Personal configuration of the Maxima CAS
Binary splitting method for computing bell number using Dobinski's formula:
Binary splitting method for computing Catalan's constant: 0.915965594177219...
(%i1) bfloat(%g),fpprec:1000;
Binary splitting method for computing exp(small rational number).
(%i1) bfloat(exp(1/3)),fpprec:10^6;
Get %pi's 1 million digits without using bigfloat in 1 sec (with sb-gmp).
Alternative ways to compute log(2).
Redefine fpround and number-of-digits to get more efficient bigfloat formatting.
Redefine $bfloat to handle extra constants like Catalan's constant, zeta funtion in positive integer.
Redefine displa to let maxima display bignum in one line and properly display bigfloat like 0.5772156649015329
instead of 5.772156649015329b-1 .
Calculate partition function p(n) using python-flint [arb] and parse it into a lisp bignum.
Fredrik Johansson's arb implementation is super efficient and nearly optimial. See his blog.
(%i1) numpart(10^9);
Compute primecount function, nth-prime function and primesum function using Kim Walisch's primecount
and my cffi bindings lib cl-primecount.
(%i1) primepi(10^14);
(%o1) 3204941750802
(%i2) prime(10^14);
(%o2) 3475385758524527
(%i3) primesum(10^10);
(%o3) 2220822432581729238
Borwein's method to compute zeta function in positive integer (translated from PARI/GP, faster than maxima's general implementation.
(%i1) bfloat(zeta(5)),fpprec:10^4;
Binary splitting method for computing Apery's constant aka zeta(3). (Amdeberhan-Zeilberger formula)
(%i1) bfloat(zeta(3)),fpprec:10^5;