Here is a proc(Mupad) I wrote for showing the steps in completing the
square for a quad
----------------------------------------------------
//Completing the Square Method of solving quadratic equation
quad:= proc(co1,co2,co3)
local a,b,c,eq1,q1,Lcoef,half2,eq2,eq3,op1,op2,op3,
eq1a,eq1b,eq1c,eq4,eq5,eq6,r1,sol1,sol2;
begin;
eq1:=co1*x^2+co2*x+co3=0;
eq2:=(eq1/co1);
q1:=[coeff(lhs(eq2))];
Lcoef:=q1[2];
op1:= op(lhs(eq2)); op2:=op(op1,3);
eq1a := subs(R1 + R2 = R3, R1=op(op1,1),
R2 =op(op1,2),R3 = -op2, Unsimplified);
half2:=(Lcoef/2)^2;
a := lhs(eq1a); b:=rhs(eq1a);
eq1b:= subs(R4 + R5 + R6 = R7 + R8, R4 =op(a,1),
R5 = op(a,2), R6 = half2, R7=b,R8 = half2,Unsimplified);
eq3:=eq2-q1[3];
eq4:=eq3+half2;
eq5:= (x+Lcoef/2)^2=rhs(eq4);
eq6:= x+Lcoef/2=sqrt(rhs(eq5));
eq6a:= x+Lcoef/2=-sqrt(rhs(eq5));
sol1:=eq6-Lcoef/2;sol2:=x=rhs(-eq6-Lcoef/2);
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I need rhs, lhs, op, coef, subs, etc. Are any of these functions in
Sage or Maxima?
Thanx
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