perm filename EINIT.CMD[AM,DBL] blob
sn#398100 filedate 1978-11-23 generic text, type C, neo UTF8
COMMENT ⊗ VALID 00002 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00002 00002 αXDEFINE B1↔
C00012 ENDMK
C⊗;
αXDEFINE B1⊗↔
αxf $$α\\foo{⊗↔αxf $α\}⊗↔αβ⊗↓
αXDEFINE B2⊗↔
α2αp⊗↔α9α9αz b1⊗↔αβ⊗↓
αXDEFINE F1⊗↔
α2αpαxf ⊗⊗α\\⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1B⊗↔
α2αpαxf \*α\\0⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2⊗↔
αxf 0``α\0''⊗↔α2αp⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3⊗↔
αxf \0.α\\1.⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ\⊗↔αβ⊗↓
αXDEFINE F4⊗↔
αxf ↓_α\{\it ⊗↔αxf _↓α\}⊗↔αβ⊗↓
αXDEFINE F5⊗↔
α2αp⊗↔α9α9αz f4⊗↔αβ⊗↓
αXDEFINE S1⊗↔
α2αp\αs({α⊗=⊗↑}⊗↔⊗↔αxf .SSEC(α\\SSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S2⊗↔
α2αp⊗↔αxf .SSSEC(α\\SSSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S3⊗↔
α2αpαxf . SSSEC(α\ \SSSEC{⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S4⊗↔
α⊗=⊗↑}⊗↔αp⊗↔⊗↑αβ⊗↓
αXDEFINE S5⊗↔
α2αpα9α9αzs4⊗↔αβ⊗↓
αXDEFINE ⊗↔
\SSSEC{Rippling}Given a concept C, how can AM find all the concepts wh
ich claim C asan example?The most obvious scheme is to store this infor
mation explicitly. Sothe Examples facet of C would point to all known
examples of C, andthe Isa facet of C would point to all known concept
s claiming C asone of their examples. Why not just do this? Because
one can substitute amodest amount of processing time (via chasing link
s around) for thevast amount of storage space that would be needed to h
ave ``everythingpoint to everything"..GENLSPEC: PAGEEach facet contains
only enough pointers so that the entire graph ofExs/Isa and Spec/Genl l
inks could be \4reconstructed\0 if needed. Since``Genl".if false then
start;$$ ``Genl" is an abbreviation for the Generalizations facet of a c
oncept;similarly, ``Spec" means Specializations, Exs means Examples, etc
.``Isa" is the converse facet to Exs; i.e., A ε B.Exs iff B ε A.Isa.Sayi
ng ``Genl is transitive" just means the following: if A is ageneralizati
on of B, and B of C, then A is also a generalization of C.$ .end;is a tr
ansitive relation, AM can compute that Numbers is ageneralization of
Mersenne-primes, if the facet Mersenne-primes.Genlcontains the entry
``Odd-primes", and Odd-primes.Genl contains apointer to ``Primes",
and Primes.Genl points to ``Numbers". This kindof ``\4rippling\0'' acti
vity is used to efficiently locate all conceptsrelated to a given one
X. In particular, AM knows how to ``rippleupward in the Isa directi
on", and quickly$$ With about 200 knownconcepts, with each Isa facet
and each Genl facet pointing to about 3other concepts, about 25 links
will be traced along in order tolocate about a dozen final concepts
, each of which claims the givenone as an example. This whole rippling
process, tracing 25 linkages,uses less than .01 cpu seconds, in comp
iled Interlisp, on a KI-10type PDP-10. $ locate all concepts which c
laim X as one of theirexamples..ONCE TURN ON ``{}``It turns out that
AM cannot simply call for X.Isa, then the Isafacets of those concep
ts, etc., because Isa is not transitive$$ If xisa y, and y isa z, th
en x is (generally) {\it NOT} a z. This is due to theintransitivity
of ``member-of". Generalization is transitive, on theother hand, becau
se ``subset-of" is transitive. $. For the interestedreader, the algorit
hm AM uses to collect Isa's of X is given below.$$For the {\it very}
interested reader, it is explained in great detailin file RIPPLE[dis,db
l] at SAIL. This filehas beenpermanently archived at SAIL. $.RIPPL: MYF
OOT-1;.BN ONCE PREFACE 1λλ All generalizations of the given concept
X are located. AMaccesses X.Genl, then the Genl facets of \4those\0
concepts, etc.λλ The ``Isa" facet of each of those concepts is accessed.
λλ AM locates all generalizations of these newly-found higher-levelcon
cepts. This is the list of all known concepts which claim X asone of
their examples..E.EXISA: PAGE;.GIGPAGE: PAGE;.ONCE TURN ON ``{}``In reg
ular form, one might express this rippling recipe more compactly as:\6Ge
nl↑*(Isa(Genl↑*(X)))\1. .if false then start;There is not much needfor
a detailed understanding of this process, hence it will not bedelved
into further in this book. This section probably alreadycontains more t
han anyone would want to know about rippling.\A{[3]RIPPL}\0.end;αβ⊗↓
αXDEFINE B1⊗↔
αxf $$α\\foo{⊗↔αxf $α\}⊗↔αβ⊗↓
αXDEFINE B2⊗↔
α2αp⊗↔α9α9αz b1⊗↔αβ⊗↓
αXDEFINE B3⊗↔
αxf ⊗α{α\$\{$⊗↔αxf ⊗α}α\$\}$⊗↔αβ⊗↓
αXDEFINE B4⊗↔
α2αpα9α9α9αzb3⊗↔αβ⊗↓
αXDEFINE B5⊗↔
α2αpαxf -- α\ --- ⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1⊗↔
α2αpαxf ⊗⊗α\\⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1B⊗↔
α2αpαxf \*α\\0⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2⊗↔
αxf 0``α\0''⊗↔α2αp⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3⊗↔
αxf \0.α\\1.⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ\⊗↔αβ⊗↓
αXDEFINE F4⊗↔
αxf ↓_α\{\it ⊗↔αxf _↓α\}⊗↔αβ⊗↓
αXDEFINE F5⊗↔
α2αp⊗↔α9α9αz f4⊗↔αβ⊗↓
αXDEFINE S1⊗↔
α2αp\αs({α⊗=⊗↑}⊗↔⊗↔αxf .SSEC(α\\SSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S2⊗↔
α2αp⊗↔αxf .SSSEC(α\\SSSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S3⊗↔
α2αpαxf . SSSEC(α\ \SSSEC{⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S4⊗↔
α⊗=⊗↑}⊗↔αp⊗↔⊗↑αβ⊗↓
αXDEFINE S5⊗↔
α2αpα9α9αzs4⊗↔αβ⊗↓
αXDEFINE ⊗↔
b4⊗↔αβ⊗↓
αXDEFINE H3⊗↔
⊗↔β\βhβaβnβ3β{β{β\βiβtβ α⊗=}}⊗↔αβ⊗↓
αXDEFINE H4⊗↔
αdαdαdαdαdαd⊗↔β\βhβaβnβ3β{β{β\β6αk αs:α α β{β\βiβtβ α⊗=⊗↑}}}⊗↔αβ⊗↓
αXDEFINE H5⊗↔
αzh3⊗↔αβ⊗↓
αXDEFINE B1⊗↔
αxf $$α\\foo{⊗↔αxf $α\}⊗↔αβ⊗↓
αXDEFINE B2⊗↔
α2αp⊗↔α9α9αz b1⊗↔αβ⊗↓
αXDEFINE B3⊗↔
αxf ⊗α{α\$\{$⊗↔αxf ⊗α}α\$\}$⊗↔αβ⊗↓
αXDEFINE B4⊗↔
α2αpα9α9α9αzb3⊗↔αβ⊗↓
αXDEFINE B5⊗↔
α2αpαxf -- α\ --- ⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE B6⊗↔
αxf {⊗↔αs{β$β\α β$⊗↔⊗↑αxf }⊗↔αs}β$β\α β$⊗↔αβ⊗↓
αXDEFINE C1⊗↔
αxf -o-α\$\circ$⊗↔αβ⊗↓
αXDEFINE F1⊗↔
α2αpαxf ⊗⊗α\\⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1B⊗↔
α2αpαxf \*α\\0⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2⊗↔
αxf 0``α\0''⊗↔α2αp⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3⊗↔
αxf \0.α\\1.⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ\⊗↔αβ⊗↓
αXDEFINE F4⊗↔
αxf ↓_α\{\it ⊗↔αxf _↓α\}⊗↔αβ⊗↓
αXDEFINE F5⊗↔
α2αp⊗↔α9α9αz f4⊗↔αβ⊗↓
αXDEFINE H3⊗↔
⊗↔β\βhβaβnβ3β{β{β\βiβtβ α⊗=}}⊗↔αβ⊗↓
αXDEFINE H4⊗↔
αdαdαdαdαdαd⊗↔β\βhβaβnβ3β{β{β\β6αk αs:α α β{β\βiβtβ α⊗=⊗↑}}}⊗↔αβ⊗↓
αXDEFINE H5⊗↔
αzh3⊗↔αβ⊗↓
αXDEFINE N1⊗↔
αxf n α\{⊗↑ {\it n} ⊗↔αβ⊗↓
αXDEFINE S1⊗↔
α2αp\αs({α⊗=⊗↑}⊗↔⊗↔αxf .SSEC(α\\SSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S2⊗↔
α2αp⊗↔αxf .SSSEC(α\\SSSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S3⊗↔
α2αpαxf . SSSEC(α\ \SSSEC{⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S4⊗↔
α⊗=⊗↑}⊗↔αp⊗↔⊗↑αβ⊗↓
αXDEFINE S5⊗↔
α2αpα9α9αzs4⊗↔αβ⊗↓
αXDEFINE ⊗↔
b4⊗↔αβ⊗↓
αXDEFINE B1⊗↔
αxf $$α\\foo{⊗↔αxf $α\}⊗↔αβ⊗↓
αXDEFINE B2⊗↔
α2αp⊗↔α9α9αz b1⊗↔αβ⊗↓
αXDEFINE B3⊗↔
αxf ⊗α{α\$\{$⊗↔αxf ⊗α}α\$\}$⊗↔αβ⊗↓
αXDEFINE B4⊗↔
α2αpα9α9α9αzb3⊗↔αβ⊗↓
αXDEFINE B5⊗↔
α2αpαxf -- α\ --- ⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE B6⊗↔
αxf {⊗↔αs{β$β\α β$⊗↔⊗↑αxf }⊗↔αs}β$β\α β$⊗↔αβ⊗↓
αXDEFINE C1⊗↔
αxf -o-α\$\circ$⊗↔αβ⊗↓
αXDEFINE F1⊗↔
α2αpαxf ⊗⊗α\\⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1B⊗↔
α2αpαxf \*α\\0⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2⊗↔
αxf 0``α\0''⊗↔α2αp⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2C⊗↔
α2αpαxf \0'α\\1'⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2D⊗↔
α2αpαxf \0"α\\1"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2E⊗↔
α2αpαxf \6"α\\6``⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2F⊗↔
α2αpαxf λα\$\lambda $⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3⊗↔
αxf \0.α\\1.⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ\⊗↔αβ⊗↓
αXDEFINE F4⊗↔
αxf ↓_α\{\it ⊗↔αxf _↓α\}⊗↔αβ⊗↓
αXDEFINE F5⊗↔
α2αp⊗↔α9α9αz f4⊗↔αβ⊗↓
αXDEFINE H3⊗↔
⊗↔β\βhβaβnβ3β{β{β\βiβtβ α⊗=}}⊗↔αβ⊗↓
αXDEFINE H4⊗↔
αdαdαdαdαdαd⊗↔β\βhβaβnβ3β{β{β\β6αk αs:α α β{β\βiβtβ α⊗=⊗↑}}}⊗↔αβ⊗↓
αXDEFINE H5⊗↔
αzh3⊗↔αβ⊗↓
αXDEFINE N1⊗↔
αxf n α\{⊗↑ {\it n} ⊗↔αβ⊗↓
αXDEFINE S1⊗↔
α2αp\αs({α⊗=⊗↑}⊗↔⊗↔αxf .SSEC(α\\SSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S2⊗↔
α2αp⊗↔αxf .SSSEC(α\\SSSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S3⊗↔
α2αpαxf . SSSEC(α\ \SSSEC{⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S4⊗↔
α⊗=⊗↑}⊗↔αp⊗↔⊗↑αβ⊗↓
αXDEFINE S5⊗↔
α2αpα9α9αzs4⊗↔αβ⊗↓
αXDEFINE ⊗↔
⊗↔αβ⊗↓
αXDEFINE AA⊗↔
⊗↔αdαdαdαdαdαi⊗↔α⊗↔αβ⊗↓
αXDEFINE B1⊗↔
αxf $$α\\foo{⊗↔αxf $α\}⊗↔αβ⊗↓
αXDEFINE B2⊗↔
α2αp⊗↔α9α9αz b1⊗↔αβ⊗↓
αXDEFINE B3⊗↔
αxf ⊗α{α\$\{$⊗↔αxf ⊗α}α\$\}$⊗↔αβ⊗↓
αXDEFINE B4⊗↔
α2αpα9α9α9αzb3⊗↔αβ⊗↓
αXDEFINE B5⊗↔
α2αpαxf -- α\ --- ⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE B6⊗↔
αxf {⊗↔αs{β$β\α β$⊗↔⊗↑αxf }⊗↔αs}β$β\α β$⊗↔αβ⊗↓
αXDEFINE BU⊗↔
⊗↔αi$\bullet $ \ α⊗↔⊗↔αβ⊗↓
αXDEFINE C1⊗↔
αxf -o-α\$\circ$⊗↔αβ⊗↓
αXDEFINE F1⊗↔
α2αpαxf ⊗⊗α\\⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1B⊗↔
α2αpαxf \*α\\0⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2⊗↔
αxf 0``α\0''⊗↔α2αp⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2C⊗↔
α2αpαxf \0'α\\1'⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2D⊗↔
α2αpαxf \0"α\\1"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2E⊗↔
α2αpαxf \6"α\\6``⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2F⊗↔
α2αpαxf λα\$\lambda $⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2G⊗↔
α2αpαxf )``α\)"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2H⊗↔
α2αp⊗↔αxf ,``α\,"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3⊗↔
αxf \0.α\\1.⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ\⊗↔αβ⊗↓
αXDEFINE F4⊗↔
αxf ↓_α\{\it ⊗↔αxf _↓α\}⊗↔αβ⊗↓
αXDEFINE F5⊗↔
α2αp⊗↔α9α9αz f4⊗↔αβ⊗↓
αXDEFINE H3⊗↔
⊗↔β\βhβaβnβ3β{β{β\βiβtβ α⊗=}}⊗↔αβ⊗↓
αXDEFINE H3B⊗↔
⊗↔αihan3{{⊗↑αs:α α αi{\it α⊗=⊗↑}}⊗↔αβ⊗↓
αXDEFINE H4⊗↔
αdαdαdαdαdαd⊗↔β\βhβaβnβ3β{β{β\β6αk αs:α α β{β\βiβtβ α⊗=⊗↑}}}⊗↔αβ⊗↓
αXDEFINE H5⊗↔
αzh3⊗↔αβ⊗↓
αXDEFINE N1⊗↔
αxf n α\{⊗↑ {\it n} ⊗↔αβ⊗↓
αXDEFINE S1⊗↔
α2αp\αs({α⊗=⊗↑}⊗↔⊗↔αxf .SSEC(α\\SSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S2⊗↔
α2αp⊗↔αxf .SSSEC(α\\SSSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S3⊗↔
α2αpαxf . SSSEC(α\ \SSSEC{⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S4⊗↔
α⊗=⊗↑}⊗↔αp⊗↔⊗↑αβ⊗↓
αXDEFINE S5⊗↔
α2αpα9α9αzs4⊗↔αβ⊗↓
αXDEFINE ⊗↔
⊗↔αβ⊗↓
αXDEFINE AA⊗↔
⊗↔αdαdαdαdαdαi⊗↔α⊗↔αβ⊗↓
αXDEFINE B1⊗↔
αxf $$α\\foo{⊗↔αxf $α\}⊗↔αβ⊗↓
αXDEFINE B2⊗↔
α2αp⊗↔α9α9αz b1⊗↔αβ⊗↓
αXDEFINE B3⊗↔
αxf ⊗α{α\$\{$⊗↔αxf ⊗α}α\$\}$⊗↔αβ⊗↓
αXDEFINE B4⊗↔
α2αpα9α9α9αzb3⊗↔αβ⊗↓
αXDEFINE B5⊗↔
α2αpαxf -- α\ --- ⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE B6⊗↔
αxf {⊗↔αs{β$β\α β$⊗↔⊗↑αxf }⊗↔αs}β$β\α β$⊗↔αβ⊗↓
αXDEFINE BU⊗↔
⊗↔αi$\bullet $ \ α⊗↔⊗↔αβ⊗↓
αXDEFINE BU3⊗↔
⊗↔\han3{ $\bullet $ αk}αdα⊗= }αβ⊗↓
αXDEFINE BU4⊗↔
⊗↔αi\noindent $\bullet $ α⊗↔αβ⊗↓
αXDEFINE C1⊗↔
αxf -o-α\$\circ$⊗↔αβ⊗↓
αXDEFINE F1⊗↔
α2αpαxf ⊗⊗α\\⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1B⊗↔
α2αpαxf \*α\\0⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2⊗↔
αxf 0``α\0''⊗↔α2αp⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2C⊗↔
α2αpαxf \0'α\\1'⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2D⊗↔
α2αpαxf \0"α\\1"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2E⊗↔
α2αpαxf \6"α\\6``⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2F⊗↔
α2αpαxf λα\$\lambda $⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2G⊗↔
α2αpαxf )``α\)"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2H⊗↔
α2αp⊗↔αxf ,``α\,"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3⊗↔
αxf \0.α\\1.⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ\⊗↔αβ⊗↓
αXDEFINE F4⊗↔
αxf ↓_α\{\it ⊗↔αxf _↓α\}⊗↔αβ⊗↓
αXDEFINE F5⊗↔
α2αp⊗↔α9α9αz f4⊗↔αβ⊗↓
αXDEFINE H3⊗↔
⊗↔β\βhβaβnβ3β{β{β\βiβtβ α⊗=}}⊗↔αβ⊗↓
αXDEFINE H3B⊗↔
⊗↔αihan3{{⊗↑αs:α α αi{\it α⊗=⊗↑}}⊗↔αβ⊗↓
αXDEFINE H4⊗↔
αdαdαdαdαdαd⊗↔β\βhβaβnβ3β{β{β\β6αk αs:α α β{β\βiβtβ α⊗=⊗↑}}}⊗↔αβ⊗↓
αXDEFINE H5⊗↔
αzh3⊗↔αβ⊗↓
αXDEFINE H8⊗↔
αk<αi\han3{\it α α α αs⊗ααdαi$α α α α α α αi$α α⊗=⊗↑}}⊗↔αβ⊗↓
αXDEFINE N1⊗↔
αxf n α\{⊗↑ {\it n} ⊗↔αβ⊗↓
αXDEFINE S1⊗↔
α2αp\αs({α⊗=⊗↑}⊗↔⊗↔αxf .SSEC(α\\SSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S2⊗↔
α2αp⊗↔αxf .SSSEC(α\\SSSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S3⊗↔
α2αpαxf . SSSEC(α\ \SSSEC{⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S4⊗↔
α⊗=⊗↑}⊗↔αp⊗↔⊗↑αβ⊗↓
αXDEFINE S5⊗↔
α2αpα9α9αzs4⊗↔αβ⊗↓
αXDEFINE ⊗↔
⊗↔αβ⊗↓
αXDEFINE AA⊗↔
⊗↔αdαdαdαdαdαi⊗↔α⊗↔αβ⊗↓
αXDEFINE B1⊗↔
αxf $$α\\foo{⊗↔αxf $α\}⊗↔αβ⊗↓
αXDEFINE B2⊗↔
α2αp⊗↔α9α9αz b1⊗↔αβ⊗↓
αXDEFINE B3⊗↔
αxf ⊗α{α\$\{$⊗↔αxf ⊗α}α\$\}$⊗↔αβ⊗↓
αXDEFINE B4⊗↔
α2αpα9α9α9αzb3⊗↔αβ⊗↓
αXDEFINE B5⊗↔
α2αpαxf -- α\ --- ⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE B6⊗↔
αxf {⊗↔αs{β$β\α β$⊗↔⊗↑αxf }⊗↔αs}β$β\α β$⊗↔αβ⊗↓
αXDEFINE BU⊗↔
⊗↔αi$\bullet $ \ α⊗↔⊗↔αβ⊗↓
αXDEFINE BU3⊗↔
⊗↔\han3{ $\bullet $ αk}αdα⊗= }αβ⊗↓
αXDEFINE BU4⊗↔
⊗↔αi\noindent $\bullet $ α⊗↔αβ⊗↓
αXDEFINE C1⊗↔
αxf -o-α\$\circ$⊗↔αβ⊗↓
αXDEFINE F1⊗↔
α2αpαxf ⊗⊗α\\⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1B⊗↔
α2αpαxf \*α\\0⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1C⊗↔
α2αpαxf λλα\\hh⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2⊗↔
αxf 0``α\0''⊗↔α2αp⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2C⊗↔
α2αpαxf \0'α\\1'⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2D⊗↔
α2αpαxf \0"α\\1"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2E⊗↔
α2αpαxf \6"α\\6``⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2F⊗↔
α2αpαxf λα\$\lambda $⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2G⊗↔
α2αpαxf )``α\)"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2H⊗↔
α2αp⊗↔αxf ,``α\,"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3⊗↔
αxf \0.α\\1.⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ\⊗↔αβ⊗↓
αXDEFINE F4⊗↔
αxf ↓_α\{\it ⊗↔αxf _↓α\}⊗↔αβ⊗↓
αXDEFINE F5⊗↔
α2αp⊗↔α9α9αz f4⊗↔αβ⊗↓
αXDEFINE H3⊗↔
⊗↔β\βhβaβnβ3β{β{β\βiβtβ α⊗=}}⊗↔αβ⊗↓
αXDEFINE H3B⊗↔
⊗↔αihan3{{⊗↑αs:α α αi{\it α⊗=⊗↑}}⊗↔αβ⊗↓
αXDEFINE H4⊗↔
αdαdαdαdαdαd⊗↔β\βhβaβnβ3β{β{β\β6αk αs:α α β{β\βiβtβ α⊗=⊗↑}}}⊗↔αβ⊗↓
αXDEFINE H5⊗↔
αzh3⊗↔αβ⊗↓
αXDEFINE H8⊗↔
αk<αi\han3{\it α α α αs⊗ααdαi$α α α α α α αi$α α⊗=⊗↑}}⊗↔αβ⊗↓
αXDEFINE N1⊗↔
αxf n α\{⊗↑ {\it n} ⊗↔αβ⊗↓
αXDEFINE S1⊗↔
α2αp\αs({α⊗=⊗↑}⊗↔⊗↔αxf .SSEC(α\\SSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S2⊗↔
α2αp⊗↔αxf .SSSEC(α\\SSSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S3⊗↔
α2αpαxf . SSSEC(α\ \SSSEC{⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S4⊗↔
α⊗=⊗↑}⊗↔αp⊗↔⊗↑αβ⊗↓
αXDEFINE S5⊗↔
α2αpα9α9αzs4⊗↔αβ⊗↓
αXDEFINE S6⊗↔
α2αpαxf .assecp(α\\ASSECP{⊗↔α9α9α\⊗↔αβ⊗↓
αXDEFINE S7⊗↔
α2αpαxf .assec(α\\ASSEC{⊗↔α9α9α\⊗↔αβ⊗↓
αXDEFINE S8⊗↔
α3αpαxf . asssec(α\ \ASSSEC{⊗↔α9α9α\⊗↔αβ⊗↓
αXDEFINE S9⊗↔
α2αpαxf polyaα\P\'olya⊗↔α9α9α\⊗↔αβ⊗↓
αXDEFINE ⊗↔
⊗↔αβ⊗↓
αXDEFINE SUB⊗↔
αi$↓α αi$α αβ⊗↓
αXDEFINE AA⊗↔
⊗↔αdαdαdαdαdαi⊗↔α⊗↔αβ⊗↓
αXDEFINE B1⊗↔
αxf $$α\\foo{⊗↔αxf $α\}⊗↔αβ⊗↓
αXDEFINE B2⊗↔
α2αp⊗↔α9α9αz b1⊗↔αβ⊗↓
αXDEFINE B3⊗↔
αxf ⊗α{α\$\{$⊗↔αxf ⊗α}α\$\}$⊗↔αβ⊗↓
αXDEFINE B4⊗↔
α2αpα9α9α9αzb3⊗↔αβ⊗↓
αXDEFINE B5⊗↔
α2αpαxf -- α\ --- ⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE B6⊗↔
αxf {⊗↔αs{β$β\α β$⊗↔⊗↑αxf }⊗↔αs}β$β\α β$⊗↔αβ⊗↓
αXDEFINE BEG1⊗↔
αxf Beginning ⊗↔αi\yskip⊗↔⊗↔\ctrline{α⊗=}⊗↔αi⊗↔\yskip⊗↔α⊗↔αβ⊗↓
αXDEFINE BU⊗↔
⊗↔αi$\bullet $ \ α⊗↔⊗↔αβ⊗↓
αXDEFINE BU3⊗↔
⊗↔\han3{ $\bullet $ αk}αdα⊗= }αβ⊗↓
αXDEFINE BU4⊗↔
⊗↔αi\noindent $\bullet $ α⊗↔αβ⊗↓
αXDEFINE C1⊗↔
αxf -o-α\$\circ$⊗↔αβ⊗↓
αXDEFINE CHO1⊗↔
αxf I choos⊗↔αi\han1{αs\αi{\it αdαdαs\}}⊗↔αi⊗↔\yskip⊗↔⊗↔αβ⊗↓
αXDEFINE CHO2⊗↔
αxf I choos⊗↔αi\yskip⊗↔⊗↔α⊗↔αzcho1⊗↔αβ⊗↓
αXDEFINE CHOO⊗↔
αxf I choose firstα\αi⊗↔\yskip⊗↔⊗↔\han1{αs\αdαdαi{\it αs\}}⊗↔αi⊗↔\yskip⊗↔
⊗↔αβ⊗↓
αXDEFINE F1⊗↔
α2αpαxf ⊗⊗α\\⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1B⊗↔
α2αpαxf \*α\\0⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F1C⊗↔
α2αpαxf λλα\\hh⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2⊗↔
αxf 0``α\0''⊗↔α2αp⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2C⊗↔
α2αpαxf \0'α\\1'⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2D⊗↔
α2αpαxf \0"α\\1"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2E⊗↔
α2αpαxf \6"α\\6``⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2F⊗↔
α2αpαxf λα\$\lambda $⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2G⊗↔
α2αpαxf )``α\)"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F2H⊗↔
α2αp⊗↔αxf ,``α\,"⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3⊗↔
αxf \0.α\\1.⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE F3B⊗↔
α2αpαxf \0,α\\1,⊗↔α9α9α9α\⊗↔αβ\⊗↔αβ⊗↓
αXDEFINE F4⊗↔
αxf ↓_α\{\it ⊗↔αxf _↓α\}⊗↔αβ⊗↓
αXDEFINE F5⊗↔
α2αp⊗↔α9α9αz f4⊗↔αβ⊗↓
αXDEFINE H1⊗↔
αi\han1{α⊗=}α⊗↔αi\par α⊗↔⊗↔αβ⊗↓
αXDEFINE H3⊗↔
αi\han3{α⊗=}⊗↔αβ⊗↓
αXDEFINE H3B⊗↔
⊗↔αihan3{{⊗↑αs:α α αi{\it α⊗=⊗↑}}⊗↔αβ⊗↓
αXDEFINE H4⊗↔
αdαdαdαdαdαd⊗↔β\βhβaβnβ3β{β{β\β6αk αs:α α β{β\βiβtβ α⊗=⊗↑}}}⊗↔αβ⊗↓
αXDEFINE H5⊗↔
αzh3⊗↔αβ⊗↓
αXDEFINE H8⊗↔
αk<αi\han3{\it α α α αs⊗ααdαi$α α α α α α αi$α α⊗=⊗↑}}⊗↔αβ⊗↓
αXDEFINE N1⊗↔
αxf n α\{⊗↑ {\it n} ⊗↔αβ⊗↓
αXDEFINE S1⊗↔
α2αp\αs({α⊗=⊗↑}⊗↔⊗↔αxf .SSEC(α\\SSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S2⊗↔
α2αp⊗↔αxf .SSSEC(α\\SSSEC{⊗↔⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S3⊗↔
α2αpαxf . SSSEC(α\ \SSSEC{⊗↔α9α9α9α\⊗↔αβ⊗↓
αXDEFINE S4⊗↔
α⊗=⊗↑}⊗↔αp⊗↔⊗↑αβ⊗↓
αXDEFINE S5⊗↔
α2αpα9α9αzs4⊗↔αβ⊗↓
αXDEFINE S6⊗↔
α2αpαxf .assecp(α\\ASSECP{⊗↔α9α9α\⊗↔αβ⊗↓
αXDEFINE S7⊗↔
α2αpαxf .assec(α\\ASSEC{⊗↔α9α9α\⊗↔αβ⊗↓
αXDEFINE S8⊗↔
α3αpαxf . asssec(α\ \ASSSEC{⊗↔α9α9α\⊗↔αβ⊗↓
αXDEFINE S9⊗↔
α2αpαxf polyaα\P\'olya⊗↔α9α9α\⊗↔αβ⊗↓
αXDEFINE SUB⊗↔
αi$↓α αi$α αβ⊗↓
αXDEFINE TOP1⊗↔
αxf The top 3 Cands are:⊗↔αi\yyskip⊗↔⊗↔α⊗↔⊗↔αi\par \han3{α⊗=}⊗↔αi\par \h
an3{α⊗=}⊗↔αi\par \han3{α⊗=}⊗↔αβ⊗↓
αXDEFINE USED1⊗↔
αxf This Cand used⊗↔αi\yskip⊗↔⊗↔α⊗↔⊗↔αβ⊗↓
αXDEFINE ⊗↔
⊗↔αβ⊗↓