Hi,
The \triangle operator is used for instance in the « symmetric difference » of two subsets: if $E$ is a set and $A \subset E$, and $B \susbet E$, then one defines
\startformula
A \triangle B := (A \cup B) \setminus (A \cap B).
\stopformula
Then the mapping $(A,B) \mapsto A \triangle B$ is a commutative, associative binary operator on the subsets of $E$.
Some people use instead $A \Delta B$, but this is not the traditional, nor the correct way, to write this « symmetric difference » of two sets. This is why, I guess, in TeX \triangle is an operator.
I have seen also \triangledown as an operator, but I don’t recall the context in which it was used…
Regarding the notation \nabla to denote the gradient, and \Delta, to denote the Laplace operator (which by the way can be defined as $\Delta u := \nabla \cdot (\nabla u)$), Mikael Sundqvist gave the correct observations.
Best regards: OK
On 11 avr. 2014, at 05:48, Aditya Mahajan
On Thu, 10 Apr 2014, Sanjoy Mahajan wrote:
Jannik,
You are right. \nabla looks much nicer and is placed correctly. (I still think the \triangledown placement is slightly off.)
My environment files from MkII days have \def\nabla{\triangledown}, so I never tried the true \nabla until your suggestion.
In MkIV: \triangledown is mapped to 0x25BD while nabla is mapped to 0x2207. These are different glyphs.
IIUC, the difference in placement is because \triangledown is defined as a mathop (and hence centered on the math-axis) while \nabla is defined as a mathord. Compare:
\startformula \nabla T \quad \triangledown T \quad \mathop{\nabla} T \stopformula
From what I remember, I was the one who added the mappings for triangledown as a mathop based on, I believe, unicode-math package in LaTeX. I don't understand what all the "triangle operators" are supposed to do. As such, I cannot say whether the wrong placement is due to the wrong font metrics or the wrong mapping (mathop vs mathord) by ConTeXt.
Aditya ___________________________________________________________________________________ If your question is of interest to others as well, please add an entry to the Wiki!
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