This is a program set I wrote for the RPN calculator that runs on the Palm Pilot. It implements factorial, permutations, combinations, Stirling numbers of the first kind, Stirling numbers of the second kind, and a program that will factor an integer.

This can be pasted into the Memo application and from there added to the RPN calculator.

// Factorial, permutations, // combinations, stirling #s 2nd kind, // factoring numbers. // // ! (factrial) returns the factorial of // the number in the X register after // taking the absolute value and then // truncating it to a whole number. // // Pyx (permutations) returns // permutations of y taken x at a // time. This has been extended // for negative numbers as // suggested in Knuth's book // Concrete Mathematics. It is: // (y)*(y-1)*...*(y-x+1). If x is 0 // then 1 is returned by definition. // If x is negative, then 0 is // returned. // // Cyx (combinations) returns the // number of ways of selecting x // items out of y where order // doesn't matter. It too has been // extended like Pyx. If x is // negative then 0 is returned, but // if y is negative, then Pyx/x! is // returned. // // S1yx (Stirling numbers of the // first kind). This is the number // of ways to partition y items into // x rings. This is computationally // intensive to calculate. It can // handle any pair of whole // whole number values where // y-x < 26, but cases where x is // fairly large and y is quite a bit // larger take a very long time. // Beware of large values. // // S2yx (Stirling numbers of the // second kind) This is the number // of ways to partition y items into // x sets. // // Factors. This function takes // the absolute value and then the // integer portion of the number // entered. It then decomposes // it into all of its prime factors // which are placed on the stack. // // By Truman Collins // (tcollins@teleport.com) // 1/98 RPN.1.z [f] Vv2<(1:v{_vv2<(B)v*}); [p] g10<(d1d10:g11<(d1d11:g2r2- #'.5'+XaVv{v1-Vvxa<(B)v*}))); [c] g10<(d1d10:g20>(g2f0=9 (g2g2>(g2g2-g1g3> (d1:d2))))g1Cfk3Cpr2/); [z] xzV1{vx@*_vv1<(B)}+; "Combinatorics" "_!: Factorial" ?1wbCf; "Pyx: Permutations. y items\taken x at a time when the\order matters." ?2wCp; "Cyx: Combination. y items\taken x at a time when the\order does not matter." ?2wCc; ~ "S1yx: Stirling #s of 1st kind.\# of ways y items can be parti-\tioned into x rings." ?2g2g2<(d1d10;)g2g2-g10=9(d1d1 d11;)g1#'24'>(d1d1d1E.)Xzd1Xyxz V{vvX@_vv1<(B)}xyxz1+X@ xzV0{vxz>(B)v1<(Czv1+Vvx@1+ vX@:vx@v1+x@=9(vvX@v1+ Vvx@1+vX@:_v))}; "S2yx: Stirling #s of 2nd kind.\# of ways y items can be parti-\tioned into x non-empty sets." ?2wr2wr2g1XcVXb1Xa0 {xavxbP*vCf/xcv-Cf/+ xanXa_vv1<(B)}; ~ "Factors: Factors an integer\and places all of its prime\factors on the stack." ?1g1swXaXb2V {vxa>(B)xbv%0=9 (vxbv/#'.0000001'+wg1XbswXa: vv2=9(1:2)+V)}xb;

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For comments, email: Truman Collins (truman@tkcs-collins.com)

Most recent update: January 5, 2005

http://www.tkcs-collins.com/truman/rpn/rpn_comb.shtml