连分式因子分解程序，如何修改

wsc810

1. d = 1241445153765162090376032461564730757085137334450817128010073; \
   
2. pell = -1; P[0] = 0; Q[0] = 1;
   
3. t[0] = (P[0] + Sqrt[d])/Q[0]
   
4. a[0] = IntegerPart[t[0]];
   
5. i = 0; While[
   
6. i <= 100 && (t[i] != 1/(t[0] - a[0]) && P[i] != pell) || i == 1,
   
7. P[i + 1] = Q[i] a[i] - P[i];
   
8. Q[i + 1] = (d - P[i + 1]^2)/Q[i];
   
9. t[i + 1] = (P[i + 1] + Sqrt[d])/Q[i + 1];
   
10. a[i + 1] = Floor[t[i + 1]];
    
11. p[-1] = 0; p[0] = 1; p[i + 1] = a[i] p[i] + p[i - 1];
    
12. q[-1] = 1; q[0] = 0; q[i + 1] = a[i] q[i] + q[i - 1];
    
13. If[Q[i + 1] == Q[i] || P[i + 1] == P[i] ||
    
14.    FractionalPart[Sqrt[Q[i + 1]]] == 0, Break[]];
    
15. Print[{i, Q[i], P[i], a[i]}] i++];
    
16. {i, Q[i], P[i], a[i]}
    
17. {i + 1, Q[i + 1], P[i + 1], a[i + 1]}
    
18. GCD[Q[0] p[i + 1] - P[0] q[i + 1] + Sqrt[Q[i + 1] Q[0]], d]
    

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怎样将以上代码修改为动态计算，即不保存中间的运算过程，直接输出最后计算结果

wsc810

参考代码

1. Clear[test, x, a, f, t]
   
2. d = 4993; pell = 65; p = 1; q = 2;
   
3. x[p_, q_] := (p + Sqrt[d])/q;
   
4. a[p_, q_] := IntegerPart[x[p, q]];
   
5. t = 1/(x[p, q] - a[p, q]);
   
6. f[{_, {i_, p_, q_}}] := {{i, p, q}, {i + 1, q a[p, q] - p, (d - (q a[p, q] - p)^2)/q}}
   
7. test[{_, {i_, p_, q_}}] := (x[p, q] != t && p != pell) || i == 1
   
8. First@NestWhile[f, {Null, {0, p, q}}, test] // AbsoluteTiming
   

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wsc810

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