Storing Variables
=================

The `s s' (`calc-store') command stores the value at the top of the
stack into a specified variable.  It prompts you to enter the name of
the variable.  If you press a single digit, the value is stored
immediately in one of the "quick" variables `var-q0' through `var-q9'.
Or you can enter any variable name.  The prefix `var-' is supplied for
you; when a name appears in a formula (as in `a+q2') the prefix `var-'
is also supplied there, so normally you can simply forget about `var-'
everywhere.  Its only purpose is to enable you to use Calc variables
without fear of accidentally clobbering some variable in another Emacs
package.  If you really want to store in an arbitrary Lisp variable,
just backspace over the `var-'.

The `s s' command leaves the stored value on the stack.  There is also
an `s t' (`calc-store-into') command, which removes a value from the
stack and stores it in a variable.

If the top of stack value is an equation `a = 7' or assignment `a :=
7' with a variable on the lefthand side, then Calc will assign that
variable with that value by default, i.e., if you type `s s RET' or `s
t RET'.  In this example, the value 7 would be stored in the variable
`a'.  (If you do type a variable name at the prompt, the top-of-stack
value is stored in its entirety, even if it is an equation: `s s b
RET' with `a := 7' on the stack stores `a := 7' in `b'.)

In fact, the top of stack value can be a vector of equations or
assignments with different variables on their lefthand sides; the
default will be to store all the variables with their corresponding
righthand sides simultaneously.

It is also possible to type an equation or assignment directly at the
prompt for the `s s' or `s t' command: `s s foo = 7'.  In this case
the expression to the right of the `=' or `:=' symbol is evaluated as
if by the `=' command, and that value is stored in the variable.  No
value is taken from the stack; `s s' and `s t' are equivalent when
used in this way.

The prefix keys `s' and `t' may be followed immediately by a digit; `s
9' is equivalent to `s s 9', and `t 9' is equivalent to `s t 9'.  (The
`t' prefix is otherwise used for trail and time/date commands.)

There are also several "arithmetic store" commands.  For example,
`s +' removes a value from the stack and adds it to the specified
variable.  The other arithmetic stores are `s -', `s *', `s /',
`s ^', and `s |' (vector concatenation), plus `s n' and
`s &' which negate or invert the value in a variable, and `s ['
and `s ]' which decrease or increase a variable by one.

All the arithmetic stores accept the Inverse prefix to reverse the
order of the operands.  If `v' represents the contents of the
variable, and `a' is the value drawn from the stack, then regular
`s -' assigns `v := v - a', but `I s -' assigns
`v := a - v'.  While `I s *' might seem pointless, it is
useful if matrix multiplication is involved.  Actually, all the
arithmetic stores use formulas designed to behave usefully both
forwards and backwards:

     s +        v := v + a          v := a + v
     s -        v := v - a          v := a - v
     s *        v := v * a          v := a * v
     s /        v := v / a          v := a / v
     s ^        v := v ^ a          v := a ^ v
     s |        v := v | a          v := a | v
     s n        v := v / (-1)       v := (-1) / v
     s &        v := v ^ (-1)       v := (-1) ^ v
     s [        v := v - 1          v := 1 - v
     s ]        v := v - (-1)       v := (-1) - v

In the last four cases, a numeric prefix argument will be used in
place of the number one.  (For example, `M-2 s ]' increases a variable
by 2, and `M-2 I s ]' replaces a variable by minus-two minus the
variable.

The first six arithmetic stores can also be typed `s t +', `s t -',
etc.  The commands `s s +', `s s -', and so on are analogous
arithmetic stores that don't remove the value `a' from the stack.

All arithmetic stores report the new value of the variable in the
Trail for your information.  They signal an error if the variable
previously had no stored value.  If default simplifications have been
turned off, the arithmetic stores temporarily turn them on for numeric
arguments only (i.e., they temporarily do an `m N' command).
See Simplification Modes.  Large vectors put in the trail by
these commands always use abbreviated (`t .') mode.

The `s m' command is a general way to adjust a variable's value using
any Calc function.  It is a "mapping" command analogous to `V M', `V
R', etc.  See Reducing and Mapping, to see how to specify a
function for a mapping command.  Basically, all you do is type the
Calc command key that would invoke that function normally.  For
example, `s m n' applies the `n' key to negate the contents of the
variable, so `s m n' is equivalent to `s n'.  Also, `s m Q' takes the
square root of the value stored in a variable, `s m v v' uses `v v' to
reverse the vector stored in the variable, and `s m H I S' takes the
hyperbolic arcsine of the variable contents.

If the mapping function takes two or more arguments, the additional
arguments are taken from the stack; the old value of the variable is
provided as the first argument.  Thus `s m -' with `a' on the stack
computes `v - a', just like `s -'.  With the Inverse prefix, the
variable's original value becomes the *last* argument instead of the
first.  Thus `I s m -' is also equivalent to `I s -'.

The `s x' (`calc-store-exchange') command exchanges the value of a
variable with the value on the top of the stack.  Naturally, the
variable must already have a stored value for this to work.

You can type an equation or assignment at the `s x' prompt.  The
command `s x a=6' takes no values from the stack; instead, it pushes
the old value of `a' on the stack and stores `a = 6'.

Until you store something in them, variables are "void," that is, they
contain no value at all.  If they appear in an algebraic formula they
will be left alone even if you press `=' (`calc-evaluate').  The `s u'
(`calc-unstore') command returns a variable to the void state.

The only variables with predefined values are the "special constants"
`pi', `e', `i', `phi', and `gamma'.  You are free to unstore these
variables or to store new values into them if you like, although some
of the algebraic-manipulation functions may assume these variables
represent their standard values.  Calc displays a warning if you
change the value of one of these variables, or of one of the other
special variables `inf', `uinf', and `nan' (which are normally void).

Note that `var-pi' doesn't actually have 3.14159265359 stored in it,
but rather a special magic value that evaluates to `pi' at the current
precision.  Likewise `var-e', `var-i', and `var-phi' evaluate
according to the current precision or polar mode.  If you recall a
value from `pi' and store it back, this magic property will be lost.

The `s c' (`calc-copy-variable') command copies the stored value of
one variable to another.  It differs from a simple `s r' followed by
an `s t' in two important ways.  First, the value never goes on the
stack and thus is never rounded, evaluated, or simplified in any way;
it is not even rounded down to the current precision.  Second, the
"magic" contents of a variable like `var-e' can be copied into another
variable with this command, perhaps because you need to unstore
`var-e' right now but you wish to put it back when you're done.  The
`s c' command is the only way to manipulate these magic values intact.