The commands described in this section convert numbers from one form to another; they are two-key sequences beginning with the letter c.
The c f (
pfloat] command converts the
number on the top of the stack to floating-point form. For example,
‘23’ is converted to ‘23.0’, ‘3:2’ is converted to
‘1.5’, and ‘2.3’ is left the same. If the value is a composite
object such as a complex number or vector, each of the components is
converted to floating-point. If the value is a formula, all numbers
in the formula are converted to floating-point. Note that depending
on the current floating-point precision, conversion to floating-point
format may lose information.
As a special exception, integers which appear as powers or subscripts are not floated by c f. If you really want to float a power, you can use a j s command to select the power followed by c f. Because c f cannot examine the formula outside of the selection, it does not notice that the thing being floated is a power. See Selecting Subformulas.
The normal c f command is “pervasive” in the sense that it
applies to all numbers throughout the formula. The
algebraic function never stays around in a formula; ‘pfloat(a + 1)’
changes to ‘a + 1.0’ as soon as it is evaluated.
With the Hyperbolic flag, H c f [
only on the number or vector of numbers at the top level of its
argument. Thus, ‘float(1)’ is 1.0, but ‘float(a + 1)’
is left unevaluated because its argument is not a number.
You should use H c f if you wish to guarantee that the final value, once all the variables have been assigned, is a float; you would use c f if you wish to do the conversion on the numbers that appear right now.
The c F (
pfrac] command converts a
floating-point number into a fractional approximation. By default, it
produces a fraction whose decimal representation is the same as the
input number, to within the current precision. You can also give a
numeric prefix argument to specify a tolerance, either directly, or,
if the prefix argument is zero, by using the number on top of the stack
as the tolerance. If the tolerance is a positive integer, the fraction
is correct to within that many significant figures. If the tolerance is
a non-positive integer, it specifies how many digits fewer than the current
precision to use. If the tolerance is a floating-point number, the
fraction is correct to within that absolute amount.
pfrac function is pervasive, like
There is also a non-pervasive version, H c F [
which is analogous to H c f discussed above.
The c d (
deg] command converts a
number into degrees form. The value on the top of the stack may be an
HMS form (interpreted as degrees-minutes-seconds), or a real number which
will be interpreted in radians regardless of the current angular mode.
The c r (
rad] command converts an
HMS form or angle in degrees into an angle in radians.
The c h (
hms] command converts a real
number, interpreted according to the current angular mode, to an HMS
form describing the same angle. In algebraic notation, the
function also accepts three arguments: ‘hms(h, m, s)’.
(The three-argument version is independent of the current angular mode.)
calc-from-hms command converts the HMS form on the top of the
stack into a real number according to the current angular mode.
The c p (
calc-polar) command converts the complex number on
the top of the stack from polar to rectangular form, or from rectangular
to polar form, whichever is appropriate. Real numbers are left the same.
This command is equivalent to the
functions in algebraic formulas, depending on the direction of
conversion. (It uses
polar, except that if the argument is
already a polar complex number, it uses
rect instead. The
I c p command always uses
The c c (
pclean] command “cleans” the
number on the top of the stack. Floating point numbers are re-rounded
according to the current precision. Polar numbers whose angular
components have strayed from the -180 to +180 degree range
are normalized. (Note that results will be undesirable if the current
angular mode is different from the one under which the number was
produced!) Integers and fractions are generally unaffected by this
operation. Vectors and formulas are cleaned by cleaning each component
number (i.e., pervasively).
If the simplification mode is set below basic simplification, it is raised for the purposes of this command. Thus, c c applies the basic simplifications even if their automatic application is disabled. See Simplification Modes.
A numeric prefix argument to c c sets the floating-point precision to that value for the duration of the command. A positive prefix (of at least 3) sets the precision to the specified value; a negative or zero prefix decreases the precision by the specified amount.
The keystroke sequences c 0 through c 9 are equivalent to c c with the corresponding negative prefix argument. If roundoff errors have changed 2.0 into 1.999999, typing c 1 to clip off one decimal place often conveniently does the trick.
The c c command with a numeric prefix argument, and the c 0 through c 9 commands, also “clip” very small floating-point numbers to zero. If the exponent is less than or equal to the negative of the specified precision, the number is changed to 0.0. For example, if the current precision is 12, then c 2 changes the vector ‘[1e-8, 1e-9, 1e-10, 1e-11]’ to ‘[1e-8, 1e-9, 0, 0]’. Numbers this small generally arise from roundoff noise.
If the numbers you are using really are legitimately this small, you should avoid using the c 0 through c 9 commands. (The plain c c command rounds to the current precision but does not clip small numbers.)
One more property of c 0 through c 9, and of c c with a prefix argument, is that integer-valued floats are converted to plain integers, so that c 1 on ‘[1., 1.5, 2., 2.5, 3.]’ produces ‘[1, 1.5, 2, 2.5, 3]’. This is not done for huge numbers (‘1e100’ is technically an integer-valued float, but you wouldn’t want it automatically converted to a 100-digit integer).
With the Hyperbolic flag, H c c and H c 0 through H c 9
operate non-pervasively [