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13.1 Definitions 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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