"use math";"use strict"; function assert(actual, expected, message) {    if (arguments.length == 1)        expected = true;     if (actual === expected)        return;     if (actual !== null && expected !== null    &&  typeof actual == 'object' && typeof expected == 'object'    &&  actual.toString() === expected.toString())        return;     throw Error("assertion failed: got |" + actual + "|" +                ", expected |" + expected + "|" +                (message ? " (" + message + ")" : ""));} function assertThrows(err, func){    var ex;    ex = false;    try {        func();    } catch(e) {        ex = true;        assert(e instanceof err);    }    assert(ex, true, "exception expected");} // load more elaborate version of assert if availabletry { __loadScript("test_assert.js"); } catch(e) {} /*----------------*/ function pow(a, n){    var r, i;    r = 1;    for(i = 0; i < n; i++)        r *= a;    return r;} function test_integer(){    var a, r;    a = pow(3, 100);    assert((a - 1) != a);    assert(a == 515377520732011331036461129765621272702107522001);    assert(a == 0x5a4653ca673768565b41f775d6947d55cf3813d1);    assert(Integer.isInteger(1) === true);    assert(Integer.isInteger(1.0) === false);     assert(Integer.floorLog2(0) === -1);    assert(Integer.floorLog2(7) === 2);     r = 1 << 31;    assert(r, 2147483648, "1 << 31 === 2147483648");        r = 1 << 32;    assert(r, 4294967296, "1 << 32 === 4294967296");        r = (1 << 31) < 0;    assert(r, false, "(1 << 31) < 0 === false");     assert(typeof 1 === "number");    assert(typeof 9007199254740991 === "number");    assert(typeof 9007199254740992 === "bigint");} function test_float(){    assert(typeof 1.0 === "bigfloat");    assert(1 == 1.0);    assert(1 !== 1.0);} /* jscalc tests */ function test_modulo(){    var i, p, a, b;     /* Euclidian modulo operator */    assert((-3) % 2 == 1);    assert(3 % (-2) == 1);     p = 101;    for(i = 1; i < p; i++) {        a = Integer.invmod(i, p);        assert(a >= 0 && a < p);        assert((i * a) % p == 1);    }     assert(Integer.isPrime(2^107-1));    assert(!Integer.isPrime((2^107-1) * (2^89-1)));    a = Integer.factor((2^89-1)*2^3*11*13^2*1009);    assert(a == [ 2,2,2,11,13,13,1009,618970019642690137449562111 ]);} function test_fraction(){    assert((1/3 + 1).toString(), "4/3")    assert((2/3)^30, 1073741824/205891132094649);    assert(1/3 < 2/3);    assert(1/3 < 1);    assert(1/3 == 1.0/3);    assert(1.0/3 < 2/3);} function test_mod(){    var a, b, p;        a = Mod(3, 101);    b = Mod(-1, 101);    assert((a + b) == Mod(2, 101));    assert(a ^ 100 == Mod(1, 101));     p = 2 ^ 607 - 1; /* mersenne prime */    a = Mod(3, p) ^ (p - 1);    assert(a == Mod(1, p));} function test_polynomial(){    var a, b, q, r, t, i;    a = (1 + X) ^ 4;    assert(a == X^4+4*X^3+6*X^2+4*X+1);        r = (1 + X);    q = (1+X+X^2);    b = (1 - X^2);    a = q * b + r;    t = Polynomial.divrem(a, b);    assert(t[0] == q);    assert(t[1] == r);     a = 1 + 2*X + 3*X^2;    assert(a.apply(0.1) == 1.23);     a = 1-2*X^2+2*X^3;    assert(deriv(a) == (6*X^2-4*X));    assert(deriv(integ(a)) == a);     a = (X-1)*(X-2)*(X-3)*(X-4)*(X-0.1);    r = polroots(a);    for(i = 0; i < r.length; i++) {        b = abs(a.apply(r[i]));        assert(b <= 1e-13);    }} function test_poly_mod(){    var a, p;     /* modulo using polynomials */    p = X^2 + X + 1;    a = PolyMod(3+X, p) ^ 10;    assert(a == PolyMod(-3725*X-18357, p));     a = PolyMod(1/X, 1+X^2);    assert(a == PolyMod(-X, X^2+1));} function test_rfunc(){    var a;    a = (X+1)/((X+1)*(X-1));    assert(a == 1/(X-1));    a = (X + 2) / (X - 2);    assert(a.apply(1/3) == -7/5);     assert(deriv((X^2-X+1)/(X-1)) == (X^2-2*X)/(X^2-2*X+1));} function test_series(){    var a, b;    a = 1+X+O(X^5);    b = a.inverse();    assert(b == 1-X+X^2-X^3+X^4+O(X^5));    assert(deriv(b) == -1+2*X-3*X^2+4*X^3+O(X^4));    assert(deriv(integ(b)) == b);     a = Series(1/(1-X), 5);    assert(a == 1+X+X^2+X^3+X^4+O(X^5));    b = a.apply(0.1);    assert(b == 1.1111);     assert(exp(3*X^2+O(X^10)) == 1+3*X^2+9/2*X^4+9/2*X^6+27/8*X^8+O(X^10));    assert(sin(X+O(X^6)) == X-1/6*X^3+1/120*X^5+O(X^6));    assert(cos(X+O(X^6)) == 1-1/2*X^2+1/24*X^4+O(X^6));    assert(tan(X+O(X^8)) == X+1/3*X^3+2/15*X^5+17/315*X^7+O(X^8));        assert((1+X+O(X^6))^(2+X) == 1+2*X+2*X^2+3/2*X^3+5/6*X^4+5/12*X^5+O(X^6));} function test_matrix(){    var a, b, r;    a = [[1, 2],[3, 4]];    b = [3, 4];    r = a * b;    assert(r == [11, 25]);    r = (a^-1) * 2;    assert(r == [[-4, 2],[3, -1]]);     assert(norm2([1,2,3]) == 14);     assert(diag([1,2,3]) == [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 3 ] ]);    assert(trans(a) == [ [ 1, 3 ], [ 2, 4 ] ]);    assert(trans([1,2,3]) == [[1,2,3]]);    assert(trace(a) == 5);     assert(charpoly(Matrix.hilbert(4)) == X^4-176/105*X^3+3341/12600*X^2-41/23625*X+1/6048000);    assert(det(Matrix.hilbert(4)) == 1/6048000);     a = [[1,2,1],[-2,-3,1],[3,5,0]];    assert(rank(a) == 2);    assert(ker(a) == [ [ 5 ], [ -3 ], [ 1 ] ]);     assert(dp([1, 2, 3], [3, -4, -7]) === -26);    assert(cp([1, 2, 3], [3, -4, -7]) == [ -2, 16, -10 ]);} function assert_eq(a, ref){    assert(abs(a / ref - 1.0) <= 1e-15);} function test_trig(){    assert_eq(sin(1/2), 0.479425538604203);    assert_eq(sin(2+3*I), 9.154499146911428-4.168906959966565*I);    assert_eq(cos(2+3*I), -4.189625690968807-9.109227893755337*I);    assert_eq((2+0.5*I)^(1.1-0.5*I), 2.494363021357619-0.23076804554558092*I);    assert_eq(sqrt(2*I), 1 + I);} test_integer();test_float(); test_modulo();test_fraction();test_mod();test_polynomial();test_poly_mod();test_rfunc();test_series();test_matrix();test_trig();