Mathematics of MOS: Difference between revisions

Line 81:

'''nextfarey''' := proc(q, n)

# next in row n of Farey sequence from q, 0 <= q <= 1

local a, b, r, s;

if q >= (n-1)/n then RETURN(1) fi;

a := numer(q);

b := denom(q);

Line 91:

'''prevfarey''' := proc(q, n)

# previous in row n of Farey sequence from q, 0 <= q <= 1

local a, b, r, s;

if q=0 then RETURN(0) fi;

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# expansion of a convergent list to semiconvergents

local i, j, s, d;

if nops(l)<3 then RETURN(l) fi;

d[1] := l[1];

d[2] := l[2];

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if u[2]=1 then RETURN(1/(u[1]+1)) fi;

r := igcd(u[1], u[2]);

if r>1 then RETURN(medi([u[1]/r, u[2]/r])) fi;

q := '''penult'''(u[1]/u[2]);

if q > u[1]/u[2] then RETURN((numer(q)+denom(q))/(u[1]+u[2])) fi;

(u[1]+u[2]-numer(q)-denom(q))/(u[1]+u[2]) end:

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w := n/denom(q);

u := '''fareypair'''(q);

if g<u[1] or g>u[2] or g=q then RETURN('false') fi;

if g<q then RETURN([w*denom(u[1]), w*denom(u[2])]) fi;

[w*denom(u[2]), w*denom(u[1])] end:

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n := round(2^w * y);

i :=0;

while n>0 do

i := i+1;

if modp(n,2)=0 then

@@ Line 81: / Line 81: @@
   '''nextfarey''' := proc(q, n)
-  # next in row n of Farey sequence from q, 0 <= q <= 1
+  # next in row n of Farey sequence from q, 0 &lt;= q &lt;= 1
   local a, b, r, s;
-  if q >= (n-1)/n then RETURN(1) fi;
+  if q &gt;= (n-1)/n then RETURN(1) fi;
   a := numer(q);
   b := denom(q);
@@ Line 91: / Line 91: @@
   '''prevfarey''' := proc(q, n)
-  # previous in row n of Farey sequence from q, 0 <= q <= 1
+  # previous in row n of Farey sequence from q, 0 &lt;= q &lt;= 1
   local a, b, r, s;
   if q=0 then RETURN(0) fi;
@@ Line 120: / Line 120: @@
   # expansion of a convergent list to semiconvergents
   local i, j, s, d;
-  if nops(l)<3 then RETURN(l) fi;
+  if nops(l)&lt;3 then RETURN(l) fi;
   d[1] := l[1];
   d[2] := l[2];
@@ Line 155: / Line 155: @@
   if u[2]=1 then RETURN(1/(u[1]+1)) fi;
   r := igcd(u[1], u[2]);
-  if r>1 then RETURN(medi([u[1]/r, u[2]/r])) fi;
+  if r&gt;1 then RETURN(medi([u[1]/r, u[2]/r])) fi;
   q := '''penult'''(u[1]/u[2]);
-  if q > u[1]/u[2] then RETURN((numer(q)+denom(q))/(u[1]+u[2])) fi;
+  if q &gt; u[1]/u[2] then RETURN((numer(q)+denom(q))/(u[1]+u[2])) fi;
   (u[1]+u[2]-numer(q)-denom(q))/(u[1]+u[2]) end:
@@ Line 166: / Line 166: @@
   w := n/denom(q);
   u := '''fareypair'''(q);
-  if g<u[1] or g>u[2] or g=q then RETURN('false') fi;
+  if g&lt;u[1] or g&gt;u[2] or g=q then RETURN('false') fi;
-  if g<q then RETURN([w*denom(u[1]), w*denom(u[2])]) fi;
+  if g&lt;q then RETURN([w*denom(u[1]), w*denom(u[2])]) fi;
   [w*denom(u[2]), w*denom(u[1])] end:
@@ Line 214: / Line 214: @@
   n := round(2^w * y);
   i :=0;
-  while n>0 do
+  while n&gt;0 do
   i := i+1;
   if modp(n,2)=0 then