Maxima collecting specific terms in an expression

Question

I have an expression that actually can be expressed in simple form by collecting the specific terms. I have problem in Maxima to substitute or simplify the expression to the known terms.

(%i1) expr:(16*h^2*v_0^2+(38*h*u_0-38*h*u_1)*v_0+25*u_1^2-50*u_0*u_1+25*u_0^2)/3;


                                            2    2                                     2                      2

                                        16 h  v_0  + (38 h u_0 - 38 h u_1) v_0 + 25 u_1  - 50 u_0 u_1 + 25 u_0

(%o1)                                   -----------------------------------------------------------------------

                                                                           3

(%i2) eq1:a1=-h*v_0+2*u_1-2*u_0;
eq2:a2=-2*(h*v_0-u_1+u_0);


(%o2)                                                       a1 = (- h v_0) + 2 u_1 - 2 u_0

(%i3) 

(%o3)                                                        a2 = - 2 (h v_0 - u_1 + u_0)

(%i4) subst([eq1,eq2],expr);


                                            2    2                                     2                      2

                                        16 h  v_0  + (38 h u_0 - 38 h u_1) v_0 + 25 u_1  - 50 u_0 u_1 + 25 u_0

(%o4)                                   -----------------------------------------------------------------------

                                                                           3

What I want is something like this

expr=c1*(a1)^q1 + c2*(a2)^q2

where c1,c2,q1,q2 are the constant that would generated by simplifying expr using known term a1,a2. How to do that? Is there any specific syntax?

score 0 · Answer 1 · answered Apr 22 '23 at 14:44

Can it be that it is ratsubst what you want?

(%i31) rat(ratsubst(lhs(eq1), rhs(eq1), expr), a1);
               2                                  2                      2
          16 a1  + (- 26 u_1 + 26 u_0) a1 + 13 u_1  - 26 u_0 u_1 + 13 u_0
(%o31)/R/ ----------------------------------------------------------------
                                         3
(%i32) rat(ratsubst(lhs(eq2), rhs(eq2), expr), a2);
               2                             2                    2
           4 a2  + (3 u_1 - 3 u_0) a2 + 3 u_1  - 6 u_0 u_1 + 3 u_0
(%o32)/R/  --------------------------------------------------------
                                      3

ratsubst(to, from, e) susbstitutes from to to while "rewriting" e to fit from. Note that subst is only able to substitute literallly, it cannot transform your expression. In my example above I also use rat with the second argument a1 or a2 so that it expresses both the numerator and the denominator as polynomials in a1 or a2.

Maxima collecting specific terms in an expression

1 Answers1