Case of sqrt(11)

Now try another, namely sqrt(11)

>    A:=matrix(2,4,[1,0,1,0,0,1,0,-11]);tvals:=[];

A := matrix([[1, 0, 1, 0], [0, 1, 0, -11]])

tvals := []

>    fun(A)(1,1);

-10

>    seq([t,fun(A)(t,1)],t=1..5);

[1, -10], [2, -7], [3, -2], [4, 5], [5, 14]

>    tvals:=[op(tvals),3];

tvals := [3]

>    A1:=ch(A,3,1);

A1 := matrix([[1, 0, 1, 3], [3, 1, 3, -2]])

>    fun(A1)(1,1);

5

>    seq([t,fun(A1)(1,t)],t=1..5);

[1, 5], [2, 5], [3, 1], [4, -7], [5, -19]

>    tvals:=[op(tvals),3];A2:=ch(A1,3,2);

tvals := [3, 3]

A2 := matrix([[10, 3, 1, -3], [3, 1, -3, -2]])

>    fun(A2)(1,1);

-7

>    seq([t,fun(A2)(t,1)],t=1..8);

[1, -7], [2, -10], [3, -11], [4, -10], [5, -7], [6, -2], [7, 5], [8, 14]

>    tvals:=[op(tvals),6];A3:=ch(A2,6,1);

tvals := [3, 3, 6]

A3 := matrix([[10, 3, 1, 3], [63, 19, 3, -2]])

>    fun(A3)(1,1);

5

>    seq([t,fun(A3)(1,t)],t=1..8);

[1, 5], [2, 5], [3, 1], [4, -7], [5, -19], [6, -35], [7, -55], [8, -79]

>    tvals:=[op(tvals),3];A4:=ch(A3,3,2);

tvals := [3, 3, 6, 3]

A4 := matrix([[199, 60, 1, -3], [63, 19, -3, -2]])

>    seq(cat(A,i)=op(cat(A,i)),i=1..4);tvals;

A1 = matrix([[1, 0, 1, 3], [3, 1, 3, -2]]), A2 = matrix([[10, 3, 1, -3], [3, 1, -3, -2]]), A3 = matrix([[10, 3, 1, 3], [63, 19, 3, -2]]), A4 = matrix([[199, 60, 1, -3], [63, 19, -3, -2]])

[3, 3, 6, 3]

Note that A2 and A4 have the same second part! So, now we repeat!

>    unassign('ans11');convert(sqrt(11),confrac,8,ans11);

[3, 3, 6, 3, 6, 3, 6, 3]

>    ans11;

[3, 10/3, 63/19, 199/60, 1257/379, 3970/1197, 25077/7561, 79201/23880]

>   

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