Python软件包，用于将大系数多项式相乘

Question

I want to multiply multiply polynomials with large coefficients in python. I tried this in numpy.

import numpy as np
p = np.poly1d([1])
for i in range(250):
    p = np.polymul(p, [1, 2])
print ("P : ", p)

But suprisingly, numpy is giving wrong results! Ideally the program should expand the polynomial (x+2)^250 and output it. But it outputs the following.

P :     250       249             248             247             246
1 x   + 500 x   + 1.245e+05 x   + 2.058e+07 x   + 2.542e+09 x  
              245             244             243             242
 + 2.501e+11 x   + 2.043e+13 x   + 1.424e+15 x   + 8.652e+16 x  
              241             240            239             238
 + 4.653e+18 x   + 2.901e+18 x   + 9.18e+18 x   + 9.015e+18 x  
              237             236             235             234
 - 7.634e+18 x   - 1.988e+17 x   - 8.716e+18 x   + 6.834e+18 x  
              233             232            231            230
 - 3.933e+18 x   + 2.712e+18 x   + 6.03e+18 x   - 4.58e+18 x  
              229             228             227             226
 + 7.714e+18 x   - 5.435e+18 x   + 3.734e+18 x   + 4.537e+18 x  
              225             224             223            222
 - 6.507e+18 x   - 1.937e+18 x   + 6.602e+17 x   + 2.61e+18 x  
              221             220             219             218
 - 3.935e+18 x   + 8.436e+18 x   + 6.076e+18 x   - 5.604e+18 x  
              217             216             215             214
 + 2.542e+18 x   + 3.146e+18 x   + 3.515e+18 x   - 3.458e+16 x  
              213             212             211             210
 - 5.884e+18 x   + 5.881e+18 x   - 3.702e+18 x   + 6.049e+17 x  
              209            208             207             206
 - 9.101e+18 x   - 5.37e+18 x   - 8.623e+18 x   + 5.234e+18 x  
              205             204             203             202
 + 4.466e+18 x   + 8.528e+18 x   - 5.645e+18 x   + 6.822e+18 x  
              201             200             199             198
 + 2.037e+18 x   - 2.809e+18 x   + 5.819e+18 x   + 2.675e+18 x  
              197             196             195             194
 + 7.458e+18 x   + 5.224e+18 x   + 2.018e+18 x   - 9.007e+18 x  
              193             192
 - 1.441e+18 x   - 2.594e+18 x  

There seems to be some precision issues with the function. Is there any library in python that is suitable for multiplying polynomials with large coefficients?

Answer 1

Sympy would be a good bet. Doing this in sympy would look something like:

import sympy
x = sympy.var('x')
p = (x+2)**250
p = sympy.expand(p)
print(p)

I have not included the output as it is quite long, but spot checking it looks correct. Sympy uses arbitrary precision libraries, so all coefficients are expanded out. You can get individual coefficients by using the coeff method. Eg:

>> p.coeff(x**249)
250