Hi Andrey,


Here attached I have an other case where the symbolic optimisation gives a completely false results.
Hoping to serve for yours futures improvements.


Best regards,


Ioan

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rotsys.sm (22,78 KiB) scaricato 1435 volta(e).

Hello

The function norme(v) is buggy (known issue in the forum). Use [MATH]sqrt(v^2)[/MATH] instead if v is a single column as in your example. Works with both numeric and symbolic optimization.

Best regards, Martin Kraska

Hello Martin,


Thanks for your answer.
I replaced all norme(v) as you suggest (see attached file) and for case of symbolic optimisation the results are still wrongs (?).


Best regards,


Ioan

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rotsys2.sm (27,08 KiB) scaricato 1400 volta(e).

Wrote

Thanks for your answer.
I replaced all norme(v) as you suggest (see attached file) and for case of symbolic optimisation the results are still wrongs (?).

Hello Ioan,

ok, you are right. Replacing enorm is not sufficient to solve the problem. There is another one with trig operations. The problem is that [MATH]sin(θ)[/MATH] is symbolically evaluated to zero, whereas the correct value is [MATH]sqrt(2)/sqrt(3)[/MATH]. If you ask SMath to simplify [MATH]sin(acos(a))[/MATH] you get [MATH]sin(acos(a))=sqrt(1-a^2)[/MATH]. If you use that instead of [MATH]sin(θ)[/MATH] :

[MATH lang=ENG]Ridentity(3)+sqrt(1-({v.f*v.i}/{sqrt(v.f^2)*sqrt(v.i^2)})^2)*mat(0,-el(p,3),el(p,2),el(p,3),0,-el(p,1),-el(p,2),el(p,1),0,3,3)+(1-cos(θ))*(p*transpose(p)-identity(3)))[/MATH]

then you get the correct symbolic result.

[MATH lang=ENG]R=mat(-{1-sqrt(3)}/{2*sqrt(3)},{1+sqrt(3)}/{2*sqrt(3)},1/sqrt(3),{1+sqrt(3)}/{2*sqrt(3)},-{1-sqrt(3)}/{2*sqrt(3)},-1/sqrt(3),-1/sqrt(3),1/sqrt(3),-1/sqrt(3),3,3)[/MATH]

Symbolic evaluation seems to be not really reliable. Simplifications are not done even if SMath is well aware of that they could be done.
An example is

[MATH lang=ENG]cos(θ)={mat(0,0,-1,3,1)*mat(1/sqrt(3),-1/sqrt(3),1/sqrt(3),3,1)}/{sqrt(mat(0,0,-1,3,1)^2)*sqrt(mat(1/sqrt(3),-1/sqrt(3),1/sqrt(3),3,1)^2)}[/MATH]

which is not simplified although the following works:

[MATH lang=ENG]{mat(0,0,-1,3,1)*mat(1/sqrt(3),-1/sqrt(3),1/sqrt(3),3,1)}/{sqrt(mat(0,0,-1,3,1)^2)*sqrt(mat(1/sqrt(3),-1/sqrt(3),1/sqrt(3),3,1)^2)}=-1/sqrt(3)[/MATH]


Also, if [MATH]sin(acos(a))=sqrt(1-a^2)[/MATH] then the following cannot be correct:

[MATH lang=ENG]sin(θ)=sqrt({sqrt(mat(0,0,-1,3,1)^2)^2*sqrt(mat(1/sqrt(3),-1/sqrt(3),1/sqrt(3),3,1)^2)^2-1}/{sqrt(mat(0,0,-1,3,1)^2)^2*sqrt(mat(1/sqrt(3),-1/sqrt(3),1/sqrt(3),3,1)^2)^2})[/MATH]

Here, perhaps the symbolic engine tries to apply the square to the dot product by applying the square to the factors individually. This yields 1 because both vectors are unit vectors. It might be correct for scalars but definitely not for vectors. BTW it does not help to use matrix formulation of the dot product [MATH lang=ENG]el(transpose(v)*v,1)[/MATH]. We had such issues already with SMath assuming matrix multiplication to be commutative.


By the way, instead of your special function you could write [MATH lang=ENG]v.i†v.f=mat(1/sqrt(3),1/sqrt(3),0,3,1)[/MATH].

Best regards, Martin Kraska

Hello Martin,


Thanks a lot for your useful analysis.


Best regards,


Ioan

Hi,

here is one more example for incomplete symbolic simplification in trig context. SMath knows that sin(30° ) equals 1/2 but can't find out symbolically that cosec(30° )=1/sin(30° ) is 2.

Best regards, Martin Kraska

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trig.sm (9,29 KiB) scaricato 1409 volta(e).

Wrote

Hi,

here is one more example for incomplete symbolic simplification in trig context. SMath knows that sin(30° ) equals 1/2 but can't find out symbolically that cosec(30° )=1/sin(30° ) is 2.

Best regards, Martin Kraska

Wow, so difficult to me