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77. ratpow

The package ratpow provides functions that find the exponents of the denominator in a CRE polynomial. If the exponents in the denominator are needed instead ratdenom can be used to extract this denominator first. Returned coefficients are in CRE form except for numbers.

In order to get a list of vars in a CRE polynomial showratvars can be used.

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


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77.1 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

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)]


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