MathAction SandBoxChoose

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$\label{eq1} \left( {\begin{array}{<em>{20}c} S \ k \ \end{array}} \right)$

spad

)abbrev package CHOO Choose
Choose(X:SetCategory): with
    choose:(List X,NonNegativeInteger) -> List List X
  == add
    choose(S,k) ==
      j:List NonNegativeInteger := [i for i in 1..k]
      R:List List X := [[S(j(i)) for i in 1..k]]
      n:Integer := k
      while n>0 and j(n)+k-n<#S repeat
        j(n):=j(n)+1
        for i in n..k-1 repeat j(i+1):=j(i)+1
        R:=concat(R,[S(j(i)) for i in 1..k])
        n:=k; while j(n)+k-n>=#S and n>1 repeat n:=n-1
      if binomial(#S,k)~=#R then error "error in choose"
      return R

spad

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5705694974207640903-25px001.spad
      using old system compiler.
   CHOO abbreviates package Choose 
------------------------------------------------------------------------
   initializing NRLIB CHOO for Choose 
   compiling into NRLIB CHOO 
   compiling exported choose : (List X,NonNegativeInteger) -> List List X
Time: 0.05 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |Choose| REDEFINED

;;;     ***       |Choose| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor Choose
      Time: 0.05 seconds

   finalizing NRLIB CHOO 
   Processing Choose for Browser database:
--->-->Choose(constructor): Not documented!!!!
--->-->Choose((choose ((List (List X)) (List X) (NonNegativeInteger)))): Not documented!!!!
--->-->Choose(): Missing Description
; compiling file "/var/aw/var/LatexWiki/CHOO.NRLIB/CHOO.lsp" (written 04 APR 2022 07:55:38 PM):

; /var/aw/var/LatexWiki/CHOO.NRLIB/CHOO.fasl written
; compilation finished in 0:00:00.027
------------------------------------------------------------------------
   Choose is now explicitly exposed in frame initial 
   Choose will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/CHOO.NRLIB/CHOO

$\label{eq2} \left( {\begin{array}{<em>{20}c} \{r_1,r_2,r_4 \} \ 2 \ \end{array}} \right) = \{ \{r_1,r_2 \} \{r_1,r_4 \} \{r_2,r_4 \} \}$

(2)

fricas

choose([r[q] for q in 1..4|q~=3],2)

$\label{eq3}\left[{\left[{r_{1}}, \:{r_{2}}\right]}, \:{\left[{r_{1}}, \:{r_{4}}\right]}, \:{\left[{r_{2}}, \:{r_{4}}\right]}\right]$

(3)

Type: List(List(Symbol))

$\label{eq4} \left( {\begin{array}{<em>{20}c} \{r_1,r_2,r_4 \} \ 2 \ \end{array}} \right)_2 = \{r_1,r_4 \}$

(4)

fricas

choose([r[q] for q in 1..4|q~=3],2).2

$\label{eq5}\left[{r_{1}}, \:{r_{4}}\right]$

(5)

Type: List(Symbol)

fricas

choose([1],1)

$\label{eq6}\left[{\left[ 1 \right]}\right]$