This script computes the formal series expansion of a mathematical function on the command line using the python module swiginac, an interface to the CAS Ginac. Typical invocation in a linux terminal looks like $ serexp.py -n 7 "log(1+x)*(1+x+x**2)**(-1)" 1*x+(-3/2)*x**2+5/6*x**3+5/12*x**4+(-21/20)*x**5+7/15*x**6+Order(x**7) As far as I know, swiginac does not work in windows, so use a virtual (k)ubuntu machine in this case. |
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Hello, I have used taylor polynomials to approximate floating-point values before. I am wondering whether there is a way to still apply them to functions with complex arguments, and if there is a way what its constraints would be. For example, to calculate the sine of a floating-point number to a specific precision I keep adding terms until the error value is less than the precision. However, I noticed (by testing it with the taylor expansion of ln(x) ) that this gives the wrong value when I use complex numbers (with the standard operators appropriately defined). For example: ln(0.5)~=-(0.5+(0.5^2)/2+(0.5^3)/3) --- … |
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