My students were building a multifocal ellipse and... almost went crazy. My ellipse is correct, but the student's is incorrect. Although the formulas are the same.
Can you guess where the error is and whether it is necessary to modify SMath so that such an error is visible?
Do you know more some examples?

Ellipse4.sm (11.6 KiB) downloaded 912 time(s).

In fact only apparently the written formula is the same but in the first case "S" is outside the summation while in the second case it is inside the summation. You can verify this by copying and pasting the two formulas into a text editor.

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sergio

Further illustrated by adding parenthesis around the summation in each formula

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Wrote

In fact only apparently the written formula is the same but in the first case "S" is outside the summation while in the second case it is inside the summation. You can verify this by copying and pasting the two formulas into a text editor.

Show Spoiler

sergio

You can also select/double-click the sum symbol to check what belongs to it.

The problem is that in the first Ellipse(x,y) definition, variable S is outside Sum function, but in the definition of your students is inside:

Your definition:
Ellipse(x,y):sum(sqrt((x-el(X.F,i))^2+(y-el(Y.F,i))^2),i,1,N)-S

Student´s definition:
Ellipse(x,y):sum(sqrt((x-el(X.F,i))^2+(y-el(Y.F,i))^2)-S,i,1,N)


Maybe, this explicit form is most clear for students:

Better so

Wrote

Better so ...

You can tell your students that you are using the Note under Example 3 of point 7.1.3 of ISO 80000-1:2009(E) Quantities and units, Part 1: General.



Best regards.
Alvaro.

It if Mathcad 15

1 ln(x)
2 ln*x - why not