eigenmath/doc/manual/symbols.tex

\subsection{Defining symbols}
As we saw earlier, Eigenmath uses the same syntax as dear old Fortran.

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\verb$N=212^17$

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\noindent
No result is printed when a symbol is defined.
To see a symbol's value, just evaluate it.

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\verb$N$

$$3529471145760275132301897342055866171392$$

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\noindent
Beyond its prosaic syntax, Eigenmath does have a few tricks up its sleeve.
For example, a symbol can have a subscript.

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\verb$NA=6.02214*10^23$

\verb$NA$

$$N_A=6.02214\times10^{23}$$

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\noindent
A symbol can be the name of a Greek letter.

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\verb$xi=1/2$

\verb$xi$

$$\xi=\hbox{$1\over2$}$$

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\noindent
Since xi is $\xi$, how is $x_i$ entered?
Well, that is an issue that may get resolved in the future.
For now, xi is always $\xi$.

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\noindent
Greek letters can appear in the subscript too.

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\verb$Amu=2.0$

\verb$Amu$

$$A_\mu=2.0$$

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\noindent
The general rule is this.
Eigenmath scans the entire symbol looking for Greek letters.

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\verb$alphamunu$

$$\alpha_{\mu\nu}$$

\newpage

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\noindent
Let us turn now to what happens when a symbolic expression is evaluated.
The most important point is that
Eigenmath exhaustively evaluates symbolic subexpressions.

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\verb$A=B$

\verb$B=C$

\verb$C=D$

\verb$sin(A)$

$$\sin(D)$$

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\noindent
In the above example, evaluating $\sin(A)$ yields $\sin(D)$ because Eigenmath
resolves $A$ as far as it can, in this case down to $D$.
However, internally the binding of $A$ is still $B$, as can be seen with
the $binding$ function.

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\verb$binding(A)$

$$B$$

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\noindent
Let us return to symbolic definitions for a moment.
It should be kept in mind that the right hand side of the definition is an
expression that is evaluated before the binding is done.
For example,

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\verb$B=1$

\verb$A=B$

\verb$binding(A)$

$$1$$

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\noindent
The binding of $A$ is 1 and not $B$ because $B$ was already defined before
the $A=B$ occurred.
The $quote$ function can be used to give a literal binding.

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\verb$A=quote(B)$

\verb$binding(A)$

$$B$$

\newpage

\noindent
What this all means is that symbols have a dual nature.
A symbol has a binding which may be different from its evaluation.
Normally this difference is not important.
The functions $quote$ and $binding$ are mentioned here mainly to provide insight
into what is happening belowdecks.
Normally you should not really need to use these functions.
However, one notable exception is the use of $quote$ to clear a symbol.

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\verb$x=3$

\verb$x$

$$x=3$$

\verb$x=quote(x)$

\verb$x$

$$x$$