Constants
=========

Functions and Variables for Constants
-------------------------------------

 -- Constant: %e

     %e represents the base of the natural logarithm, also known as Euler's number.  The numeric value of %e is the double-precision floating-point value 2.718281828459045d0.  (See eqn 4.1.16, 67, 4.1.17, 67.)

     Categories: Constants

 -- Constant: %i

     %i represents the imaginary unit, sqrt(- 1) .

     Categories: Constants

 -- Constant: false

     false represents the Boolean constant of the same name. Maxima implements false by the value NIL in Lisp.

     Categories: Constants

 -- Constant: %gamma

     The Euler-Mascheroni constant, 0.5772156649015329.... It is defined by (eqn 6.1.3, 255 and 5.2.ii)

                                             n
                                            ====
                                            \     1
                         %gamma = limit    ( >    - - log(n))
                                  n -> inf  /     k
                                            ====
                                            k = 1

     Categories: Constants

 -- Constant: ind

     ind represents a bounded, indefinite result.

     See also limit

     Example:

          (%i1) limit (sin(1/x), x, 0);
          (%o1)                          ind

     Categories: Constants

 -- Constant: inf

     inf represents real positive infinity.

     Categories: Constants

 -- Constant: infinity

     infinity represents complex infinity.

     Categories: Constants

 -- Constant: least_negative_float
     The least negative floating-point number in Maxima.  That is, the negative floating-point number closest to 0.  It is approximately -4.94065e-324, when denormal (https://en.wikipedia.org/wiki/Subnormal_number) numbers are supported.  Otherwise it is the same as least_negative_normalized_float.

     Categories: Constants

 -- Constant: least_negative_normalized_float
     The least negative normalized floating-point number in Maxima.  That is, the negative normalized floating-point number closest to 0.  It is approximately -2.22507e-308.

     Categories: Constants

 -- Constant: least_positive_float
     The least positive floating-point number in Maxima.  That is, the positive floating-point number closest to 0.  It is approximately 4.94065e-324, when denormal (https://en.wikipedia.org/wiki/Subnormal_number) numbers are supported.  Otherwise it is the same as least_positive_normalized_float.

     Categories: Constants

 -- Constant: least_positive_normalized_float
     The least positive normalized floating-point number in Maxima.  That is, the positive normalized floating-point number closest to 0.  It is approximately 2.22507e-308.

     Categories: Constants

 -- Constant: minf

     minf represents real minus (i.e., negative) infinity.

     Categories: Constants

 -- Constant: most_negative_float
     The most negative floating-point number in Maxima.  It is approximately -1.79769e+308.

     Categories: Constants

 -- Constant: most_positive_float
     The most positive floating-point number in Maxima.  It is approximately 1.797693e+308.

     Categories: Constants

 -- Constant: %phi

     %phi represents the so-called golden mean, (1 + sqrt(5))/2 . The numeric value of %phi is the double-precision floating-point value 1.618033988749895d0.

     fibtophi expresses Fibonacci numbers fib(n) in terms of %phi.

     By default, Maxima does not know the algebraic properties of %phi. After evaluating tellrat(%phi^2 - %phi - 1) and algebraic: true, ratsimp can simplify some expressions containing %phi.

     Examples:

     fibtophi expresses Fibonacci numbers fib(n) in terms of %phi.

          (%i1) fibtophi (fib (n));
                                     n             n
                                 %phi  - (1 - %phi)
          (%o1)                  -------------------
                                     2 %phi - 1
          (%i2) fib (n-1) + fib (n) - fib (n+1);
          (%o2)          - fib(n + 1) + fib(n) + fib(n - 1)
          (%i3) fibtophi (%);
                      n + 1             n + 1       n             n
                  %phi      - (1 - %phi)        %phi  - (1 - %phi)
          (%o3) - --------------------------- + -------------------
                          2 %phi - 1                2 %phi - 1
                                                    n - 1             n - 1
                                                %phi      - (1 - %phi)
                                              + ---------------------------
                                                        2 %phi - 1
          (%i4) ratsimp (%);
          (%o4)                           0

     By default, Maxima does not know the algebraic properties of %phi. After evaluating tellrat (%phi^2 - %phi - 1) and algebraic: true, ratsimp can simplify some expressions containing %phi.

          (%i1) e : expand ((%phi^2 - %phi - 1) * (A + 1));
                           2                      2
          (%o1)        %phi  A - %phi A - A + %phi  - %phi - 1
          (%i2) ratsimp (e);
                            2                     2
          (%o2)        (%phi  - %phi - 1) A + %phi  - %phi - 1
          (%i3) tellrat (%phi^2 - %phi - 1);
                                      2
          (%o3)                  [%phi  - %phi - 1]
          (%i4) algebraic : true;
          (%o4)                         true
          (%i5) ratsimp (e);
          (%o5)                           0

     Categories: Constants

 -- Constant: %pi

     %pi represents the ratio of the perimeter of a circle to its diameter. The numeric value of %pi is the double-precision floating-point value 3.141592653589793d0.

     Categories: Constants

 -- Constant: true

     true represents the Boolean constant of the same name. Maxima implements true by the value T in Lisp.

     Categories: Constants

 -- Constant: und

     und represents an undefined result.

     See also limit

     Example:

          (%i1) limit (x*sin(x), x, inf);
          (%o1)                          und

     Categories: Constants

 -- Constant: zeroa

     zeroa represents an infinitesimal above zero.  zeroa can be used in expressions.  limit simplifies expressions which contain infinitesimals.

     See also zerob and limit

     Example:

     limit simplifies expressions which contain infinitesimals:

          (%i1) limit(zeroa);
          (%o1)                           0
          (%i2) limit(x+zeroa);
          (%o2)                           x

     Categories: Constants

 -- Constant: zerob

     zerob represents an infinitesimal below zero.  zerob can be used in expressions.  limit simplifies expressions which contain infinitesimals.

     See also zeroa and limit

     Categories: Constants