### Related

##### subst

profit: (c2/q2-c1/q1)...

subst([c2=10, q2=-2, ...

Calculate

##### subst

h:[%i/(w^3*c^2*l-2*%i...

p:h*subst(-w,w,h);

Calculate

##### subst

G1: Uteil = U48 * R2/...

G2: Uaus = R2/R1 * (U...

G3: Ue2 = Uteil;

Calculate

##### subst

eq1:(28.785*(10^-3)*T...

eq2:T=(V-91)*(1+(92*(...

eq3: subst((V-91)*(1+...

Calculate

##### subst

eq1: f=(p*W-q*L)*W*L;

eq2: W=100/350;

eq3: L=W;

Calculate

##### subst

var1: E[6063] = 1.0e7;

var2: E[ABS] = 3.04e5;

eq1: I = %pi/4*(R[2]^...

Calculate

##### subst

subst (a, x+y, (x+y) ...

Calculate

Calculate

##### subst

f:(1+x+(1/2*x^2)+(1/3...

subst(0.091,x,f);

Calculate

##### subst

f:1+x+x^2/2!+x^3/3!+x...

A:x=pqr/1000;

subst(A,f);

Calculate

### subst

Run Example
(%i1)derivabbrev:true ;
(%o1)                                true
(%i2) mainvar: t;
(%o2)                                  t
(%i3) x(t):= r(t)*sin(theta(t));
(%o3)                     x(t) := r(t) sin(theta(t))
(%i4) y(t):=r(t)*cos(theta(t));
(%o4)                     y(t) := r(t) cos(theta(t))
(%i5) xdot(t):= diff(x(t), t, 1);
(%o5)                     xdot(t) := diff(x(t), t, 1)
(%i6) ydot(t):= diff(y(t), t, 1);
(%o6)                     ydot(t) := diff(y(t), t, 1)
(%i7) xdotdot(t):= diff(xdot(t), t, 1);
(%o7)                  xdotdot(t) := diff(xdot(t), t, 1)
(%i8) ydotdot(t):= diff(ydot(t), t, 1);
(%o8)                  ydotdot(t) := diff(ydot(t), t, 1)
(%o9)                 thetadot(t) := diff(theta(t), t, 1)
(%i11) Assumption1: xdotdot(t)=0;
2
(%o11) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
t t                               t
+ 2 r(t)  cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
t                       t       t t
(%i12) solve(Assumption1, r(t));
sin(theta(t)) r(t)    + 2 cos(theta(t)) theta(t)  r(t)
t t                           t     t
(%o12) [r(t) = - -------------------------------------------------------]
2
cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
t t                          t
(%i13) Assumption2: ydotdot(t)=0;
2
(%o13) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
t t                               t
- 2 r(t)  sin(theta(t)) theta(t)  + r(t)    cos(theta(t)) = 0
t                       t       t t
(%i14) E1_1: subst(rdot(t), diff(r(t), t, 1), Assumption1);
2
(%o14) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
t t                               t
+ 2 rdot(t) cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
t       t t
(%i15) E1_2: subst(rdotdot(t), diff(diff(r(t), t, 1),t,1), E1_1);
2
(%o15) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
t t                               t
+ 2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t)) = 0
t
(%i16) E1_3: subst(rr(t), r(t), E1_2);
2
(%o16) rr(t) cos(theta(t)) theta(t)    - rr(t) sin(theta(t)) (theta(t) )
t t                                t
+ 2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t)) = 0
t
(%i17) E1_4: solve(E1_3, rr(t));
2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t))
t
(%o17) [rr(t) = - ------------------------------------------------------------]
2
cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
t t                          t
(%i18) E1_5: subst(r(t), rr(t), E1_4[1]);
2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t))
t
(%o18) r(t) = - ------------------------------------------------------------
2
cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
t t                          t
(%i19)
Run Example
m: 4;
(%o1)                                  4
(%i2) e0: ((m+1)*x+(m-1)*y)/(2*m);
3 y + 5 x
(%o2)                              ---------
8
(%i3) e1: ((m-1)*x+(m+1)*y)/(2*m);
5 y + 3 x
(%o3)                              ---------
8
(%i4) fullratsimp(subst(e0, y, e1));
15 y + 49 x
(%o4)                             -----------
64
(%i5)  solve((a-r)*(d-r)-b*c,r);
2                    2
sqrt(d  - 2 a d + 4 b c + a ) - d - a
(%o5) [r = - -------------------------------------,
2
2                    2
sqrt(d  - 2 a d + 4 b c + a ) + d + a
r = -------------------------------------]
2
(%i6) a0: 0;
(%o6)                                  0
(%i7) a1: 1;
(%o7)                                  1
(%i8) a: 49/64;
49
(%o8)                                 --
64
(%i9) b: 15/64;
15
(%o9)                                 --
64
(%i10) c: 3/8;
3
(%o10)                                 -
8
(%i11) d: 5/8;
5
(%o11)                                 -
8
(%i12) sqrt(a^2+d^2-2*a*d+4*b*c);
39
(%o12)                                --
64
(%i13) a1*b/sqrt(a^2+d^2-2*a*d+4*b*c);
5
(%o13)                                --
13
(%i14)
Run Example
1;
(%o1)                                  1
(%i2) 1;
(%o2)                                  1
(%i3) 1;
(%o3)                                  1
(%i4) 1;
(%o4)                                  1
(%i5) 1;
(%o5)                                  1
(%i6) 1;
(%o6)                                  1
(%i7) 1;
(%o7)                                  1
(%i8) 1;
(%o8)                                  1
(%i9) 1;
(%o9)                                  1
(%i10) 1;
(%o10)                                 1
(%i11) 1;
(%o11)                                 1
(%i12) 1;
(%o12)                                 1
(%i13) 1;
(%o13)                                 1
(%i14) 1;
(%o14)                                 1
(%i15) 1;
(%o15)                                 1
(%i16) 1;
(%o16)                                 1
(%i17) 1;
(%o17)                                 1
(%i18) 1;
(%o18)                                 1
(%i19) 1;
(%o19)                                 1
(%i20) 1;
(%o20)                                 1
(%i21) 1;
(%o21)                                 1
(%i22) 1;
(%o22)                                 1
(%i23) 1;
(%o23)                                 1
(%i24) 1;
(%o24)                                 1
(%i25) 1;
(%o25)                                 1
(%i26) 1;
(%o26)                                 1
(%i27) 1;
(%o27)                                 1
(%i28) 1;
(%o28)                                 1
(%i29) 1;
(%o29)                                 1
(%i30) 1;
(%o30)                                 1
(%i31) A:u^4+4*p*u+3*q;
4
(%o31)                         u  + 4 p u + 3 q
(%i32) B:a*u*u+p*u*v+a*b*u+q*v;
2
(%o32)                    p u v + q v + a u  + a b u
(%i33) C:expand(resultant(A,B,u));
4  4    4    4      2  3  2       2      2  2      2  2  2    2
(%o33) q  v  - p  q v  + 6 a  q  v  - 12 a  b p q  v  + 6 a  b  p  q v
3  2  2        3  2          3  3            4  2       4
- 12 a  b  q  v + 4 a  p  q v + 8 a  b  p q v + 9 a  q  - 12 a  b p q
4  4
+ 3 a  b  q
(%i34) D0:factor(coeff(C,v,0));
4                   4
(%o34)                     3 a  q (3 q - 4 b p + b )
(%i35) D1:factor(coeff(C,v));
3       2      2      3
(%o35)                  - 4 a  q (3 b  q - p  - 2 b  p)
(%i36) D2:factor(coeff(C,v,2));
2            2
(%o36)                         6 a  q (q - b p)
(%i37) D3:factor(coeff(C,v,3));
(%o37)                                 0
(%i38) D4:factor(coeff(C,v,4));
3    4
(%o38)                            q (q  - p )
(%i39) E:factor(resultant(expand(0/12/p),expand(D3/8),d));
(%o39)                                 1
(%i40)  F:solve(D2=0,z);
(%o40)                                []
(%i41) G:subst(d=q+sqrt(q^2+p^3),z);
(%o41)                                 z
(%i42) H:expand(G);
(%o42)                                 z
(%i43) J:ratsimp(H);
(%o43)                                 z
(%i44) K:factor(J);
(%o44)                                 z
(%i45)

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