It makes me troubles so many times.

Yes Radovan but so gorgeous solving on the running canvas.
Something like Mathcad 'root', much easier to implement.
Cheers ... Jean

Inst_Mach Number Pitot.sm (187 KiB) downloaded 66 time(s).

Function roots() will do the job in this example. But Mathcad root() function will not let you down in the case of srict numerical cases (I am repeating myself to often...).

By the way, there is an error in Int() function (z not defined). I think this was also already mentioned few times...



Regards,
Radovan

Wrote

By the way, there is an error in Int() function (z not defined)

Quite right Radovan, transit via 'z' not needed 6179.
Pitot Mach was one of my very first SS 5346.

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Function roots() will do the job in this example. But Mathcad root() function will not let you down in the case of strict numerical cases

Mathcad 11.2a "root" works same as Smath "roots", plot on scalar canvas.
I may have an example, considered useless compared to assigning Given/Find
lot more universal for about any project ... all done perfect.
Attached Mach-Pitot