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 by default 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.
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 D (calc-default-simplify-mode) command restores the
default 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 2 x.
The m B (calc-bin-simplify-mode) mode applies the default
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 section Binary Number Functions. Real numbers
are rounded to the nearest integer and then clipped; other kinds of
results (after the default simplifications) are left alone.
The m A (calc-alg-simplify-mode) mode does algebraic
simplification; it applies all the default simplifications, and also
the more powerful (and slower) simplifications made by a s
(calc-simplify). See section Algebraic Simplifications.
The m E (calc-ext-simplify-mode) mode does "extended"
algebraic simplification, as by the a e (calc-simplify-extended)
command. See section "Unsafe" Simplifications.
The m U (calc-units-simplify-mode) mode does units
simplification; it applies the command u s
(calc-simplify-units), which in turn
is a superset of a s. In this mode, 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. See section Programming with Formulas, for another sample use of no-simplification mode.