SymPy学习之Elementary

sympy.functions.elementary.complexes

re

#返回复数实数部分>>> from sympy import re, im, I, E>>> from sympy.abc import x, y>>> re(2*E)2*E>>> re(2*I + 17)17>>> re(2*I)0>>> re(im(x) + x*I + 2)2#as_real_imag(deep=True, **hints)#Returns the real number with a zero imaginary part.

im

#返回复数的虚数部分>>> from sympy import re, im, E, I>>> from sympy.abc import x, y>>> im(2*E)0>>> re(2*I + 17)17>>> im(x*I)re(x)>>> im(re(x) + y)im(y)#as_real_imag(deep=True, **hints)#Return the imaginary part with a zero real part.>>> from sympy.functions import im>>> from sympy import I>>> im(2 + 3*I).as_real_imag()(3, 0)

sign

>>> from sympy.functions import sign>>> from sympy.core.numbers import I#实数时，正返回1,0返回0，负返回-1>>> sign(-1)-1>>> sign(0)0#纯虚数时，正返回I，负返回-I>>> sign(-3*I)-I#复数返回原式>>> sign(1 + I)sign(1 + I)#evalf方法返回cos(arg(expr)) + I*sin(arg(expr)).#即将原式化为单位长度向量>>> _.evalf()0.707106781186548 + 0.707106781186548*I

Abs

#返回绝对值>>> from sympy import Abs, Symbol, S>>> Abs(-1)1>>> x = Symbol('x', real=True)>>> Abs(-x)Abs(x)>>> Abs(x**2)x**2>>> abs(-x) # The Python built-in 传入符号变量自动转换成AbsAbs(x)

arg

#返回参数角度，实数总是0，纯虚数总是pi/2>>> from sympy.functions import arg>>> from sympy import I, sqrt>>> arg(2.0)0>>> arg(I)pi/2>>> arg(sqrt(2) + I*sqrt(2))pi/4

conjugate

#返回共轭数>>> from sympy import conjugate, I>>> conjugate(2)2>>> conjugate(I)-I

sympy.functions.elementary.trigonometric

sin

#返回正弦值>>> from sympy import sin, pi>>> from sympy.abc import x>>> sin(x**2).diff(x)2*x*cos(x**2)>>> sin(1).diff(x)0>>> sin(pi)0>>> sin(pi/2)1>>> sin(pi/6)1/2>>> sin(pi/12)-sqrt(2)/4 + sqrt(6)/4

cos

#返回余弦值>>> from sympy import cos, pi>>> from sympy.abc import x>>> cos(x**2).diff(x)-2*x*sin(x**2)>>> cos(1).diff(x)0>>> cos(pi)-1>>> cos(pi/2)0>>> cos(2*pi/3)-1/2>>> cos(pi/12)sqrt(2)/4 + sqrt(6)/4

tan

#返回正切值>>> from sympy import tan, pi>>> from sympy.abc import x>>> tan(x**2).diff(x)2*x*(tan(x**2)**2 + 1)>>> tan(1).diff(x)0>>> tan(pi/8).expand()-1 + sqrt(2)

cot

#返回余切值>>> from sympy import cot, pi>>> from sympy.abc import x>>> cot(x**2).diff(x)2*x*(-cot(x**2)**2 - 1)>>> cot(1).diff(x)0>>> cot(pi/12)sqrt(3) + 2

sec

#返回正割值>>> from sympy import sec>>> from sympy.abc import x>>> sec(x**2).diff(x)2*x*tan(x**2)*sec(x**2)>>> sec(1).diff(x)0

csc

#返回余割值>>> from sympy import csc>>> from sympy.abc import x>>> csc(x**2).diff(x)-2*x*cot(x**2)*csc(x**2)>>> csc(1).diff(x)0

sinc

#辛格函数 sinc(x) = sin(x)/x>>> sinc(0)1>>> sinc(oo)0

asin

#反正弦函数>>> from sympy import asin, oo, pi>>> asin(1)pi/2>>> asin(-1)-pi/2

acos

#反余弦函数>>> from sympy import acos, oo, pi>>> acos(1)0>>> acos(0)pi/2>>> acos(oo)oo*I

atan

#反正切函数>>> from sympy import atan, oo, pi>>> atan(0)0>>> atan(1)pi/4>>> atan(oo)pi/2

acot

#反余切函数>>> acot(0)pi/2>>> acot(1)pi/4>>> acot(oo)0

asec

#反正割函数>>> from sympy import asec, oo, pi>>> asec(1)0>>> asec(-1)pi

acsc

#反余割函数>>> from sympy import acsc, oo, pi>>> acsc(1)pi/2>>> acsc(-1)-pi/2

sympy.functions.elementary.integers

ceiling

#返回大于给定值的最小整值>>> from sympy import ceiling, E, I, Float, Rational>>> ceiling(17)17>>> ceiling(Rational(23, 10))3>>> ceiling(2*E)6>>> ceiling(-Float(0.567))0>>> ceiling(I/2)I

floor

#返回小于给定值的最大整值>>> from sympy import floor, E, I, Float, Rational>>> floor(17)17>>> floor(Rational(23, 10))2>>> floor(2*E)5>>> floor(-Float(0.567))-1>>> floor(-I/2)-I

round

#返回四舍五入值>>> round(5.5)6>>> round(5.4)5

frac

#取小数部分>>> from sympy import Symbol, frac, Rational, floor, ceiling, I>>> frac(Rational(4, 3))1/3>>> frac(-Rational(4, 3))2/3

sympy.functions.elementary.exponential

exp

#指数函数>>> from sympy import I>>> from sympy.abc import x>>> from sympy.functions import exp>>> exp(x).as_real_imag()(exp(re(x))*cos(im(x)), exp(re(x))*sin(im(x)))>>> exp(1).as_real_imag()(E, 0)>>> exp(I).as_real_imag()(cos(1), sin(1))>>> exp(1+I).as_real_imag()(E*cos(1), E*sin(1))>>> exp(3).baseE

log

#对数函数>>> from sympy import I>>> from sympy.abc import x>>> from sympy.functions import log>>> log(x).as_real_imag()(log(Abs(x)), arg(x))>>> log(I).as_real_imag()(0, pi/2)>>> log(1 + I).as_real_imag()(log(sqrt(2)), pi/4)>>> log(I*x).as_real_imag()(log(Abs(x)), arg(I*x))

sympy.functions.elementary.piecewise

Piecewise

#分段函数>>> from sympy import Piecewise, log>>> from sympy.abc import x>>> f = x**2>>> g = log(x)>>> p = Piecewise( (0, x<-1), (f, x<=1), (g, True))>>> p.subs(x,1)1>>> p.subs(x,5)log(5)#重新构成一个分段函数>>> from sympy import Piecewise, piecewise_fold, sympify as S>>> from sympy.abc import x>>> p = Piecewise((x, x < 1), (1, S(1) <= x))>>> piecewise_fold(x*p)Piecewise((x**2, x < 1), (x, 1 <= x))

sympy.functions.elementary.miscellaneous

Min

#返回最小值>>> from sympy import Min, Symbol, oo>>> from sympy.abc import x, y>>> p = Symbol('p', positive=True)>>> n = Symbol('n', negative=True)>>> Min(x, -2) Min(x, -2)>>> Min(x, -2).subs(x, 3)-2>>> Min(p, -3)-3>>> Min(x, y) Min(x, y)>>> Min(n, 8, p, -7, p, oo) Min(n, -7)

Max

#返回最大值>>> from sympy import Max, Symbol, oo>>> from sympy.abc import x, y>>> p = Symbol('p', positive=True)>>> n = Symbol('n', negative=True)>>> Max(x, -2) Max(x, -2)>>> Max(x, -2).subs(x, 3)3>>> Max(p, -2)p>>> Max(x, y) Max(x, y)>>> Max(x, y) == Max(y, x)True>>> Max(x, Max(y, z)) Max(x, y, z)>>> Max(n, 8, p, 7, -oo) Max(8, p)>>> Max (1, x, oo)oo

root

#开n次方根>>> from sympy import root, Rational>>> from sympy.abc import x, n>>> root(x, 2)sqrt(x)>>> root(x, 3)x**(1/3)Run code block in SymPy Live>>> root(x, n)x**(1/n)>>> root(x, -Rational(2, 3))x**(-3/2)

sqrt

#开根号>>> from sympy import sqrt, Symbol>>> x = Symbol('x')>>> sqrt(x)sqrt(x)>>> sqrt(x)**2x