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SandBoxChoose

Edit detail for SandBoxChoose revision 3 of 6

	1 2 3 4 5 6
Editor: Bill page Time: 2014/09/25 16:08:18 GMT+0
Note:

added:
\begin{equation}
\left( {\begin{array}{*{20}c} 
S \\ 
k \\ 
\end{array}} \right) 
\end{equation}


changed:
-choose(a,n) ==
-  j:=[i for i in 1..n]
-  r:=[[a(j(i)) for i in 1..n]]
-  k:=n
-  while k>0 and j(k)+n-k<#a repeat
-    j(k):=j(k)+1
-    for i in k..n-1 repeat j(i+1):=j(i)+1
-    r:=concat(r,[a(j(i)) for i in 1..n])
-    k:=n; while j(k)+n-k>=#a and k>1 repeat k:=k-1
-  if binomial(#a,n)~=#r then error "error in choose"
-  return r
choose(S,k) ==
  j:=[i for i in 1..k]
  R:=[[S(j(i)) for i in 1..k]]
  n:=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

added:

\begin{equation}
\left( {\begin{array}{*{20}c} 
\{r_1,r_2,r_4 \} \\ 
2 \\ 
\end{array}} \right) = \{ \{r_1,r_2 \} \{r_1,r_4 \} \{r_2,r_4 \} \}
\end{equation}

\begin{axiom}
choose([r[q] for q in 1..4|q~=3],2)
\end{axiom}

\begin{equation}
\left( {\begin{array}{*{20}c} 
\{r_1,r_2,r_4 \} \\ 
2 \\ 
\end{array}} \right)_2 = \{r_1,r_4 \}
\end{equation}

\begin{axiom}
choose([r[q] for q in 1..4|q~=3],2).2
\end{axiom}

added:

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

(1)

fricas

choose(S,k) ==
  j:=[i for i in 1..k]
  R:=[[S(j(i)) for i in 1..k]]
  n:=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

Type: Void

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

(2)

fricas

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

fricas

Compiling function choose with type (List(Symbol),PositiveInteger)
       -> List(List(Symbol))

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

(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)

fricas

Compiling function choose with type (List(PositiveInteger),
      PositiveInteger) -> List(List(PositiveInteger))

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