13. Constants

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13.1 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.

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@ref{Category: Constants}

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

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@ref{Category: Constants}

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

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@ref{Category: Constants}

Constant: ind

ind represents a bounded, indefinite result.

See also limit.

Example:

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

@ref{Category: Constants}

Constant: inf: inf represents real positive infinity.

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@ref{Category: Constants}

Constant: infinity: infinity represents complex infinity.

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@ref{Category: Constants}

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

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@ref{Category: 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

@ref{Category: 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.

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@ref{Category: Constants}

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

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@ref{Category: Constants}

Constant: und

und represents an undefined result.