(maxima.info)Functions and Variables for ratpow

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78.1 Functions and Variables for ratpow
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 -- Function: ratp_hipow (<expr>, <x>)

     Finds the highest power of the main variable in 'ratnumer(expr)'

          (%i1) load("ratpow")$
          (%i2) ratp_hipow( x^(5/2) + x^2 , x);
          (%o2)                           2
          (%i3) ratp_hipow( x^(5/2) + x^2 , sqrt(x));
          (%o3)                           5

 -- Function: ratp_lopow (<expr>, <x>)

     Finds the lowest power of the main variable in 'ratnumer(expr)'

          (%i1) load("ratpow")$
          (%i2) ratp_lopow( x^5 + x^2 , x);
          (%o2)                           2

     The following example will return 0 since '1' equals 'x^0':
          (%i1) load("ratpow")$
          (%i2) ratp_lopow( x^5 + x^2 + 1, x);
          (%o2)                           0

     The CRE form of the following equation contains 'sqrt(x)' and 'x'.
     Since they are interpreted as independent variables 'ratp_lopow'
     returns '0' in this case:
          (%i1) load("ratpow")$
          (%i2) g:sqrt(x)^5 + sqrt(x)^2;
                                       5/2
          (%o2)                       x    + x
          (%i3) showratvars(g);
                                        1/2
          (%o3)                       [x   , x]
          (%i4) ratp_lopow( g, x);
          (%o4)                           0
          (%i5) ratp_lopow( g, sqrt(x));
          (%o5)                           0

 -- Function: ratp_coeffs (<expr>, <x>)

     Generates a list of powers and coefficients of the main variable
     'ratnumer(expr)'.
          (%i1) load("ratpow")$
          (%i2) ratp_coeffs( 4*x^3 + x + sqrt(x), x);
          (%o2)/R/         [[3, 4], [1, 1], [0, sqrt(x)]]

 -- Function: ratp_dense_coeffs (<expr>, <x>)

     Generates a list of coefficients in 'ratnumer(expr)'; returned
     coefficients are in CRE form except for numbers.

          (%i1) load("ratpow")$
          (%i2) ratp_dense_coeffs( 4*x^3 + x + sqrt(x), x);
          (%o2)/R/               [4, 0, 1, sqrt(x)]