CODEWITHSUNDEEP
pythonpython-3.xnumpy
user133140
user133140

Reputation: 169

How can I replace x in a polynomial by some other polynomial in Python?

How can I replace x in a polynomial by some other polynomial in Python? For example, I had p = poly1d([1,1,1]), which is x^2+x+1, now I want to replace x by y^2 and get y^4+y^2+1. It's like the composition of two functions.

Upvotes: 1

Views: 1940

Answers (2)

xnx
xnx

Reputation: 25548

You can substitute polynomials into other polynomials in NumPy:

In [2]: p = np.poly1d([1,1,1])    # x^2 + x + 1
In [3]: y2 = np.poly1d([1,0,0])   # x^2
In [4]: p(y2)
Out[4]: poly1d([ 1.,  0.,  1.,  0.,  1.])   # x^4 + x^2 + 1

Upvotes: 4

Ross Ridge
Ross Ridge

Reputation: 39621

You can use numpy.polyval to compose polynomials using NumPy. For example:

import numpy as np

p1 = np.poly1d([1, 1, 1])
print (p1)
p2 = np.poly1d([1, 0, 0], variable = 'y')
print (p2)
p = np.polyval(p1, p2)
p = np.poly1d(p, variable = 'y')
print (p)

will print:

   2
1 x + 1 x + 1
   2
1 y
   4     2
1 y + 1 y + 1

Upvotes: 3

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