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1 %!PS-Adobe-2.0
2 %%Creator: dvips 5.518 Copyright 1986, 1993 Radical Eye Software
3 %%Title: pois2m.dvi
4 %%CreationDate: Thu Sep 7 16:25:45 1995
5 %%Pages: 2
6 %%PageOrder: Ascend
7 %%BoundingBox: 0 0 612 792
8 %%EndComments
9 %DVIPSCommandLine: dvips -o pois2m.ps pois2m.dvi
10 %DVIPSSource: TeX output 1995.09.07:1618
11 %%BeginProcSet: tex.pro
12 /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
13 /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72
14 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1}
15 ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
16 isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div
17 hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul
18 TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get
19 round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{
20 statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0
21 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn
22 begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X
23 array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo
24 setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{/sf 1 N /fntrx
25 FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /E{
26 pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}
27 B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup
28 length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B
29 /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type
30 /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp
31 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2
32 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff
33 ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice
34 ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{
35 ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn
36 /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1
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38 }B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0
39 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add
40 .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore showpage
41 userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook
42 known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X
43 /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for
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45 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V
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47 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false}
48 ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley
49 false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley
50 scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave
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52 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta
53 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}
54 B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{
55 3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p
56 -1 w}B /q{p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{
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564 03C0078003C003C0078003C0018007C007C0038003C007E0030003C007E0030003C00CE0
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569 E end
570 %%EndProlog
571 %%BeginSetup
572 %%Feature: *Resolution 300dpi
573 TeXDict begin
575 %%EndSetup
576 %%Page: 1 1
577 1 0 bop 449 482 a Fq(A)21 b(Brief)h(o)n(v)n(erview)g(of)f(enhancemen)n
578 (ts)g(to)550 573 y Fp(Ma)n(csyma)p Fq('s)h(P)n(oisson)e(pac)n(k)l(age)
579 812 693 y Fo(Bruce)15 b(R.)h(Miller)1146 675 y Fn(\003)781
580 791 y Fo(Septem)o(b)q(er)e(7,)i(1995)262 1023 y Fm(1)69
581 b(In)n(tro)r(duction)262 1114 y Fl(I)9 b(will)f(assume)g(the)i(reader)h
582 (is)e(famili)o(ar)e(with)i(the)h(curren)o(t)g(implemen)o(tation)c(of)j
583 (Macsyma's)1705 1099 y Fk(1)262 1164 y Fj(Poisson)16
584 b Fl(pac)o(k)n(age.)25 b(Here,)18 b(I)e(brie\015y)g(describ)q(e)i(the)f
585 (c)o(hanges)g(I)f(made)f(to)h(the)h(pac)o(k)n(age)262
586 1214 y(and)c(whether)i(they)g(are)f(exp)q(ected)i(to)e(impact)e
587 (existing)i(uses)h(of)e Fj(Poisson)p Fl(.)324 1298 y
588 Fi(\017)20 b Fl(The)c(\014rst)h(c)o(hange)f(w)o(as)g(in)f(tuning)g(the)
589 i(co)q(de)f(for)g(mo)q(dern)f(lisps)g(and)h(for)f(tuning)365
590 1347 y(the)i(data)f(structures,)j(resulting)e(in)f(10\045)f(sp)q(eedup)
591 j(generally)f(and)f(a)g(2-3)g(times)365 1397 y(sp)q(eedup)k(in)e(m)o
592 (ultiplication,)d(for)j(example.)30 b(These)20 b(c)o(hanges)f(should)f
593 (b)q(e)h(com-)365 1447 y(patible)c(unless)h(other)g(pac)o(k)n(ages)f
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595 1497 y(\(whic)o(h)f(I)g(think)g(is)f(unlik)o(ely)m(,)f(ho)o(w)o(ev)o
596 (er\).)324 1577 y Fi(\017)20 b Fl(The)15 b(m)o(ultipli)o(ers)d(of)i
597 (the)g(angles)g(in)f(the)i(trig)e(argumen)o(ts)g(are)i(pac)o(k)o(ed)f
598 (in)o(to)f(single)365 1627 y(in)o(tegers.)38 b(In)21
599 b(the)g(curren)o(t)g(implemen)o(tation,)d(the)j(pro)q(duct)g(2)7
600 b(cos)g(8)p Fh(u)13 b Fi(\002)h Fl(sin)7 b(8)p Fh(u)365
601 1677 y Fl(should)18 b(giv)o(e)f(sin)7 b(16)p Fh(u)p Fl(,)18
602 b(but)g(if)f(the)i(enco)q(ding)f(restricts)i(the)f(range)f(to)g
603 Fi(\006)p Fl(15,)g(the)365 1726 y(\014eld)13 b(for)f
604 Fh(u)g Fl(o)o(v)o(er\015o)o(ws)h(in)o(to)e(the)i(next)g(\014eld)g(\(sa)
605 o(y)f(for)g Fh(v)q Fl(\).)19 b(The)13 b(enhancemen)o(t)f(adds)365
606 1776 y(an)19 b(extra)g(`o)o(v)o(er\015o)o(w')e(bit)h(to)g(eac)o(h)h
607 (\014eld,)h(and)e(an)g(error)i(c)o(hec)o(k)f(to)g(detect)h(suc)o(h)365
608 1826 y(o)o(v)o(er\015o)o(ws)11 b(when)g(m)o(ultiplying)c(P)o(oisson)k
609 (series.)18 b(Note,)11 b(ho)o(w)o(ev)o(er,)g(that)g(the)g(default)365
610 1876 y(parameters)i(yield)e(a)h(smaller)f(range)h(for)g(eac)o(h)h
611 (argumen)o(t)e(m)o(ultiplier)f(resulting)i(in)365 1926
612 y(a)i(sligh)o(t)f(incompatibilit)n(y)m(.)324 2006 y Fi(\017)20
613 b Fl(An)c(initialization)d(pro)q(cedure)18 b(has)d(b)q(een)i(added)f
614 (for)f Fg(poisvars)f Fl(\(as)i(w)o(ell)f(as)h(the)365
615 2055 y(existing)f(one)f(for)h Fg(poislim)p Fl(\).)j(This)d(assures)h
616 (that)f Fj(Poisson)p Fl('s)g(in)o(ternal)f(parame-)365
617 2105 y(ters)h(are)g(set)f(consisten)o(tly)h(whenev)o(er)g(either)g(v)n
618 (ariable)e(is)g(c)o(hanged.)365 2170 y(Tw)o(o)h(extensions)h(are)f(pro)
619 o(vided)g(b)o(y)f(allo)o(wing)f Fg(poislim)g Fl(to)i(b)q(e)h(set)f(to:)
620 412 2250 y Ff({)21 b Fl(a)12 b(list)f(of)h(in)o(tegers)h(represen)o
621 (ting)h(the)f(maxim)n(um)8 b(m)o(ultiplier)i(for)h(eac)o(h)i(angu-)457
622 2300 y(lar)g(v)n(ariable,)f(allo)o(wing)g(a)h(di\013eren)o(t)i(range)f
623 (for)g(eac)o(h)g(m)o(ultiplier.)p 262 2332 573 2 v 307
624 2358 a Fe(\003)325 2370 y Fd(Email:)p Fc(miller)o(@ca)o(m.n)o(is)o(t.g)
625 o(ov)308 2398 y Fb(1)325 2410 y Fd(The)h(use)g(of)g(commercial)d(pro)q
626 (ducts)h(or)i(their)f(names)g(implies)g(no)g(endorsemen)o(t)e(b)o(y)j
627 (NIST,)h(the)262 2449 y(Dept.)10 b(of)h(Commerce)f(or)h(the)g(U.S.)g
628 (Go)o(v)o(ernmen)o(t)o(.)967 2574 y Fl(1)p eop
629 %%Page: 2 2
630 2 1 bop 412 307 a Ff({)21 b Fl(F)m(alse)d(\(in)h(the)g(sense)h(of)f
631 (`no)f(limit'\))d(this)k(allo)o(ws)f(the)h(m)o(ultipliers)e(of)h(the)
632 457 357 y(angles)g(in)f(trig)h(argumen)o(ts)g(to)g(b)q(e)g(arbitrary)h
633 (macsyma)c(expressions.)33 b(In)457 407 y(this)19 b(case,)i(the)e
634 (argumen)o(t)f(m)o(ultipliers)f(are)j(represen)o(ted)i(b)o(y)d(lists)g
635 (rather)457 457 y(than)13 b(pac)o(k)o(ed)i(in)o(tegers.)365
636 540 y(An)i(alternativ)o(e)g(for)g(initialization)d(is)j(the)h(function)
637 e Fg(pois_setup)f Fl(whic)o(h)i(tak)o(es)365 589 y(alternating)d(v)n
638 (ariables)f(and)g(their)i(maxim)n(um)9 b(m)o(ultiplier.)365
639 656 y(Another)h(new)g(v)n(ariable)e(is)h(pro)o(vided)h
640 Fg(pois_encode_lib)o(erali)o(ze)c Fl(\(default)j Fg(False)p
641 Fl(\):)365 706 y(when)j(true,)h(it)e(accepts)i(sine)f(and)f(cosines)i
642 (of)e(argumen)o(ts)f(whic)o(h)i(are)g(not)f(linear)g(in)365
643 756 y Fg(poisvars)j Fl(with)i(in)o(tegral)f(co)q(e\016cien)o(ts;)i(the)
644 f(non-linear)f(part)h(is)f(tak)o(en)h(in)o(to)f(the)365
645 805 y(co)q(e\016cien)o(ts)d(rather)e(than)g(signalling)e(an)i(error.)18
646 b(The)10 b(default)g(v)n(alue)f(is)h(compatible)365 855
647 y(with)k(existing)f(usage.)324 938 y Fi(\017)20 b Fl(F)m(or)12
648 b(con)o(v)o(enience,)h(the)g(functions)f Fg(poisplus)e
649 Fl(and)i Fg(poistimes)e Fl(w)o(ere)j(mo)q(di\014ed)e(to)365
650 988 y(accept)k(an)o(y)f(n)o(um)o(b)q(er)f(of)g(argumen)o(ts.)324
651 1071 y Fi(\017)20 b Fl(The)g(`5)e(argumen)o(t)f(form')g(of)h
652 Fg(poissubst)p Fl(:)26 b(I)19 b(understand)h(what)f(it)f(computes,)365
653 1121 y(but)e(frankly)m(,)e(I)i(do)f(not)g(understand)i(what)f(it)f(is)g
654 (supp)q(osed)i(to)e(represen)o(t)j(math-)365 1171 y(ematically)m(.)28
655 b(I)17 b(\014nally)g(con)o(vinced)i(m)o(yself)d(that)i
656 Fg(poissubst\(a,b,c,d)o(,n\))d Fl(w)o(as)365 1220 y Fa(intende)n(d)h
657 Fl(to)f(compute)f(the)h(equiv)n(alen)o(t)g(of)f Fg(taylor\(subst\(a+d,)
658 o(b,c\),)o(d,0,n)o(\))p Fl(,)365 1270 y(alb)q(eit)g(more)f(e\016cien)o
659 (tly)m(.)18 b(I)c(follo)o(w)o(ed)f(a)h(suggestion)g(b)o(y)g(J.)g(P)m(.)
660 f(Fitc)o(h,)h(noting)g(that)365 1320 y(di\013eren)o(tiation)20
661 b(of)g(a)f(P)o(oisson)h(series)i(is)e(quite)g(fast,)h(w)o(e)f(simply)e
662 (use)j(T)m(a)o(ylor's)365 1370 y(theorem.)d(This)c(is)g(an)f
663 (incompatible)f(c)o(hange.)262 1507 y Fm(2)69 b(Suggestions)262
664 1598 y Fl(There)15 b(are)h(further)f(c)o(hanges)h(to)e(the)i(pac)o(k)n
665 (age)e(that)h(w)o(ould)f(mak)o(e)f(it)i(more)e(robust)j(and)262
666 1648 y(useful,)i(particularly)f(b)o(y)h(making)d(the)k(use)g(of)e(p)q
667 (oisson)h(more)f(transparen)o(t)i(and)f(in)o(te-)262
668 1698 y(grated,)i(but)f(there)i(app)q(ears)f(to)e(b)q(e)i(no)f(great)h
669 (in)o(terest)g(in)f(this)g(facilit)o(y)e(in)i(the)h(user)262
670 1747 y(comm)o(uni)o(t)o(y)m(.)15 b(Is)f(this)g(wrong?)967
671 2574 y(2)p eop
672 %%Trailer
673 end
674 userdict /end-hook known{end-hook}if
675 %%EOF