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The current simplification mode controls how numbers and formulas
are “normalized” when being taken from or pushed onto the stack.
Some normalizations are unavoidable, such as rounding floating-point
results to the current precision, and reducing fractions to simplest
form. Others, such as simplifying a formula like ‘`a+a`’ (or ‘`2+3`’),
are done automatically but can be turned off when necessary.

When you press a key like `+` when ‘`2`’ and ‘`3`’ are on the
stack, Calc pops these numbers, normalizes them, creates the formula
‘`2+3`’, normalizes it, and pushes the result. Of course the standard
rules for normalizing ‘`2+3`’ will produce the result ‘`5`’.

Simplification mode commands consist of the lower-case `m` prefix key
followed by a shifted letter.

The `m O` (`calc-no-simplify-mode`

) command turns off all optional
simplifications. These would leave a formula like ‘`2+3`’ alone. In
fact, nothing except simple numbers are ever affected by normalization
in this mode. Explicit simplification commands, such as `=` or
`a s`, can still be given to simplify any formulas.
See Algebraic Definitions, for a sample use of
No-Simplification mode.

The `m N` (`calc-num-simplify-mode`

) command turns off simplification
of any formulas except those for which all arguments are constants. For
example, ‘`1+2`’ is simplified to ‘`3`’, and ‘`a+(2-2)`’ is
simplified to ‘`a+0`’ but no further, since one argument of the sum
is not a constant. Unfortunately, ‘`(a+2)-2`’ is *not* simplified
because the top-level ‘`-`’ operator's arguments are not both
constant numbers (one of them is the formula ‘`a+2`’).
A constant is a number or other numeric object (such as a constant
error form or modulo form), or a vector all of whose
elements are constant.

The `m I` (`calc-basic-simplify-mode`

) command does some basic
simplifications for all formulas. This includes many easy and
fast algebraic simplifications such as ‘`a+0`’ to ‘`a`’, and
‘`a + 2 a`’ to ‘`3 a`’, as well as evaluating functions like
‘` deriv(x^2, x)`’ to ‘

The `m B` (`calc-bin-simplify-mode`

) mode applies the basic
simplifications to a result and then, if the result is an integer,
uses the `b c` (`calc-clip`

) command to clip the integer according
to the current binary word size. See Binary Functions. Real numbers
are rounded to the nearest integer and then clipped; other kinds of
results (after the basic simplifications) are left alone.

The `m A` (`calc-alg-simplify-mode`

) mode does standard
algebraic simplifications. See Algebraic Simplifications.

The `m E` (`calc-ext-simplify-mode`

) mode does “extended”, or
“unsafe”, algebraic simplification. See Unsafe Simplifications.

The `m U` (`calc-units-simplify-mode`

) mode does units
simplification. See Simplification of Units. These include the
algebraic simplifications, plus variable names which
are identifiable as unit names (like ‘`mm`’ for “millimeters”)
are simplified with their unit definitions in mind.

A common technique is to set the simplification mode down to the lowest
amount of simplification you will allow to be applied automatically, then
use manual commands like `a s` and `c c` (`calc-clean`

) to
perform higher types of simplifications on demand.