Numbers
Date: 2020-10-07 18:10:00

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### 2.2 Numbers

There are several diﬀerent types of numbers available in REDUCE. Integers consist of a signed or unsigned sequence of decimal digits written without a decimal point, for example:

-2, 5396, +32

In principle, there is no practical limit on the number of digits permitted as exact arithmetic is used in most implementations. (You should however check the speciﬁc instructions for your particular system implementation to make sure that this is true.) For example, if you ask for the value of 22000 you get it displayed as a number of 603 decimal digits, taking up several lines of output on an interactive display. It should be borne in mind of course that computations with such long numbers can be quite slow.

Numbers that aren’t integers are usually represented as the quotient of two integers, in lowest terms: that is, as rational numbers.

In essentially all versions of REDUCE it is also possible (but not always desirable!) to ask REDUCE to work with ﬂoating point approximations to numbers again, to any precision. Such numbers are called real. They can be input in two ways:

1. as a signed or unsigned sequence of any number of decimal digits with an embedded or trailing decimal point.
2. as in 1. followed by a decimal exponent which is written as the letter E followed by a signed or unsigned integer.

e.g. 32. +32.0 0.32E2 and 320.E-1 are all representations of 32.

The declaration SCIENTIFIC_NOTATION controls the output format of ﬂoating point numbers. At the default settings, any number with ﬁve or less digits before the decimal point is printed in a ﬁxed-point notation, e.g., 12345.6. Numbers with more than ﬁve digits are printed in scientiﬁc notation, e.g., 1.234567E+5. Similarly, by default, any number with eleven or more zeros after the decimal point is printed in scientiﬁc notation. To change these defaults, SCIENTIFIC_NOTATION can be used in one of two ways.

SCIENTIFIC_NOTATION m;

where m is a positive integer, sets the printing format so that a number with more than m digits before the decimal point, or m or more zeros after the decimal point, is printed in scientiﬁc notation.

SCIENTIFIC_NOTATION{m,n},

with m and n both positive integers, sets the format so that a number with more than m digits before the decimal point, or n or more zeros after the decimal point is printed in scientiﬁc notation.

CAUTION: The unsigned part of any number may not begin with a decimal point, as this causes confusion with the CONS (.) operator, i.e., NOT ALLOWED ARE: .5 -.23 +.12; use 0.5 -0.23 +0.12 instead.

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