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85 Package ratpow

The package ratpow provides functions that return the coefficients of the numerator of a CRE polynomial in a given variable.

For example,

The returned coefficients are in CRE form except for numbers.

For the list of vars of a CRE polynomial, use showratvars. For the denominator of a CRE polynomial, use ratdenom.

For information about CREs see also rat, ratdisrep and showratvars.


85.1 Functions and Variables for ratpow

Function: ratp_hipow (expr, x)

Returns the highest power of x 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)

Returns the lowest power of x in ratnumer(expr)

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

The following example returns 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:

(%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)

Returns the powers and coefficients of x in ratnumer(expr) as a list of length-2 lists; returned coefficients are in CRE form except for numbers.

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)

Returns the coefficients of powers of x in ratnumer(expr) from highest to lowest; 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)]

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