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
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 ‘2 x’.
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 (
perform higher types of simplifications on demand.