Algebraic Entry
===============

Calculations can also be entered in algebraic form.  This is
accomplished by typing the apostrophe key, `'', followed by the
expression in standard format: `' 2+3*4 RET' computes `2+(3*4) = 14'
and pushes that on the stack.  If you wish you can ignore the RPN
aspect of Calc altogether and simply enter algebraic expressions in
this way.  You may want to use DEL every so often to clear previous
results off the stack.

You can press the apostrophe key during normal numeric entry to switch
the half-entered number into algebraic entry mode.  One reason to do
this would be to use the full Emacs cursor motion and editing keys,
which are available during algebraic entry but not during numeric
entry.

In the same vein, during either numeric or algebraic entry you can
press ``' (backquote) to switch to `calc-edit' mode, where
you complete your half-finished entry in a separate buffer.
See Editing Stack Entries.

If you prefer algebraic entry, you can use the command `m a'
(`calc-algebraic-mode') to set Algebraic mode.  In this mode, digits
and other keys that would normally start numeric entry instead start
full algebraic entry; as long as your formula begins with a digit you
can omit the apostrophe.  Open parentheses and square brackets also
begin algebraic entry.  You can still do RPN calculations in this
mode, but you will have to press RET to terminate every number: `2 RET
3 RET * 4 RET +' would accomplish the same thing as `2*3+4 RET'.

If you give a numeric prefix argument like `C-u' to the `m a' command,
it enables Incomplete Algebraic mode; this is like regular Algebraic
mode except that it applies to the `(' and `[' keys only.  Numeric
keys still begin a numeric entry in this mode.

The `m t' (`calc-total-algebraic-mode') gives you an even
stronger algebraic-entry mode, in which *all* regular letter and
punctuation keys begin algebraic entry.  Use this if you prefer typing
`sqrt( )' instead of `Q', `factor( )' instead of
`a f', and so on.  To type regular Calc commands when you are in
"total" algebraic mode, hold down the META key.  Thus `M-q'
is the command to quit Calc, `M-p' sets the precision, and
`M-m t' (or `M-m M-t', if you prefer) turns total algebraic
mode back off again.  Meta keys also terminate algebraic entry, so
that `2+3 M-S' is equivalent to `2+3 RET M-S'.  The symbol
`Alg*' will appear in the mode line whenever you are in this mode.

Pressing `'' (the apostrophe) a second time re-enters the previous
algebraic formula.  You can then use the normal Emacs editing keys to
modify this formula to your liking before pressing RET.

Within a formula entered from the keyboard, the symbol `$' represents
the number on the top of the stack.  If an entered formula contains
any `$' characters, the Calculator replaces the top of stack with that
formula rather than simply pushing the formula onto the stack.  Thus,
`' 1+2 RET' pushes 3 on the stack, and `$*2 RET' replaces it with 6.
Note that the `$' key always initiates algebraic entry; the `'' is
unnecessary if `$' is the first character in the new formula.

Higher stack elements can be accessed from an entered formula with the
symbols `$$', `$$$', and so on.  The number of stack elements removed
(to be replaced by the entered values) equals the number of dollar
signs in the longest such symbol in the formula.  For example,
`$$+$$$' adds the second and third stack elements, replacing the top
three elements with the answer.  (All information about the top stack
element is thus lost since no single `$' appears in this formula.)

A slightly different way to refer to stack elements is with a dollar
sign followed by a number: `$1', `$2', and so on are much like `$',
`$$', etc., except that stack entries referred to numerically are not
replaced by the algebraic entry.  That is, while `$+1' replaces 5 on
the stack with 6, `$1+1' leaves the 5 on the stack and pushes an
additional 6.

If a sequence of formulas are entered separated by commas, each
formula is pushed onto the stack in turn.  For example, `1,2,3' pushes
those three numbers onto the stack (leaving the 3 at the top), and
`$+1,$-1' replaces a 5 on the stack with 4 followed by 6.  Also,
`$,$$' exchanges the top two elements of the stack, just like the TAB
key.

You can finish an algebraic entry with `M-=' or `M-RET' instead of
RET.  This uses `=' to evaluate the variables in each formula that
goes onto the stack.  (Thus `' pi RET' pushes the variable `pi', but
`' pi M-RET' pushes 3.1415.)

If you finish your algebraic entry by pressing `LFD' (or `C-j')
instead of RET, Calc disables the default simplifications (as if by `m
O'; See Simplification Modes) while the entry is being pushed on
the stack.  Thus `' 1+2 RET' pushes 3 on the stack, but `' 1+2 LFD'
pushes the formula `1+2'; you might then press `=' when it is time to
evaluate this formula.