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### 3.5 Algebraic Entry

The `'` (`calc-algebraic-entry`) command can be used to enter calculations in algebraic form. This is accomplished by typing the apostrophe key, ’, followed by the expression in standard format:

    ' 2+3*4 RET.

This will compute ‘`2+(3*4) = 14`’ and push it 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 fix a typo, as the full Emacs cursor motion and editing keys are available during algebraic entry but not during numeric entry.

In the same vein, during either numeric or algebraic entry you can press ``` (grave accent) 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 simplification (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.

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