ref: 1018d7a7091fd5e0433f501a3474cdc3fec322cc
dir: /appl/math/parts.b/
implement Partitions; include "sys.m"; sys : Sys; include "draw.m"; include "ipints.m"; ipints: IPints; IPint: import ipints; # # the number p(n) of partitions of n # based upon the formula :- # p(n) = p(n-1)+p(n-2)-p(n-5)-p(n-7)+p(n-12)+p(n-15)-p(n-22)-p(n-26)+..... # where p[0] = 1 and p[m] = 0 for m < 0 # aflag := 0; cflag := 0; Partitions: module { init: fn(nil: ref Draw->Context, argv: list of string); }; init(nil: ref Draw->Context, argv: list of string) { sys = load Sys Sys->PATH; ipints = load IPints IPints->PATH; argv = tl argv; while(argv != nil){ s := hd argv; if(s != nil && s[0] == '-'){ for(i := 1; i < len s; i++){ case s[i]{ 'a' => aflag = 1; 'c' => cflag = 1; } } } else parts(int s); argv = tl argv; } } parts(m : int) { if (aflag) sys->print("n p(n)\n"); if (m <= 0) { p := 0; if (m == 0) p = 1; if (aflag) sys->print("%d %d\n", m, p); else sys->print("p[%d] = %d\n", m, p); return; } p := array[m+1] of ref IPint; if (p == nil) return; p[0] = IPint.inttoip(1); for (i := 1; i <= m; i++) { k := i; s := 1; n := IPint.inttoip(0); for (j := 1; ; j++) { k -= 2*j-1; if (k < 0) break; if (s == 1) n = n.add(p[k]); else n = n.sub(p[k]); k -= j; if (k < 0) break; if (s == 1) n = n.add(p[k]); else n = n.sub(p[k]); s = -s; } if (aflag) sys->print("%d %s\n", i, n.iptostr(10)); p[i] = n; } if (!aflag) sys->print("p[%d] = %s\n", m, p[m].iptostr(10)); if (cflag) check(m, p); } # # given p[0]..p[m], search for congruences of the form # p[ni+j] = r mod i # check(m : int, p : array of ref IPint) { one := IPint.inttoip(1); for (i := 2; i < m/3; i++) { ip := IPint.inttoip(i); for (j := 0; j < i; j++) { k := j; r := p[k].expmod(one, ip).iptoint(); s := 1; for (;;) { k += i; if (k > m) break; if (p[k].expmod(one, ip).iptoint() != r) { r = -1; break; } s++; } if (r >= 0) if (j == 0) sys->print("p(%dm) = %d mod %d ?\n", i, r, i); else sys->print("p(%dm+%d) = %d mod %d ?\n", i, j, r, i); } } }