Help:=proc(): print(`InBoard(pt,m,n), WMove(m,n,P) `): 
print(`KingNeis(pt), PathRook(pt1,pt2)`):
end:


#InBoard(pt,m,n):
InBoard:=proc(pt,m,n) local i,j:
i:=pt[1]: j:=pt[2]:

evalb(1<=i and i<=m and 1<=j and j<=n):

end:


KingNeis:=proc(pt) local i,j:
option remember:
i:=pt[1]: j:=pt[2]:
{[i+1,j],[i-1,j],[i,j+1],[i,j-1],[i+1,j-1],[i-1,j+1],
   [i+1,j+1],[i-1,j-1]}:
end:

#Inputs a position P (a triple [WK,WR,BK])
#where WK are the coordinaes of the White King
# BK are the coordinates of the Black King
#WR are the coordinates of the White Rook
#in an m by n chess-board [i,j], 1<=i<=m , 1<=j<=n
WMove:=proc(m,n,P) local WK,BK,WR,i,j,Neis,pt,eh,ES,i1:
WK:=P[1]: WR:=P[2]: BK:=P[3]:

#WK=[i,j]

i:=WK[1]: j:=WK[2]:

Neis:={[i+1,j],[i-1,j],[i,j+1],[i,j-1],[i+1,j-1],[i-1,j+1],
   [i+1,j+1],[i-1,j-1]} minus KingNeis(BK):

eh:={}:
for pt in Neis do
 if InBoard(pt,m,n)  and pt<>WR then
  eh:=eh union {[pt,WR,BK]}:
 fi:
od:

i:=WR[1]: j:=WR[2]:


Neis:=
{seq([i1,j],i1=1..m), seq([i,j1],j1=1..n)} minus {WR}:

    



  for pt in Neis do
 if InBoard(pt,m,n)  and pt<>WK then
  eh:=eh union {[pt,WR,BK]}:
 fi:
od:   
     





end:


#PathRook(pt1,pt2): all the points visited in the
#rook's move from pt1 to pt2
PathRook:=proc(pt1,pt2) local i1,j1:

if pt1[1]<>pt2[1] and pt1[2]<>pt2[2] then
 ERROR(`Rook can't go from `, pt1, `to `, pt2, `in one move`):
fi:

if pt1[1]=pt2[1] then
  RETURN({seq([pt1[1],j1],j1=min(pt1[2],pt2[2])+1..
                            max(pt1[2],pt2[2])-1)}):
else
RETURN({seq([i1,pt1[2]],i1=min(pt1[1],pt2[1])+1..
                            max(pt1[1],pt2[1])-1)}):


fi:



end: