81.1 Functions and Variables for ratpow

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

‘Category: Rational expressions’ ‘Category: Package ratpow’

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

‘Category: Rational expressions’ ‘Category: Package ratpow’

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)]]

‘Category: Rational expressions’ ‘Category: Package ratpow’

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)]

‘Category: Rational expressions’ ‘Category: Package ratpow’