Python符号计算之实现函数极限的方法
人气:0SymPy是符号数学的Python库。它的目标是成为一个全功能的计算机代数系统,同时保持代码简洁、易于理解和扩展
#coding:utf-8 ''' 函数极限 ''' import sympy sympy.init_printing() from sympy import I, pi, oo import numpy as np x = sympy.Symbol('x') expr = sympy.sin(x) / x result = sympy.limit(expr,x,0) print('limit:',result) f = sympy.Function('f') x, h = sympy.symbols("x, h") diff_limit = (f(x + h) - f(x))/h result = sympy.limit(diff_limit.subs(f, sympy.cos), h, 0) print('limit:',result) result = sympy.limit(diff_limit.subs(f, sympy.sin), h, 0) print('limit:',result) expr = (x**2 - 3*x) / (2*x - 2) p = sympy.limit(expr/x, x, sympy.oo) q = sympy.limit(expr - p*x, x, sympy.oo) print('result:p,q = ',p,q) # 求和 n = sympy.symbols("n", integer=True) s = sympy.Sum(1/(n**2), (n, 1, oo)) print('sum:',s) print('sum:',s.doit()) # 求积 p = sympy.Product(n, (n, 1, 7)) print('product:',p) print('product:',p.doit()) expr = sympy.Sum((x)**n/(sympy.factorial(n)), (n, 1, oo)).doit().simplify() print('expr:',expr)
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