Copy from one page to an other shows different behavior of sys P



I know that eval will doctor (hello Jean :-) to the same result.
but why is eval necessary in the second case und how can I see if eval is necessary?

Wrote

Copy from one page to an other shows different behavior of sys P

Something in there does not cut the mustard.
Attach the creator document to be copied on blank sheet
Jean

the 2 versions of sys
sys1.sm (23 KiB) downloaded 29 time(s).
sys2.sm (29 KiB) downloaded 24 time(s).

Wrote

Copy from one page to an other shows different behavior of sys P

Not same α° between the two documents !
Again: too specific rectangular construction of polygon.
They are constructed from vertices coordinates.
That was exemplified few days ago [Area, Perimeter, Centroid]
Arc length on Engineering curve is partial perimeter,
it goes in triplet [A,P,C].
Jean

The other conceptual pitfall is your rotation.
rot(,) *[2*2] is commutative for only [2*2] systems [square/rectangle...]
The universal code for XY longer than [2*2] ... XY*rot(,)
If you don't follow this rule, Mathcad red, Smath error ...

Wrote

The other conceptual pitfall is your rotation.

From there, you can compute [Area, Perimeter, Centroid]
as per the "Maths Polygon" previously posted.
As well for the native [full/reduced by list]
as for the rotated of any angle.
read NOT commutative

Rotate Gerono.sm (14 KiB) downloaded 26 time(s).

Wrote

From there, you can compute [Area, Perimeter, Centroid]

... complete the tour [A,P,C]

Rotate Gerono.sm (25 KiB) downloaded 25 time(s).

Difference between two calculation occurs because of numeric and symbolic optimization.
Just right click and select Optimization>Numeric for the copied formula in sys2.sm file
This false flag happens a lot. Nothing is wrong here. As usual, the culprit is optimization.

Regards

Wrote

As usual, the culprit is optimization.
Regards

Many thanks to hit the nuke of my question
and many thanks to Jean for pointing out problems which I do not see in my limited perspective.