Extracting the coefficients of a mixed polynomial

[videohead]

How can I extract the six coefficients a ... f of a mixed polynomial ax^2 + by^2 + cxy + dx + ey + f? Unfortunately, the operator coeff doesn't quite work well for mixed polynomials.

Please advise.

Regards.

[Arthur Norman]

On Mon, 14 Feb 2022, videohead wrote:

How can I extract the six coefficients a ... f of an algebraic expression ax^2 + by^2 + cxy + dx + ey + f? Unfortunately, the operator coeff doesn't quite work well for mixed polynomials.

Please advise.

Regards.

Is this the sort of thing you are looking for? You will still need a bit
more to discard or separate the x and y bits (eg subst(x=1,...))
Arthur

Reduce (CSL, rev 6186), 27-Dec-2021 ...

1: p := ax^2 + by^2 + cxy + dx + ey + f;

    2     2

p := ax + by + cxy + dx + ey + f

2: part(p, 1);

2
ax

3: part(p, 2);

2
by

4: part(p, 3);

cxy

5: part(p, 4);

dx

6: part(p, 6);

f

[Eberhard Schruefer]

Besides Arthur's suggestion, here are two other possibilities:

1: p := a*x^2 + b*y^2 + c*x*y + d*x + e*y + f;

        2      2
p := a*x  + b*y  + c*x*y + d*x + e*y + f

2: for k := 0:2 do for l := 0:2 do write x^k,",",y^l,":    ", coeffn(coeffn(p,x,k),y,l);

1,1:    f

1,y:    e

   2
1,y :    b

x,1:    d

x,y:    c

   2
x,y :    0

 2
x ,1:    a

 2
x ,y:    0

 2  2
x ,y :    0

6: 

There is also the contributed package coeff2 you could use:

1: load coeff2;

2: p := a*x^2 + b*y^2 + c*x*y + d*x + e*y + f;

        2      2
p := a*x  + b*y  + c*x*y + d*x + e*y + f

3: coeff2(p, x, y);

    2                       2
#1*x  + #2*x*y + #3*x + #4*y  + #5*y + #6

4: for k := 1:lisp symcount do write nm k;

a

c

d

b

e

f

5:

Eberhard