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74 lines
1.2 KiB
Plaintext
74 lines
1.2 KiB
Plaintext
/*
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* Copyright (c) 1995 David I. Bell
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* Permission is granted to use, distribute, or modify this source,
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* provided that this copyright notice remains intact.
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*
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* Solve Pell's equation; Returns the solution X to: X^2 - D * Y^2 = 1.
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* Type the solution to pells equation for a particular D.
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*/
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define pell(D)
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{
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local X, Y;
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X = pellx(D);
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if (isnull(X)) {
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print "D=":D:" is square";
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return;
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}
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Y = isqrt((X^2 - 1) / D);
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print X : "^2 - " : D : "*" : Y : "^2 = " : X^2 - D*Y^2;
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}
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/*
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* Function to solve Pell's equation
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* Returns the solution X to:
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* X^2 - D * Y^2 = 1
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*/
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define pellx(D)
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{
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local R, Rp, U, Up, V, Vp, A, T, Q1, Q2, n;
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local mat ans[2,2];
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local mat tmp[2,2];
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R = isqrt(D);
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Vp = D - R^2;
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if (Vp == 0)
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return;
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Rp = R + R;
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U = Rp;
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Up = U;
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V = 1;
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A = 0;
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n = 0;
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ans[0,0] = 1;
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ans[1,1] = 1;
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tmp[0,1] = 1;
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tmp[1,0] = 1;
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do {
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T = V;
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V = A * (Up - U) + Vp;
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Vp = T;
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A = U // V;
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Up = U;
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U = Rp - U % V;
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tmp[0,0] = A;
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ans *= tmp;
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n++;
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} while (A != Rp);
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Q2 = ans[[1]];
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Q1 = isqrt(Q2^2 * D + 1);
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if (isodd(n)) {
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T = Q1^2 + D * Q2^2;
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Q2 = Q1 * Q2 * 2;
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Q1 = T;
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}
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return Q1;
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}
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if (config("lib_debug") >= 0) {
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print "pell(D) defined";
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print "pellx(D) defined";
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}
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