%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.
Categories: Constants
%i represents the imaginary unit, sqrt(- 1).
Categories: Constants
false represents the Boolean constant of the same name.
Maxima implements false by the value NIL in Lisp.
Categories: Constants
The Euler-Mascheroni constant, 0.5772156649015329 ....
Categories: Constants
ind represents a bounded, indefinite result.
See also limit.
Example:
(%i1) limit (sin(1/x), x, 0); (%o1) ind
Categories: Constants
inf represents real positive infinity.
Categories: Constants
infinity represents complex infinity.
Categories: Constants
minf represents real minus (i.e., negative) infinity.
Categories: Constants
%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
%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
true represents the Boolean constant of the same name.
Maxima implements true by the value T in Lisp.
Categories: Constants
und represents an undefined result.
See also limit.
Example:
(%i1) limit (x*sin(x), x, inf); (%o1) und
Categories: Constants
zeroa represents an infinitesimal above zero. zeroa can be used
in expressions. limit simplifies expressions which contain
infinitesimals.
Example:
limit simplifies expressions which contain infinitesimals:
(%i1) limit(zeroa); (%o1) 0 (%i2) limit(x+zeroa); (%o2) x
Categories: Constants
zerob represents an infinitesimal below zero. zerob can be used
in expressions. limit simplifies expressions which contain
infinitesimals.
Categories: Constants