08-Jan-2022 08:58:10

polynomial_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test polynomial()

I4_FALL_TEST
  I4_FALL evaluates the falling factorial function.

         M         N      Exact         I4_FALL(M,N)
         5         0             1             1
         5         1             5             5
         5         2            20            20
         5         3            60            60
         5         4           120           120
         5         5           120           120
         5         6             0             0
        50         0             1             1
        10         1            10            10
      4000         1          4000          4000
        10         2            90            90
        18         3          4896          4896
         4         4            24            24
        98         3        912576        912576
         1         7             0             0

POLYNOMIAL_ADD_TEST
  POLYNOMIAL_ADD adds two polynomials.

  P1(X) =
    + 7 * x^(0,0,0)
    - 5 * x^(0,0,1)
    + 9 * x^(1,0,0)
    + 11 * x^(0,0,2)
    + 0 * x^(0,1,2)
    - 13 * x^(3,0,1).

  P2(X) =
    + 2 * x^(0,0,0)
    + 3 * x^(0,1,0)
    - 8 * x^(1,0,0)
    + 4 * x^(2,0,2)
    + 9 * x^(3,0,1).

  P1(X) + P2(X) =
    + 9 * x^(0,0,0)
    - 5 * x^(0,0,1)
    + 3 * x^(0,1,0)
    + 1 * x^(1,0,0)
    + 11 * x^(0,0,2)
    + 4 * x^(2,0,2)
    - 4 * x^(3,0,1).

POLYNOMIAL_AXPY_TEST
  POLYNOMIAL_AXPY adds a multiple of one polynomial
  to another.

  P1(X) =
    + 7 * x^(0,0,0)
    - 5 * x^(0,0,1)
    + 9 * x^(1,0,0)
    + 11 * x^(0,0,2)
    + 0 * x^(0,1,2)
    - 13 * x^(3,0,1).

  P2(X) =
    + 2 * x^(0,0,0)
    + 3 * x^(0,1,0)
    - 8 * x^(1,0,0)
    + 4 * x^(2,0,2)
    + 9 * x^(3,0,1).

  10 * P1(X) + P2(X) = 
    + 72 * x^(0,0,0)
    - 50 * x^(0,0,1)
    + 3 * x^(0,1,0)
    + 82 * x^(1,0,0)
    + 110 * x^(0,0,2)
    + 4 * x^(2,0,2)
    - 121 * x^(3,0,1).

POLYNOMIAL_PRINT_TEST
  POLYNOMIAL_PRINT prints a polynomial.

  Uncompressed P(X) =
    + 7 * x^(0,0,0)
    - 5 * x^(0,0,1)
    + 5 * x^(0,0,1)
    + 9 * x^(1,0,0)
    + 11 * x^(0,0,2)
    + 3 * x^(0,0,2)
    + 6 * x^(0,0,2)
    + 0 * x^(0,1,2)
    - 13 * x^(3,0,1)
    + 1e-20 * x^(4,0,0).

  Compressed P(X) =
    + 7 * x^(0,0,0)
    + 9 * x^(1,0,0)
    + 20 * x^(0,0,2)
    - 13 * x^(3,0,1).

POLYNOMIAL_DIF_TEST
  POLYNOMIAL_DIF computes derivatives of a polynomial.

  P(X) =
    + 2 * x^(0,0)
    + 3 * x^(3,0)
    + 4 * x^(1,3)
    + 5 * x^(3,4).

  d3 P(X) dx1 dx1 dx2 =
    + 120 * x^(1,3).

POLYNOMIAL_MUL_TEST
  POLYNOMIAL_MUL multiplies two polynomials.

  P1(X) =
    + 2 * x^(0,0)
    + 3 * x^(1,0)
    + 4 * x^(0,2)
    + 5 * x^(2,0).

  P2(X) =
    + 6 * x^(0,1)
    + 7 * x^(1,1).

  P1(X) * P2(X) =
    + 12 * x^(0,1)
    + 32 * x^(1,1)
    + 24 * x^(0,3)
    + 51 * x^(2,1)
    + 28 * x^(1,3)
    + 35 * x^(3,1).

POLYNOMIAL_PRINT_TEST
  POLYNOMIAL_PRINT prints a polynomial.

  P1(X) =
    + 7 * x^(0,0,0)
    - 5 * x^(0,0,1)
    + 9 * x^(1,0,0)
    + 11 * x^(0,0,2)
    + 0 * x^(0,1,2)
    - 13 * x^(3,0,1).

POLYNOMIAL_SCALE_TEST
  POLYNOMIAL_SCALE scales a polynomial by a multiplier S.

  P(X) = 
    + 7 * x^(0,0,0)
    - 5 * x^(0,0,1)
    + 9 * x^(1,0,0)
    + 11 * x^(0,0,2)
    + 0 * x^(0,1,2)
    - 13 * x^(3,0,1).

  Apply scale factor S = -0.5

  S * P(X) = 
    - 3.5 * x^(0,0,0)
    + 2.5 * x^(0,0,1)
    - 4.5 * x^(1,0,0)
    - 5.5 * x^(0,0,2)
    + 0 * x^(0,1,2)
    + 6.5 * x^(3,0,1).

POLYNOMIAL_SORT_TEST
  POLYNOMIAL_SORT sorts a polynomial by exponent index.

  Unsorted polynomial:
    + 0 * x^(0,1,2)
    + 9 * x^(1,0,0)
    - 5 * x^(0,0,1)
    - 13 * x^(3,0,1)
    + 7 * x^(0,0,0)
    + 11 * x^(0,0,2).

  Sorted polynomial:
    + 7 * x^(0,0,0)
    - 5 * x^(0,0,1)
    + 9 * x^(1,0,0)
    + 11 * x^(0,0,2)
    + 0 * x^(0,1,2)
    - 13 * x^(3,0,1).

polynomial_value_test():
  polynomial_value() evaluates a polynomial.

  P(X) =
    + 7 * x^(0,0,0)
    - 5 * x^(0,0,1)
    + 9 * x^(1,0,0)
    + 11 * x^(0,0,2)
    + 0 * x^(0,1,2)
    - 13 * x^(3,0,1).
  P(1,2,3) = 61
  P(-2,4,1) = 99

polynomial_test():
  Normal end of execution.

08-Jan-2022 08:58:10