Note
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This example demonstrates the use of arithmetic manipulations on polynomials.
Arithmetic Operations
Summation of polynomials
Product of polynomials
Integral of polynomials over a single or multiple variables
Derivative of polynomials
Shifting a polynomial to the left or right
Dilating a polynomial
Out:
Defining univariate polynomials (array([1, 3, 5]),), (array([0, 1, 2]),) (array([ 2, -1]),), (array([0, 1]),) ---------------------------------------- Adding two polynomials p1 and p2 (array([ 1., 3., 5., 2., -1.]),), (array([0., 1., 2., 0., 1.]),) Multiply two polynomials p1 and p2 (array([ 2, -1, 6, -3, 10, -5]),), (array([0., 1., 1., 2., 2., 3.]),) Square polynomial p1 (array([ 1, 3, 5, 3, 9, 15, 5, 15, 25]),), (array([0., 1., 2., 1., 2., 3., 2., 3., 4.]),) Shift polynomial p1 (array([27., 23., 5.]),), (array([0, 1, 2]),) Dilation polynomial p1 (array([ 1, -15, 125]),), (array([0, 1, 2]),) Integration polynomial p1 (array([1. , 1.5 , 1.66666667]),), (array([1, 2, 3]),) Differentiation polynomial p1 (array([ 0, 3, 10]),), (array([0, 0, 1]),)
import lmlib as lm print("Defining univariate polynomials") p1 = lm.Poly([1, 3, 5], [0, 1, 2]) p2 = lm.Poly([2, -1], [0, 1]) print(p1) print(p2) print("\n"+"-"*40+"\n") print("Adding two polynomials p1 and p2\n") print(lm.poly_sum((p1, p2)), '\n') print("Multiply two polynomials p1 and p2\n") print(lm.poly_prod((p1, p2)), '\n') print("Square polynomial p1\n") print(lm.poly_square(p1), '\n') print("Shift polynomial p1\n") gamma = 2 print(lm.poly_shift(p1, gamma), '\n') print("Dilation polynomial p1\n") eta = -5 print(lm.poly_dilation(p1, eta), '\n') print("Integration polynomial p1\n") print(lm.poly_int(p1), '\n') print("Differentiation polynomial p1\n") print(lm.poly_diff(p1), '\n')
Total running time of the script: ( 0 minutes 0.044 seconds)
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