Wed Jan 31 09:02:26 2024

polynomial_resultant_test():
  Python version: 3.8.10
  Test polynomial_resultant().

polynomial_resultant_roots_test():
  polynomial_resultant_roots() computes 
  the resultant R of polynomials P and Q
  based on knowledge of the roots of P and Q.

P(x):
  p(x) =   1
Q(x):
  p(x) =   2
   R (tabulated):    1
   R (calculated):   1.0

P(x):
  p(x) =   3 * x + 3
Q(x):
  p(x) =   1 * x^2 + 2 * x + 1
   R (tabulated):    0
   R (calculated):   0.0

P(x):
  p(x) =   1 * x^3 + 3 * x^2 + 3 * x + 1
Q(x):
  p(x) =   1 * x^2 - 1
   R (tabulated):    0
   R (calculated):   -0j

P(x):
  p(x) =   1 * x^3 + 2 * x^2 + 3 * x + 4
Q(x):
  p(x) =   5 * x^2 + 6 * x + 7
   R (tabulated):    832
   R (calculated):   (832-0j)

P(x):
  p(x) =   1 * x^3 + 2 * x^2 + 3 * x + 4
Q(x):
  p(x) =   4 * x^3 + 3 * x^2 + 2 * x + 1
   R (tabulated):    -2000
   R (calculated):   (-2000+0j)

P(x):
  p(x) =   1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x
Q(x):
  p(x) =   1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x + 1
   R (tabulated):    1
   R (calculated):   (1+0j)

P(x):
  p(x) =   1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x
Q(x):
  p(x) =   1 * x^7 - 12 * x^6 + 60 * x^5 - 160 * x^4 + 240 * x^3 - 192 * x^2 + 64 * x
   R (tabulated):    0
   R (calculated):   0j

polynomial_resultant_sylvester_test():
  polynomial_resultant_sylvester() computes 
  the resultant R of polynomials P and Q
  based on the determinant of the Sylvester matrix.

P(x):
  p(x) =   1
Q(x):
  p(x) =   2
   R (tabulated):    1
   R (calculated):   1.0

P(x):
  p(x) =   3 * x + 3
Q(x):
  p(x) =   1 * x^2 + 2 * x + 1
   R (tabulated):    0
   R (calculated):   0.0

P(x):
  p(x) =   1 * x^3 + 3 * x^2 + 3 * x + 1
Q(x):
  p(x) =   1 * x^2 - 1
   R (tabulated):    0
   R (calculated):   0.0

P(x):
  p(x) =   1 * x^3 + 2 * x^2 + 3 * x + 4
Q(x):
  p(x) =   5 * x^2 + 6 * x + 7
   R (tabulated):    832
   R (calculated):   832.0

P(x):
  p(x) =   1 * x^3 + 2 * x^2 + 3 * x + 4
Q(x):
  p(x) =   4 * x^3 + 3 * x^2 + 2 * x + 1
   R (tabulated):    -2000
   R (calculated):   -1999.9999999999998

P(x):
  p(x) =   1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x
Q(x):
  p(x) =   1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x + 1
   R (tabulated):    1
   R (calculated):   1.000000000000017

P(x):
  p(x) =   1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x
Q(x):
  p(x) =   1 * x^7 - 12 * x^6 + 60 * x^5 - 160 * x^4 + 240 * x^3 - 192 * x^2 + 64 * x
   R (tabulated):    0
   R (calculated):   0.0

polynomial_resultant_test()
  Normal end of execution.
Wed Jan 31 09:02:27 2024