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| 13.1 Functions and Variables for Constants |
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%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.
%i represents the imaginary unit, sqrt(- 1).
false represents the Boolean constant of the same name.
Maxima implements false by the value NIL in Lisp.
inf represents real positive infinity.
infinity represents complex infinity.
minf represents real minus (i.e., negative) infinity.
%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
%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.
true represents the Boolean constant of the same name.
Maxima implements true by the value T in Lisp.
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This document was generated by Robert Dodier on August, 25 2007 using texi2html 1.76.