%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 A&S eqn 4.1.16, A&S 4.1.17.)
false
represents the Boolean constant of the same name.
Maxima implements false
by the value NIL
in Lisp.
The Euler-Mascheroni constant, 0.5772156649015329.... It is defined by (A&S eqn 6.1.3 and DLMF 5.2.ii)
ind
represents a bounded, indefinite result.
See also limit
.
Example:
(%i1) limit (sin(1/x), x, 0); (%o1) ind
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 numbers
are supported. Otherwise it is the same as
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.
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 numbers
are supported. Otherwise it is the same as
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.
The most negative floating-point number in Maxima. It is approximately -1.79769e+308.
The most positive floating-point number in Maxima. It is approximately 1.797693e+308.
%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.
und
represents an undefined result.
See also limit
.
Example:
(%i1) limit (x*sin(x), x, inf); (%o1) und
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