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factorout-linsolve

eq1:tau=k*(v2-v1)/s;

eq2:v1=(T1+D1*tau/2)*...

eq3:v2=(T2-D2*tau/3)*...

Calculate

factorout

g:q-(q-p)/(1-p^2);

factorout(g, q);

Calculate

factorout-subst

expr: z^3 + a1*z*w + ...

factorout (subst (exp...

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factorout-false-lhs-ratsimpexpons

eq:(x^2-17*x+1)^(x^2-...

ratdisp:false;

ratsimpexpons:false;

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factorout

g:q-(q-p)/(1-p^2);

factorout(g, q);

Calculate

factorout

? factorout;

Calculate

factorout

g:q-(q-p)/(1-p^2);

factorout(g, q);

Calculate

factorout-sqrt

m=sqrt(x^2+(sqrt(e^2-...

factorout(%,x);

Calculate

factorout-subst

expr: z^3 + a1*z*w + ...

factorout (subst (exp...

Calculate

factorout

g:q-(q-p)/(1-p);

factorout(g, q, p);

Calculate

factorout

Run Example
(%i1)globalsolve: true;
(%o1)                                true
(%i2) realonly: true;
(%o2)                                true
(%i3) /* Standard (x,y)->
 (r,theta) coordinate translation */x(t) := r(t) * cos(theta(t));
(%o3)                     x(t) := r(t) cos(theta(t))
(%i4) y(t) := r(t) * sin(theta(t));
(%o4)                     y(t) := r(t) sin(theta(t))
(%i5) /* Constant course assumption */declare (slope,constant);
(%o5)                                done
(%i6) declare (slope,real);
(%o6)                                done
(%i7) declare (yintercept,constant);
(%o7)                                done
(%i8) declare (yintercept, real);
(%o8)                                done
(%i9) y(t)=slope * x(t) + yintercept;
(%o9)     r(t) sin(theta(t)) = slope r(t) cos(theta(t)) + yintercept
(%i10) eq1: y(t)=slope * x(t) + yintercept;
(%o10)    r(t) sin(theta(t)) = slope r(t) cos(theta(t)) + yintercept
(%i11) /* Constant speed assumption */declare (speedx,constant);
(%o11)                               done
(%i12) declare (speedx,real);
(%o12)                               done
(%i13) declare (speedy,constant);
(%o13)                               done
(%i14) declare (speedy,real);
(%o14)                               done
(%i15) declare (c1, constant);
(%o15)                               done
(%i16) declare (c1, real);
(%o16)                               done
(%i17) eq2: x(t) = speedx * (t + c1);
(%o17)               r(t) cos(theta(t)) = speedx (t + c1)
(%i18) declare (c2, constant);
(%o18)                               done
(%i19) declare (c2, real);
(%o19)                               done
(%i20) eq3: y(t) = speedy * (t + c1) + c2*speedx;
(%o20)         r(t) sin(theta(t)) = speedy (t + c1) + c2 speedx
(%i21) eq4: (rhs(eq3/eq2));
                          speedy (t + c1) + c2 speedx
(%o21)                    ---------------------------
                                speedx (t + c1)
(%i22) eq5: factorout(eq4, speedx*(t+c1));
                          speedy (t + c1) + c2 speedx
(%o22)                    ---------------------------
                                speedx (t + c1)
(%i23) 
Run Example
expr: -((1+s*s*l*c)*((u-s*r)*(u+s*(w+p))-u*(u+s*w)))/((u+s*(w+p))*(s*l+(1+s*s*l*c)*s*r));
                   2
             (c l s  + 1) ((u - r s) (s (w + p) + u) - u (s w + u))
(%o1)      - ------------------------------------------------------
                               2
                    (r s (c l s  + 1) + l s) (s (w + p) + u)
(%i2) factorout(expr,s);
                   2
             (c l s  + 1) ((u - r s) (s (w + p) + u) - u (s w + u))
(%o2)      - ------------------------------------------------------
                               2
                    (r s (c l s  + 1) + l s) (s (w + p) + u)
(%i3) 
Run Example
p(t):=a*t^3+b*t^2+c*t+d;
                                    3      2
(%o1)                    p(t) := a t  + b t  + c t + d
(%i2) s:solve([p(-1)=p0,p(0)=p1,p(1)=p2,p(2)=p3],[a,b,c,d]);
              - p3 + 3 p2 - 3 p1 + p0      p2 - 2 p1 + p0
(%o2) [[a = - -----------------------, b = --------------, 
                         6                       2
                                              p3 - 6 p2 + 3 p1 + 2 p0
                                        c = - -----------------------, d = p1]]
                                                         6
(%i3) r(t):=-(-p3+3*p2-3*p1+p0)/6*t^3+(p2-2*p1+p0)/2*t^2-(p3-6*p2+3*p1+2*p0)/6*t+p1;
              - (- p3 + 3 p2 + (- 3) p1 + p0)  3   p2 - 2 p1 + p0  2
(%o3) r(t) := ------------------------------- t  + -------------- t
                             6                           2
                                             - (p3 - 6 p2 + 3 p1 + 2 p0)
                                           + --------------------------- t + p1
                                                          6
(%i4) ratsimp(r(1/4)), expand;
                          5 p3   35 p2   105 p1   7 p0
(%o4)                   - ---- + ----- + ------ - ----
                          128     128     128     128
(%i5) ratsimp(r(1/2)), expand;
                              p3   9 p2   9 p1   p0
(%o5)                       - -- + ---- + ---- - --
                              16    16     16    16
(%i6) ratsimp(r(3/4)), expand;
                          7 p3   105 p2   35 p1   5 p0
(%o6)                   - ---- + ------ + ----- - ----
                          128     128      128    128
(%i7) factorout(expand(r(t)), 1-t, t);
          3       3       3       3       2       2
      p3 t    p2 t    p1 t    p0 t    p2 t    p0 t                         p3 t
(%o7) ----- - ----- + ----- - ----- + ----- + ----- - p1 (t - 1) (t + 1) - ----
        6       2       2       6       2       2                           6
                                                                    p1 t   p0 t
                                                           + p2 t - ---- - ----
                                                                     2      3
(%i8) 

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