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Python numberfields.minimal_polynomial函数代码示例

原作者: [db:作者] 来自: [db:来源] 收藏 邀请

本文整理汇总了Python中sympy.polys.numberfields.minimal_polynomial函数的典型用法代码示例。如果您正苦于以下问题：Python minimal_polynomial函数的具体用法？Python minimal_polynomial怎么用？Python minimal_polynomial使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。



在下文中一共展示了minimal_polynomial函数的12个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。

示例1: test_minpoly_domain

def test_minpoly_domain():
    assert minimal_polynomial(sqrt(2), x, domain=QQ.algebraic_field(sqrt(2))) == \
        x - sqrt(2)
    assert minimal_polynomial(sqrt(8), x, domain=QQ.algebraic_field(sqrt(2))) == \
        x - 2*sqrt(2)
    assert minimal_polynomial(sqrt(Rational(3,2)), x,
        domain=QQ.algebraic_field(sqrt(2))) == 2*x**2 - 3

    raises(NotAlgebraic, lambda: minimal_polynomial(y, x, domain=QQ))
开发者ID:A-turing-machine，项目名称:sympy，代码行数:9，代码来源:test_numberfields.py


示例2: test_minimal_polynomial_sq

def test_minimal_polynomial_sq():
    from sympy import Add, expand_multinomial
    p = expand_multinomial((1 + 5*sqrt(2) + 2*sqrt(3))**3)
    mp = minimal_polynomial(p**Rational(1, 3), x)
    assert mp == x**4 - 4*x**3 - 118*x**2 + 244*x + 1321
    p = expand_multinomial((1 + sqrt(2) - 2*sqrt(3) + sqrt(7))**3)
    mp = minimal_polynomial(p**Rational(1, 3), x)
    assert mp == x**8 - 8*x**7 - 56*x**6 + 448*x**5 + 480*x**4 - 5056*x**3 + 1984*x**2 + 7424*x - 3008
    p = Add(*[sqrt(i) for i in range(1, 12)])
    mp = minimal_polynomial(p, x)
    assert mp.subs({x: 0}) == -71965773323122507776
开发者ID:A-turing-machine，项目名称:sympy，代码行数:11，代码来源:test_numberfields.py


示例3: test_minpoly_issue_7113

def test_minpoly_issue_7113():
    # see discussion in https://github.com/sympy/sympy/pull/2234
    from sympy.simplify.simplify import nsimplify
    r = nsimplify(pi, tolerance=0.000000001)
    mp = minimal_polynomial(r, x)
    assert mp == 1768292677839237920489538677417507171630859375*x**109 - \
    2734577732179183863586489182929671773182898498218854181690460140337930774573792597743853652058046464
开发者ID:A-turing-machine，项目名称:sympy，代码行数:7，代码来源:test_numberfields.py


示例4: test_minimal_polynomial_hi_prec

def test_minimal_polynomial_hi_prec():
    p = 1 / sqrt(1 - 9 * sqrt(2) + 7 * sqrt(3) + S(1) / 10 ** 30)
    mp = minimal_polynomial(p, x)
    # checked with Wolfram Alpha
    assert (
        mp.coeff(x ** 6)
        == -1232000000000000000000000000001223999999999999999999999999999987999999999999999999999999999996000000000000000000000000000000
    )
开发者ID:smichr，项目名称:sympy，代码行数:8，代码来源:test_numberfields.py


示例5: test_minpoly_compose1

def test_minpoly_compose1():
    skip("This test hangs.")
    # this test hangs because factor_list hangs in minpoly_op_algebraic_number
    # on a polynomial of degree 96, which is factored by Sage very fast;
    # one of the factors is the minimal polynomial.
    ex = sqrt(1 + 2**Rational(1,3)) + sqrt(1 + 2**Rational(1,4)) + sqrt(2)
    mp = minimal_polynomial(ex, x)
    assert degree(mp) == 48 and mp.subs({x:0}) == -16630256576
开发者ID:batya239，项目名称:sympy，代码行数:8，代码来源:test_numberfields.py


示例6: test_minpoly_fraction_field_slow

def test_minpoly_fraction_field_slow():
    assert minimal_polynomial(minimal_polynomial(sqrt(x**Rational(1,5) - 1),
        y).subs(y, sqrt(x**Rational(1,5) - 1)), z) == z
开发者ID:A-turing-machine，项目名称:sympy，代码行数:3，代码来源:test_numberfields.py


示例7: test_minpoly_fraction_field

def test_minpoly_fraction_field():
    assert minimal_polynomial(1/x, y) == -x*y + 1
    assert minimal_polynomial(1 / (x + 1), y) == (x + 1)*y - 1

    assert minimal_polynomial(sqrt(x), y) == y**2 - x
    assert minimal_polynomial(sqrt(x + 1), y) == y**2 - x - 1
    assert minimal_polynomial(sqrt(x) / x, y) == x*y**2 - 1
    assert minimal_polynomial(sqrt(2) * sqrt(x), y) == y**2 - 2 * x
    assert minimal_polynomial(sqrt(2) + sqrt(x), y) == \
        y**4 + (-2*x - 4)*y**2 + x**2 - 4*x + 4

    assert minimal_polynomial(x**Rational(1,3), y) == y**3 - x
    assert minimal_polynomial(x**Rational(1,3) + sqrt(x), y) == \
        y**6 - 3*x*y**4 - 2*x*y**3 + 3*x**2*y**2 - 6*x**2*y - x**3 + x**2

    assert minimal_polynomial(sqrt(x) / z, y) == z**2*y**2 - x
    assert minimal_polynomial(sqrt(x) / (z + 1), y) == (z**2 + 2*z + 1)*y**2 - x

    assert minimal_polynomial(1/x, y, polys=True) == Poly(-x*y + 1, y)
    assert minimal_polynomial(1 / (x + 1), y, polys=True) == \
        Poly((x + 1)*y - 1, y)
    assert minimal_polynomial(sqrt(x), y, polys=True) == Poly(y**2 - x, y)
    assert minimal_polynomial(sqrt(x) / z, y, polys=True) == \
        Poly(z**2*y**2 - x, y)

    # this is (sqrt(1 + x**3)/x).integrate(x).diff(x) - sqrt(1 + x**3)/x
    a = sqrt(x)/sqrt(1 + x**(-3)) - sqrt(x**3 + 1)/x + 1/(x**(S(5)/2)* \
        (1 + x**(-3))**(S(3)/2)) + 1/(x**(S(11)/2)*(1 + x**(-3))**(S(3)/2))

    assert minimal_polynomial(a, y) == y

    raises(NotAlgebraic, lambda: minimal_polynomial(exp(x), y))
    raises(GeneratorsError, lambda: minimal_polynomial(sqrt(x), x))
    raises(GeneratorsError, lambda: minimal_polynomial(sqrt(x) - y, x))
    raises(NotImplementedError, lambda: minimal_polynomial(sqrt(x), y, compose=False))
开发者ID:A-turing-machine，项目名称:sympy，代码行数:35，代码来源:test_numberfields.py


示例8: test_minimal_polynomial

def test_minimal_polynomial():
    assert minimal_polynomial(-7, x) == x + 7
    assert minimal_polynomial(-1, x) == x + 1
    assert minimal_polynomial( 0, x) == x
    assert minimal_polynomial( 1, x) == x - 1
    assert minimal_polynomial( 7, x) == x - 7

    assert minimal_polynomial(sqrt(2), x) == x**2 - 2
    assert minimal_polynomial(sqrt(5), x) == x**2 - 5
    assert minimal_polynomial(sqrt(6), x) == x**2 - 6

    assert minimal_polynomial(2*sqrt(2), x) == x**2 - 8
    assert minimal_polynomial(3*sqrt(5), x) == x**2 - 45
    assert minimal_polynomial(4*sqrt(6), x) == x**2 - 96

    assert minimal_polynomial(2*sqrt(2) + 3, x) == x**2 - 6*x + 1
    assert minimal_polynomial(3*sqrt(5) + 6, x) == x**2 - 12*x - 9
    assert minimal_polynomial(4*sqrt(6) + 7, x) == x**2 - 14*x - 47

    assert minimal_polynomial(2*sqrt(2) - 3, x) == x**2 + 6*x + 1
    assert minimal_polynomial(3*sqrt(5) - 6, x) == x**2 + 12*x - 9
    assert minimal_polynomial(4*sqrt(6) - 7, x) == x**2 + 14*x - 47

    assert minimal_polynomial(sqrt(1 + sqrt(6)), x) == x**4 - 2*x**2 - 5
    assert minimal_polynomial(sqrt(I + sqrt(6)), x) == x**8 - 10*x**4 + 49

    assert minimal_polynomial(2*I + sqrt(2 + I), x) == x**4 + 4*x**2 + 8*x + 37

    assert minimal_polynomial(sqrt(2) + sqrt(3), x) == x**4 - 10*x**2 + 1
    assert minimal_polynomial(
        sqrt(2) + sqrt(3) + sqrt(6), x) == x**4 - 22*x**2 - 48*x - 23

    a = 1 - 9*sqrt(2) + 7*sqrt(3)

    assert minimal_polynomial(
        1/a, x) == 392*x**4 - 1232*x**3 + 612*x**2 + 4*x - 1
    assert minimal_polynomial(
        1/sqrt(a), x) == 392*x**8 - 1232*x**6 + 612*x**4 + 4*x**2 - 1

    raises(NotAlgebraic, lambda: minimal_polynomial(oo, x))
    raises(NotAlgebraic, lambda: minimal_polynomial(2**y, x))
    raises(NotAlgebraic, lambda: minimal_polynomial(sin(1), x))

    assert minimal_polynomial(sqrt(2)).dummy_eq(x**2 - 2)
    assert minimal_polynomial(sqrt(2), x) == x**2 - 2

    assert minimal_polynomial(sqrt(2), polys=True) == Poly(x**2 - 2)
    assert minimal_polynomial(sqrt(2), x, polys=True) == Poly(x**2 - 2)
    assert minimal_polynomial(sqrt(2), x, polys=True, compose=False) == Poly(x**2 - 2)

    a = AlgebraicNumber(sqrt(2))
    b = AlgebraicNumber(sqrt(3))

    assert minimal_polynomial(a, x) == x**2 - 2
    assert minimal_polynomial(b, x) == x**2 - 3

    assert minimal_polynomial(a, x, polys=True) == Poly(x**2 - 2)
    assert minimal_polynomial(b, x, polys=True) == Poly(x**2 - 3)

    assert minimal_polynomial(sqrt(a/2 + 17), x) == 2*x**4 - 68*x**2 + 577
    assert minimal_polynomial(sqrt(b/2 + 17), x) == 4*x**4 - 136*x**2 + 1153

    a, b = sqrt(2)/3 + 7, AlgebraicNumber(sqrt(2)/3 + 7)

    f = 81*x**8 - 2268*x**6 - 4536*x**5 + 22644*x**4 + 63216*x**3 - \
        31608*x**2 - 189648*x + 141358

    assert minimal_polynomial(sqrt(a) + sqrt(sqrt(a)), x) == f
    assert minimal_polynomial(sqrt(b) + sqrt(sqrt(b)), x) == f

    assert minimal_polynomial(
        a**Q(3, 2), x) == 729*x**4 - 506898*x**2 + 84604519

    # issue 5994
    eq = S('''
        -1/(800*sqrt(-1/240 + 1/(18000*(-1/17280000 +
        sqrt(15)*I/28800000)**(1/3)) + 2*(-1/17280000 +
        sqrt(15)*I/28800000)**(1/3)))''')
    assert minimal_polynomial(eq, x) == 8000*x**2 - 1

    ex = 1 + sqrt(2) + sqrt(3)
    mp = minimal_polynomial(ex, x)
    assert mp == x**4 - 4*x**3 - 4*x**2 + 16*x - 8

    ex = 1/(1 + sqrt(2) + sqrt(3))
    mp = minimal_polynomial(ex, x)
    assert mp == 8*x**4 - 16*x**3 + 4*x**2 + 4*x - 1

    p = (expand((1 + sqrt(2) - 2*sqrt(3) + sqrt(7))**3))**Rational(1, 3)
    mp = minimal_polynomial(p, x)
    assert mp == x**8 - 8*x**7 - 56*x**6 + 448*x**5 + 480*x**4 - 5056*x**3 + 1984*x**2 + 7424*x - 3008
    p = expand((1 + sqrt(2) - 2*sqrt(3) + sqrt(7))**3)
    mp = minimal_polynomial(p, x)
    assert mp == x**8 - 512*x**7 - 118208*x**6 + 31131136*x**5 + 647362560*x**4 - 56026611712*x**3 + 116994310144*x**2 + 404854931456*x - 27216576512

    assert minimal_polynomial(S("-sqrt(5)/2 - 1/2 + (-sqrt(5)/2 - 1/2)**2"), x) == x - 1
    a = 1 + sqrt(2)
    assert minimal_polynomial((a*sqrt(2) + a)**3, x) == x**2 - 198*x + 1

    p = 1/(1 + sqrt(2) + sqrt(3))
#.........这里部分代码省略.........
开发者ID:A-turing-machine，项目名称:sympy，代码行数:101，代码来源:test_numberfields.py


示例9: test_minpoly_issue_7574

def test_minpoly_issue_7574():
    ex = -(-1)**Rational(1, 3) + (-1)**Rational(2,3)
    assert minimal_polynomial(ex, x) == x + 1
开发者ID:A-turing-machine，项目名称:sympy，代码行数:3，代码来源:test_numberfields.py


示例10: test_minpoly_compose

def test_minpoly_compose():
    # issue 6868
    eq = S('''
        -1/(800*sqrt(-1/240 + 1/(18000*(-1/17280000 +
        sqrt(15)*I/28800000)**(1/3)) + 2*(-1/17280000 +
        sqrt(15)*I/28800000)**(1/3)))''')
    mp = minimal_polynomial(eq + 3, x)
    assert mp == 8000*x**2 - 48000*x + 71999

    # issue 5888
    assert minimal_polynomial(exp(I*pi/8), x) == x**8 + 1

    mp = minimal_polynomial(sin(pi/7) + sqrt(2), x)
    assert mp == 4096*x**12 - 63488*x**10 + 351488*x**8 - 826496*x**6 + \
        770912*x**4 - 268432*x**2 + 28561
    mp = minimal_polynomial(cos(pi/7) + sqrt(2), x)
    assert mp == 64*x**6 - 64*x**5 - 432*x**4 + 304*x**3 + 712*x**2 - \
            232*x - 239
    mp = minimal_polynomial(exp(I*pi/7) + sqrt(2), x)
    assert mp == x**12 - 2*x**11 - 9*x**10 + 16*x**9 + 43*x**8 - 70*x**7 - 97*x**6 + 126*x**5 + 211*x**4 - 212*x**3 - 37*x**2 + 142*x + 127

    mp = minimal_polynomial(sin(pi/7) + sqrt(2), x)
    assert mp == 4096*x**12 - 63488*x**10 + 351488*x**8 - 826496*x**6 + \
        770912*x**4 - 268432*x**2 + 28561
    mp = minimal_polynomial(cos(pi/7) + sqrt(2), x)
    assert mp == 64*x**6 - 64*x**5 - 432*x**4 + 304*x**3 + 712*x**2 - \
            232*x - 239
    mp = minimal_polynomial(exp(I*pi/7) + sqrt(2), x)
    assert mp == x**12 - 2*x**11 - 9*x**10 + 16*x**9 + 43*x**8 - 70*x**7 - 97*x**6 + 126*x**5 + 211*x**4 - 212*x**3 - 37*x**2 + 142*x + 127

    mp = minimal_polynomial(exp(2*I*pi/7), x)
    assert mp == x**6 + x**5 + x**4 + x**3 + x**2 + x + 1
    mp = minimal_polynomial(exp(2*I*pi/15), x)
    assert mp == x**8 - x**7 + x**5 - x**4 + x**3 - x + 1
    mp = minimal_polynomial(cos(2*pi/7), x)
    assert mp == 8*x**3 + 4*x**2 - 4*x - 1
    mp = minimal_polynomial(sin(2*pi/7), x)
    ex = (5*cos(2*pi/7) - 7)/(9*cos(pi/7) - 5*cos(3*pi/7))
    mp = minimal_polynomial(ex, x)
    assert mp == x**3 + 2*x**2 - x - 1
    assert minimal_polynomial(-1/(2*cos(pi/7)), x) == x**3 + 2*x**2 - x - 1
    assert minimal_polynomial(sin(2*pi/15), x) == \
            256*x**8 - 448*x**6 + 224*x**4 - 32*x**2 + 1
    assert minimal_polynomial(sin(5*pi/14), x) == 8*x**3 - 4*x**2 - 4*x + 1
    assert minimal_polynomial(cos(pi/15), x) == 16*x**4 + 8*x**3 - 16*x**2 - 8*x + 1

    ex = rootof(x**3 +x*4 + 1, 0)
    mp = minimal_polynomial(ex, x)
    assert mp == x**3 + 4*x + 1
    mp = minimal_polynomial(ex + 1, x)
    assert mp == x**3 - 3*x**2 + 7*x - 4
    assert minimal_polynomial(exp(I*pi/3), x) == x**2 - x + 1
    assert minimal_polynomial(exp(I*pi/4), x) == x**4 + 1
    assert minimal_polynomial(exp(I*pi/6), x) == x**4 - x**2 + 1
    assert minimal_polynomial(exp(I*pi/9), x) == x**6 - x**3 + 1
    assert minimal_polynomial(exp(I*pi/10), x) == x**8 - x**6 + x**4 - x**2 + 1
    assert minimal_polynomial(sin(pi/9), x) == 64*x**6 - 96*x**4 + 36*x**2 - 3
    assert minimal_polynomial(sin(pi/11), x) == 1024*x**10 - 2816*x**8 + \
            2816*x**6 - 1232*x**4 + 220*x**2 - 11

    ex = 2**Rational(1, 3)*exp(Rational(2, 3)*I*pi)
    assert minimal_polynomial(ex, x) == x**3 - 2

    raises(NotAlgebraic, lambda: minimal_polynomial(cos(pi*sqrt(2)), x))
    raises(NotAlgebraic, lambda: minimal_polynomial(sin(pi*sqrt(2)), x))
    raises(NotAlgebraic, lambda: minimal_polynomial(exp(I*pi*sqrt(2)), x))

    # issue 5934
    ex = 1/(-36000 - 7200*sqrt(5) + (12*sqrt(10)*sqrt(sqrt(5) + 5) +
        24*sqrt(10)*sqrt(-sqrt(5) + 5))**2) + 1
    raises(ZeroDivisionError, lambda: minimal_polynomial(ex, x))

    ex = sqrt(1 + 2**Rational(1,3)) + sqrt(1 + 2**Rational(1,4)) + sqrt(2)
    mp = minimal_polynomial(ex, x)
    assert degree(mp) == 48 and mp.subs({x:0}) == -16630256576
开发者ID:A-turing-machine，项目名称:sympy，代码行数:75，代码来源:test_numberfields.py


示例11: test_minimal_polynomial

def test_minimal_polynomial():
    assert minimal_polynomial(-7, x) == x + 7
    assert minimal_polynomial(-1, x) == x + 1
    assert minimal_polynomial( 0, x) == x
    assert minimal_polynomial( 1, x) == x - 1
    assert minimal_polynomial( 7, x) == x - 7

    assert minimal_polynomial(sqrt(2), x) == x**2 - 2
    assert minimal_polynomial(sqrt(5), x) == x**2 - 5
    assert minimal_polynomial(sqrt(6), x) == x**2 - 6

    assert minimal_polynomial(2*sqrt(2), x) == x**2 - 8
    assert minimal_polynomial(3*sqrt(5), x) == x**2 - 45
    assert minimal_polynomial(4*sqrt(6), x) == x**2 - 96

    assert minimal_polynomial(2*sqrt(2) + 3, x) == x**2 -  6*x +  1
    assert minimal_polynomial(3*sqrt(5) + 6, x) == x**2 - 12*x -  9
    assert minimal_polynomial(4*sqrt(6) + 7, x) == x**2 - 14*x - 47

    assert minimal_polynomial(2*sqrt(2) - 3, x) == x**2 +  6*x +  1
    assert minimal_polynomial(3*sqrt(5) - 6, x) == x**2 + 12*x -  9
    assert minimal_polynomial(4*sqrt(6) - 7, x) == x**2 + 14*x - 47

    assert minimal_polynomial(sqrt(1 + sqrt(6)), x) == x**4 -  2*x**2 -  5
    assert minimal_polynomial(sqrt(I + sqrt(6)), x) == x**8 - 10*x**4 + 49

    assert minimal_polynomial(2*I + sqrt(2 + I), x) == x**4 + 4*x**2 + 8*x + 37

    assert minimal_polynomial(sqrt(2) + sqrt(3), x) == x**4 - 10*x**2 + 1
    assert minimal_polynomial(sqrt(2) + sqrt(3) + sqrt(6), x) == x**4 - 22*x**2 - 48*x - 23

    a = 1 - 9*sqrt(2) + 7*sqrt(3)

    assert minimal_polynomial(1/a, x) == 392*x**4 - 1232*x**3 + 612*x**2 + 4*x - 1
    assert minimal_polynomial(1/sqrt(a), x) == 392*x**8 - 1232*x**6 + 612*x**4 + 4*x**2 - 1

    raises(NotAlgebraic, "minimal_polynomial(y, x)")
    raises(NotAlgebraic, "minimal_polynomial(oo, x)")
    raises(NotAlgebraic, "minimal_polynomial(2**y, x)")
    raises(NotAlgebraic, "minimal_polynomial(sin(1), x)")

    assert minimal_polynomial(sqrt(2)).dummy_eq(x**2 - 2)
    assert minimal_polynomial(sqrt(2), x) == x**2 - 2

    assert minimal_polynomial(sqrt(2), polys=True) == Poly(x**2 - 2)
    assert minimal_polynomial(sqrt(2), x, polys=True) == Poly(x**2 - 2)

    a = AlgebraicNumber(sqrt(2))
    b = AlgebraicNumber(sqrt(3))

    assert minimal_polynomial(a, x) == x**2 - 2
    assert minimal_polynomial(b, x) == x**2 - 3

    assert minimal_polynomial(a, x, polys=True) == Poly(x**2 - 2)
    assert minimal_polynomial(b, x, polys=True) == Poly(x**2 - 3)

    assert minimal_polynomial(sqrt(a/2 + 17), x) == 2*x**4 -  68*x**2 +  577
    assert minimal_polynomial(sqrt(b/2 + 17), x) == 4*x**4 - 136*x**2 + 1153

    a, b = sqrt(2)/3 + 7, AlgebraicNumber(sqrt(2)/3 + 7)

    f = 81*x**8 - 2268*x**6 - 4536*x**5 + 22644*x**4 + 63216*x**3 - 31608*x**2 - 189648*x + 141358

    assert minimal_polynomial(sqrt(a) + sqrt(sqrt(a)), x) == f
    assert minimal_polynomial(sqrt(b) + sqrt(sqrt(b)), x) == f

    assert minimal_polynomial(a**Rational(3, 2), x) == 729*x**4 - 506898*x**2 + 84604519
开发者ID:Jerryy，项目名称:sympy，代码行数:67，代码来源:test_numberfields.py


示例12: test_issue_14831

def test_issue_14831():
    a = -2*sqrt(2)*sqrt(12*sqrt(2) + 17)
    assert minimal_polynomial(a, x) == x**2 + 16*x - 8
    e = (-3*sqrt(12*sqrt(2) + 17) + 12*sqrt(2) +
         17 - 2*sqrt(2)*sqrt(12*sqrt(2) + 17))
    assert minimal_polynomial(e, x) == x
开发者ID:asmeurer，项目名称:sympy，代码行数:6，代码来源:test_numberfields.py



注：本文中的sympy.polys.numberfields.minimal_polynomial函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。

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