Polynomials.wxm

/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 22.04.0 ] */
/* [wxMaxima: input   start ] */
/* Date: Sat Dec 18 23:13:31 WET 2004 */
/* Contributor: Viktor T. Toth */
/* Description: returns a list of the terms of a (univariate) polynomial*/
pargs(x):=if atom(x) or length(x)=0 or op(x)#"+" then x else args(x);
pargs(x):=if atom(x) or length(x)=0 or op(x)#"+" then x else substpart("[",x,0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Sat Apr 14 05:04:30 WEST 2001 */
/* Contributor: Richard Fateman */
/* Description: Function that returns the exponents of the dependent terms of a (univariate) polynomial */
mypowers(r,x):=block(
    [ h:hipow(r,x)],
    if h=0 then [] else cons (h, mypowers(second(bothcoeff(r,x^h)),x))
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Tue Apr 16 22:40:26 WEST 2013 */
/* Contributor: Stavros Macrakis */
/* Description: Returns the coefficients of an univariate polynomial (in this form does not work; it is necessary to put p:rat(p,v) in the list of variables of the block) */
coefs(p,v):=block(
    [l:[]],
    while p # 0 do (
        l:cons(r:ratcoef(p,v,0),l),
        p:(p-r)/v),
    l
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Fri Apr 19 10:10:53 WEST 2013 */
/* Contributor: Wilhelm Haager */
/* Description: Lists the coefficients of a univariate polynomial n ascendin order 
(for the usual order for polynomials put makelist(i,i,n,0,-1) instead of makelist(i,i,0,n) */
coefficient_list(p,s) :=block(
        [n:floor(hipow(p,s))],
        p:expand(p),
        map(lambda([u],coeff(p,s,u)),makelist(i,i,0,n))
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Thu Apr 24 18:28:49 WEST 2008 */
/* Contributor: Andre Maute */
/* Description: Tries to extract the coefficients of a multivariate polynomial */
my_coeff(v,exps,poly) := block(
    [c,k,l,h],
    c : [],
    for k : 1 thru length(exps) do block(
        h : poly,
        for l : 1 thru length(v) do block(
            if exps[k][l] # 0 then block(
                h : coeff(h,v[l],exps[k][l])
            )
        ),
        for l : 1 thru length(v) do block(
            h : subst(0,v[l],h)
        ),
        h : ratsimp(h),
        c : append(c,[h])
    ),
    return(c)
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Thu Apr 24 20:16:34 WEST 2008 */
/* Contributor: Andre Maute */
/* Description: Tries to extract the coefficients of a multivariate polynomial */
my_coeff2(v,exps,poly) := block(
    [c,k,l,h,rpoly],
    rpoly : rat(poly,v),
    c : [],
    for k : 1 thru length(exps) do block(
        h : rpoly,
        for l : 1 thru length(v) do block(
            h : ratcoeff(h,v[l],exps[k][l])
        ),
        c : append(c,[h])
    ),
    return(c)
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Thu Apr 24 20:16:34 WEST 2008 */
/* Contributor: Andre Maute */
/* Description: Tries to extract the coefficients of a multivariate polynomial */
my_coeff3(v,exps,poly) := block(
    [c,k,l,h,rpoly],
    rpoly : rat(poly,v),
    c : [],
    for k : 1 thru length(exps) do block(
        h : rpoly,
        for l : 1 thru length(v) do block(
            h : ratcoeff(h,v[length(v)+1-l],exps[k][length(v)+1-l])
        ),
        c : append(c,[h])
    ),
    return(c)
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Thu Apr 24 20:26:16 WEST 2008 */
/* Contributor: Richard Fateman */
/* Description: Tries to extract the coefficients of a multivariate polynomial */
my_coeff4(v,exps,poly) := block(
    [c:[],k,l,h,rpoly,lv:length(v)],
    rpoly : rat(poly,v),
    for k : 1 thru length(exps) do block(
        h : rpoly,
        for l : 1 thru length(v) do block(
            h : ratcoeff(h,v[lv+1-l],exps[k][lv+1-l])
        ),
        c : cons(h,c)
    ),
    return(reverse(c))
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Thu Apr 24 20:30:43 WEST 2008 */
/* Contributor: Richard Fateman */
/* Description: Tries to extract the coefficients of a multivariate polynomial */
my_coeff5(v,exps,poly) := block(
    [c:[],k,l,h,rpoly,lv:length(v), ratvars:v], /*maybe should be ratvars:reverse[v] ?*/
    rpoly : rat(poly),
    for k : 1 thru length(exps) do block(
        h : rpoly,
        for l : 1 thru lv do block(
            h : ratcoeff(h,v[lv+1-l],exps[k][lv+1-l])
        ),
        c : cons(h,c)
    ),
    return(reverse(c))
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Thu Apr 24 22:01:39 WEST 2008 */
/* Contributor: Andre Maute */
/* Description: Tries to extract the coefficients of a multivariate polynomial */
my_coeff6(v,exps,poly) := block(
    [c,k,l,h],
    c : [],
    for k : 1 thru length(exps) do block(
        h : poly,
        for l : 1 thru length(v) do block(
            h : coeff(h,v[l],exps[k][l])
        ),
        h : ratsimp(h),
        c : append(c,[h])
    ),
    return(c)
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Fri Apr 25 15:29:18 WEST 2008 */
/* Contributor: Richard Fateman */
/* Description: Tries to extract the coefficients of a multivariate polynomial */
my_coeff7(v,exps,poly) := block(
    [c:[],rpoly:rat(poly), ratvars:reverse(v)],
    for k in exps do block(
        [h:rpoly],
        for L in v do block(
            [e: k],
            h : ratcoeff(h,L,first(e)),
            e : rest(e)
        ),
        c : cons(h,c)
    ),
    return(reverse(c))
)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Sat Jan 15 20:23:32 WET 2005 */
/* Contributor: Boris Gaertner */
/* Description: Collects all the terms of a polynomial w.r.t. a variable */
rewriteAsPolynomialIn (p, t) :=block(
    [expanded, degreeInT, result],
    expanded : expand(p),
    degreeInT: hipow(expanded, t),
    result : 0,
    for idx : 0 thru degreeInT do result : result + t^idx*ratcoeff(expanded, t, idx),
    result
);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/* Date: Sun Jan 16 18:46:52 WET 2005 */
/* Contributor: Stavros Macrakis */
/* Description: Collects all the terms of a polynomial w.r.t. a variable */
polyform(expr,var):= ev(ratdisrep(rat(isolate(expr,var),var)),eval);
/* [wxMaxima: input   end   ] */



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