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remove

? remove ;

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remove

? remove ;

Calculate

remove

Run Example
(%i1)depends(y,u);
(%o1)                               [y(u)]
(%i2) depends(u,x);
(%o2)                               [u(x)]
(%i3) diff(y,x);
                                     du dy
(%o3)                                -- --
                                     dx du
(%i4) y(u):=u^2-u+7;
                                       2
(%o4)                         y(u) := u  - u + 7
(%i5) remove([u,x],dependency);
(%o5)                                done
(%i6) 
Run Example
? remove;

 -- Function: remove (<a_1>, <p_1>, ..., <a_n>, <p_n>)
 -- Function: remove ([<a_1>, ..., <a_m>], [<p_1>, ..., <p_n>], ...)
 -- Function: remove ("<a>", operator)
 -- Function: remove (<a>, transfun)
 -- Function: remove (all, <p>)
     Removes properties associated with atoms.

     `remove (<a_1>, <p_1>, ..., <a_n>, <p_n>)' removes property `p_k'
     from atom `a_k'.

     `remove ([<a_1>, ..., <a_m>], [<p_1>, ..., <p_n>], ...)' removes
     properties `<p_1>, ..., <p_n>' from atoms <a_1>, ..., <a_m>.
     There may be more than one pair of lists.

     `remove (all, <p>)' removes the property <p> from all atoms which
     have it.

     The removed properties may be system-defined properties such as
     `function', `macro', or `mode_declare', or user-defined properties.

     A property may be `transfun' to remove the translated Lisp version
     of a function.  After executing this, the Maxima version of the
     function is executed rather than the translated version.

     `remove ("<a>", operator)' or, equivalently, `remove ("<a>", op)'
     removes from <a> the operator properties declared by `prefix',
     `infix', `nary', `postfix', `matchfix', or `nofix'.  Note that the
     name of the operator must be written as a quoted string.

     `remove' always returns `done' whether or not an atom has a
     specified property.  This behavior is unlike the more specific
     remove functions `remvalue', `remarray', `remfunction', and
     `remrule'.


  There are also some inexact matches for `remove'.
  Try `?? remove' to see them.

(%o1)                                true
(%i2) 
Run Example
/*[1] Fedosov, Dmitry A. Multiscale modeling of blood flow and softmatter. Brown University, 2010.[42] Dao, M., J. Li, and S. Suresh. "Molecularly based analysis ofdeformation of spectrin network and human erythrocyte." MaterialsScience and Engineering: C 26.8 (2006): 1232-1244.*/load ("scifac") ;
(%o1)      /usr/share/maxima/5.21.1/share/simplification/scifac.lisp
(%i2) load("abs_integrate");
(%o2) /usr/share/maxima/5.21.1/share/contrib/integration/abs_integrate.mac
(%i3) load("abs_integrate");
(%o3) /usr/share/maxima/5.21.1/share/contrib/integration/abs_integrate.mac
(%i4)  /* `safe_op' */load("scifac");
(%o4)      /usr/share/maxima/5.21.1/share/simplification/scifac.lisp
(%i5) load("fourie");
(%o5)         /usr/share/maxima/5.21.1/share/calculus/fourie.mac
(%i6)  /* `funp' and `remfun' */dotassoc  : false;
(%o6)                                false
(%i7) dotdistrib: false;
(%o7)                                false
(%i8) dot2tic_tac(e):= block([inflag: true],  if safe_op(e)#"." then error("op(e) shoule be '.'"),  if length(e)#2 then error("the number of arguments should be 2"),  tic(first(e))*tac(second(e)));
(%o8) dot2tic_tac(e) := block([inflag : true], 
if safe_op(e) # "." then error("op(e) shoule be '.'"), 
if length(e) # 2 then error("the number of arguments should be 2"), 
tic(first(e)) tac(second(e)))
(%i9) tic_tacify(e):= block([op: safe_op(e), inflag: true, seen_dot: false, prederror: true],  if op="." then dot2tic_tac(e)  else if op="*" then map(lambda([el],      if not seen_dot and op="." then (seen_dot: true, dot2tic_tac(el)) else el), e)  else e);
(%o9) tic_tacify(e) := block([op : safe_op(e), inflag : true, 
seen_dot : false, prederror : true], if op = "." then dot2tic_tac(e)
 else (if op = "*" then map(lambda([el], 
if (not seen_dot) and (op = ".") then (seen_dot : true, dot2tic_tac(el))
 else el), e) else e))
(%i10) ntic_or_ntac(e):= is(not funp('tic, e) or not funp('tac, e));
(%o10) ntic_or_ntac(e) := is((not funp('tic, e)) or (not funp('tac, e)))
(%i11) de_tic_tacify_aux(e):= block([fst: 1, scn: 1, rst: 1, inflag: true, prederror: true],  for el in e do (if funp('tic, el) then fst: remfun('tic, el)    else if funp('tac, el) then scn: remfun('tac, el)    else rst: rst*el),  rst*(fst . scn));
(%o11) de_tic_tacify_aux(e) := block([fst : 1, scn : 1, rst : 1, 
inflag : true, prederror : true], for el in e do if funp('tic, el)
 then fst : remfun('tic, el) else (if funp('tac, el)
 then scn : remfun('tac, el) else rst : rst el), rst (fst . scn))
(%i12) de_tic_tacify(e):= block([inflag: true, prederror: true, op: safe_op(e)],  if op="*" and every(ntic_or_ntac, args(e)) then de_tic_tacify_aux(e)  else if op#false then map('de_tic_tacify, e)  else e);
(%o12) de_tic_tacify(e) := block([inflag : true, prederror : true, 
op : safe_op(e)], if (op = "*") and every(ntic_or_ntac, args(e))
 then de_tic_tacify_aux(e) else (if op # false then map('de_tic_tacify, e)
 else e))
(%i13) nc_factor_aux([L]):= block([M, op],  M: map('tic_tacify, L),  M: gcfac(factor(apply("+", M))),  de_tic_tacify(M));
(%o13) nc_factor_aux([L]) := block([M, op], M : map('tic_tacify, L), 
                            M : gcfac(factor(apply("+", M))), de_tic_tacify(M))
(%i14) nc_factor(e):= (e: subst(nc_factor_aux, "+", e), ev(e, nc_factor_aux));
(%o14) nc_factor(e) := (e : subst(nc_factor_aux, "+", e), ev(e, nc_factor_aux))
(%i15) mdiff(e):= block([prederror: true, inflag: true, op: safe_op(e), arg],  if op="+" or op="[" or op="=" then map(mdiff, e)  else if op="*" then mdiff(first(e))*rest(e) + first(e)*mdiff(rest(e))  else if op="." then mdiff(first(e)).rest(e) + first(e).mdiff(rest(e))                                                         /* diff(a^n) */  else if op="^"  then block([a: first(e), n: second(e)], a^n*log(a)*mdiff(n)+a^(n-1)*n*mdiff(a))  else if op='sk  then map('mdiff, e)  else diff(e));
(%o15) mdiff(e) := block([prederror : true, inflag : true, op : safe_op(e), 
arg], if (op = "+") or (op = "[") or (op = "=") then map(mdiff, e)
 else (if op = "*" then mdiff(first(e)) rest(e) + first(e) mdiff(rest(e))
 else (if op = "." then mdiff(first(e)) . rest(e) + first(e) . mdiff(rest(e))
 else (if op = "^" then block([a : first(e), n : second(e)], 
 n                    n - 1
a  log(a) mdiff(n) + a      n mdiff(a))
 else (if op = 'sk then map('mdiff, e) else diff(e))))))
(%i16) declare([p1_v, p2_v, p3_v, p4_v],                  nonscalar) ;
(%o16)                               done
(%i17) declare([a21_v, a31_v, a32_v],                     nonscalar) ;
(%o17)                               done
(%i18) declare([a34_v, a24_v       ],                     nonscalar) ;
(%o18)                               done
(%i19) declare([ksi_v, sig_v, tc_v ],                     nonscalar) ;
(%o19)                               done
(%i20) declare([Cq, q, ka, kb, A0tot, theta0],            constant) ;
(%o20)                               done
(%i21) /*Replace cross product by product of a skew-symmetric matrix and avectorhttp://en.wikipedia.org/wiki/Cross_product#Conversion_to_matrix_multiplication*/cross(a, b):= sk(a) . b;
(%o21)                     cross(a, b) := sk(a) . b
(%i22) declare(sk, nonscalar);
(%o22)                               done
(%i23)  /* `sk' returns a matrix */declare(sk, linear);
(%o23)                               done
(%i24)     /* `sk' is linear *//*  '.' is not associative, not commutative and can return a vector */dotassoc: false;
(%o24)                               false
(%i25) remove(".",commutative);
(%o25)                               done
(%i26) declare(".", nonscalar);
(%o26)                               done
(%i27) /* get rid of sk(del) using anticommutativity of cross(a, b) */matchdeclare([a, b], true);
(%o27)                               done
(%i28) tellsimpafter(sk(del(a)).b, -sk(b).del(a));
(%o28)                         [.rule1, simpnct]
(%i29) constrains: [/*1*/ a21_v  - (p2_v - p1_v),      a31_v  - (p3_v - p1_v),      a32_v  - (p3_v - p2_v),  /* See Fig A.1 and Fig. A.2 [1]  */      a34_v  - (p3_v - p4_v),/*5*/ a24_v  - (p2_v - p4_v),      tc_v   - (p1_v  + p2_v + p3_v)/3,      ksi_v  - cross(a21_v, a31_v),      sig_v  - cross(a34_v, a24_v),      cos(theta) - (ksi_v . sig_v)/sqrt(ksi_v.ksi_v)/sqrt(sig_v.sig_v),/*10*/4*Ak^2 - ksi_v.ksi_v,      4*A2^2 - sig_v.sig_v,      Varea  - ka*(Ak - A0tot)^2/(2*A0tot),      Vst    - Cq/Ak^q,      Vk     - 1/6*ksi_v . tc_v,/*15*/Vb     - kb*(1-cos(theta - theta0))];
(%o29) [- p2_v + p1_v + a21_v, - p3_v + p1_v + a31_v, - p3_v + p2_v + a32_v, 
                                                 p3_v + p2_v + p1_v
p4_v - p3_v + a34_v, p4_v - p2_v + a24_v, tc_v - ------------------, 
                                                         3
ksi_v - sk(a21_v) . a31_v, sig_v - sk(a34_v) . a24_v, 
                     ksi_v . sig_v              2        <2>
cos(theta) - -----------------------------, 4 Ak  - ksi_v   , 
                       <2>            <2>
             sqrt(ksi_v   ) sqrt(sig_v   )
                                         2
    2        <2>          ka (Ak - A0tot)         Cq        ksi_v . tc_v
4 A2  - sig_v   , Varea - ----------------, Vst - ---, Vk - ------------, 
                              2 A0tot               q            6
                                                  Ak
Vb - kb (1 - cos(theta - theta0))]
(%i30) eq: mdiff(constrains);
(%o30) [- del(p2_v) + del(p1_v) + del(a21_v), 
- del(p3_v) + del(p1_v) + del(a31_v), - del(p3_v) + del(p2_v) + del(a32_v), 
del(p4_v) - del(p3_v) + del(a34_v), del(p4_v) - del(p2_v) + del(a24_v), 
            del(p3_v) + del(p2_v) + del(p1_v)
del(tc_v) - ---------------------------------, 
                            3
del(ksi_v) + sk(a31_v) . del(a21_v) - sk(a21_v) . del(a31_v), 
del(sig_v) - sk(a34_v) . del(a24_v) + sk(a24_v) . del(a34_v), 
                           del(ksi_v) . sig_v + ksi_v . del(sig_v)
- sin(theta) del(theta) - (---------------------------------------
                                                 <2>
                                       sqrt(sig_v   )
   (ksi_v . sig_v) (del(sig_v) . sig_v + sig_v . del(sig_v))            <2>
 - ---------------------------------------------------------)/sqrt(ksi_v   )
                                <2> 3/2
                        2 (sig_v   )
   (ksi_v . sig_v) (del(ksi_v) . ksi_v + ksi_v . del(ksi_v))
 + ---------------------------------------------------------, 
                        <2> 3/2           <2>
                2 (ksi_v   )    sqrt(sig_v   )
8 Ak del(Ak) - del(ksi_v) . ksi_v - ksi_v . del(ksi_v), 
8 A2 del(A2) - del(sig_v) . sig_v - sig_v . del(sig_v), 
             ka (Ak - A0tot) del(Ak)                    - q - 1
del(Varea) - -----------------------, del(Vst) + Cq q Ak        del(Ak), 
                      A0tot
          del(ksi_v) . tc_v + ksi_v . del(tc_v)
del(Vk) - -------------------------------------, 
                            6
del(Vb) - kb sin(theta - theta0) del(theta)]
(%i31) lin_sb : solve([eq[1], eq[2], eq[3], eq[4], eq[5], eq[6], eq[9], eq[10], eq[11]],  map('del, [a21_v, a31_v, a32_v, a34_v, a24_v, tc_v, theta, Ak, A2]))[1];
(%o31) [del(a21_v) = del(p2_v) - del(p1_v), 
del(a31_v) = del(p3_v) - del(p1_v), del(a32_v) = del(p3_v) - del(p2_v), 
del(a34_v) = del(p3_v) - del(p4_v), del(a24_v) = del(p2_v) - del(p4_v), 
            del(p3_v) + del(p2_v) + del(p1_v)
del(tc_v) = ---------------------------------, 
                            3
                   <2>
del(theta) = (ksi_v    (ksi_v . sig_v) (del(sig_v) . sig_v)
          <2>      <2>
 - 2 ksi_v    sig_v    (del(ksi_v) . sig_v)
                        <2>
 + (ksi_v . sig_v) sig_v    (del(ksi_v) . ksi_v)
        <2>
 + ksi_v    (ksi_v . sig_v) (sig_v . del(sig_v))
          <2>                           <2>
 - 2 ksi_v    (ksi_v . del(sig_v)) sig_v
                                             <2>
 + (ksi_v . sig_v) (ksi_v . del(ksi_v)) sig_v   )
          <2> 3/2       <2> 3/2
/(2 (ksi_v   )    (sig_v   )    sin(theta)), 
          del(ksi_v) . ksi_v + ksi_v . del(ksi_v)
del(Ak) = ---------------------------------------, 
                           8 Ak
          del(sig_v) . sig_v + sig_v . del(sig_v)
del(A2) = ---------------------------------------]
                           8 A2
(%i32) sb_ak  : solve(subst(lin_sb, [eq[7], eq[8]]), map('del, [ksi_v, sig_v]))[1];
(%o32) [del(ksi_v) = sk(a21_v) . (del(p3_v) - del(p1_v))
 - sk(a31_v) . (del(p2_v) - del(p1_v)), 
del(sig_v) = sk(a34_v) . (del(p2_v) - del(p4_v))
 - sk(a24_v) . (del(p3_v) - del(p4_v))]
(%i33) lin_sb : append(lin_sb, sb_ak);
(%o33) [del(a21_v) = del(p2_v) - del(p1_v), 
del(a31_v) = del(p3_v) - del(p1_v), del(a32_v) = del(p3_v) - del(p2_v), 
del(a34_v) = del(p3_v) - del(p4_v), del(a24_v) = del(p2_v) - del(p4_v), 
            del(p3_v) + del(p2_v) + del(p1_v)
del(tc_v) = ---------------------------------, 
                            3
                   <2>
del(theta) = (ksi_v    (ksi_v . sig_v) (del(sig_v) . sig_v)
          <2>      <2>
 - 2 ksi_v    sig_v    (del(ksi_v) . sig_v)
                        <2>
 + (ksi_v . sig_v) sig_v    (del(ksi_v) . ksi_v)
        <2>
 + ksi_v    (ksi_v . sig_v) (sig_v . del(sig_v))
          <2>                           <2>
 - 2 ksi_v    (ksi_v . del(sig_v)) sig_v
                                             <2>
 + (ksi_v . sig_v) (ksi_v . del(ksi_v)) sig_v   )
          <2> 3/2       <2> 3/2
/(2 (ksi_v   )    (sig_v   )    sin(theta)), 
          del(ksi_v) . ksi_v + ksi_v . del(ksi_v)
del(Ak) = ---------------------------------------, 
                           8 Ak
          del(sig_v) . sig_v + sig_v . del(sig_v)
del(A2) = ---------------------------------------, 
                           8 A2
del(ksi_v) = sk(a21_v) . (del(p3_v) - del(p1_v))
 - sk(a31_v) . (del(p2_v) - del(p1_v)), 
del(sig_v) = sk(a34_v) . (del(p2_v) - del(p4_v))
 - sk(a24_v) . (del(p3_v) - del(p4_v))]
(%i34) sb_ak  : solve(subst(lin_sb, [eq[12], eq[13], eq[14], eq[15]]),  map('del, [Vst, Varea, Vb, Vk]))[1];
                        - q - 2
(%o34) [del(Vst) = - (Ak        (Cq q (ksi_v
 . (sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v)
 . (del(p2_v) - del(p1_v)))) + Cq q
 ((sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v) . (del(p2_v) - del(p1_v)))
 . ksi_v)))/8, del(Varea) = ((ka Ak - A0tot ka)
 (ksi_v . (sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v)
 . (del(p2_v) - del(p1_v))))
 + ka ((sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v) . (del(p2_v) - del(p1_v)))
 . ksi_v) Ak - A0tot ka ((sk(a21_v) . (del(p3_v) - del(p1_v))
 - sk(a31_v) . (del(p2_v) - del(p1_v))) . ksi_v))/(8 A0tot Ak), 
                    <2>
del(Vb) = ((kb ksi_v    (ksi_v . sig_v)
 (sig_v . (sk(a34_v) . (del(p2_v) - del(p4_v)) - sk(a24_v) . (del(p3_v)
 - del(p4_v))))
                <2>
 + (- 2 kb ksi_v    (ksi_v . (sk(a34_v) . (del(p2_v) - del(p4_v))
 - sk(a24_v) . (del(p3_v) - del(p4_v))))
 - 2 kb ((sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v) . (del(p2_v) - del(p1_v)))
               <2>       <2>
 . sig_v) ksi_v   ) sig_v    + kb ((sk(a34_v) . (del(p2_v) - del(p4_v))
                                                      <2>
 - sk(a24_v) . (del(p3_v) - del(p4_v))) . sig_v) ksi_v    (ksi_v . sig_v))
 sin(theta - theta0) + kb (ksi_v . (sk(a21_v) . (del(p3_v) - del(p1_v))
                                                              <2>
 - sk(a31_v) . (del(p2_v) - del(p1_v)))) (ksi_v . sig_v) sig_v
 sin(theta - theta0) + kb ((sk(a21_v) . (del(p3_v) - del(p1_v))
                                                                      <2>
 - sk(a31_v) . (del(p2_v) - del(p1_v))) . ksi_v) (ksi_v . sig_v) sig_v
                               <2> 3/2       <2> 3/2
 sin(theta - theta0))/(2 (ksi_v   )    (sig_v   )    sin(theta)), 
del(Vk) = (ksi_v . (del(p3_v) + del(p2_v) + del(p1_v))
 + 3 ((sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v) . (del(p2_v) - del(p1_v)))
 . tc_v))/18]
(%i35) matchdeclare([A, B]     , all);
(%o35)                               done
(%i36) matchdeclare(N          , lambda([N], N#sig_v and N#ksi_v));
(%o36)                               done
(%i37) tellsimpafter(A.sk(B)    , -sk(A).B);
(%o37)                     [.rule2, .rule1, simpnct]
(%i38) tellsimpafter(ksi_v.ksi_v, ksi^2);
(%o38)                       [^^rule1, simpncexpt]
(%i39) tellsimpafter(sig_v.sig_v, ksi^2);
(%o39)                  [^^rule2, ^^rule1, simpncexpt]
(%i40) tellsimpafter(ksi_v.sig_v, ksi_dot_sig);
(%o40)                 [.rule3, .rule2, .rule1, simpnct]
(%i41) tellsimpafter(sk(A).B, cp(A,B));
(%o41)             [.rule4, .rule3, .rule2, .rule1, simpnct]
(%i42) tellsimpafter(cp(ksi_v,N), -cp(N,ksi_v));
(%o42)                         [cprule1, false]
(%i43) tellsimpafter(cp(sig_v,N), -cp(N,sig_v));
(%o43)                     [cprule2, cprule1, false]
(%i44) Vk_expr : assoc(del('Vk), sb_ak);
(%o44) (ksi_v . (del(p3_v) + del(p2_v) + del(p1_v))
 + 3 ((sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v) . (del(p2_v) - del(p1_v)))
 . tc_v))/18
(%i45) Vrea_expr : assoc(del('Varea), sb_ak);
(%o45) ((ka Ak - A0tot ka) (ksi_v . (sk(a21_v) . (del(p3_v) - del(p1_v))
 - sk(a31_v) . (del(p2_v) - del(p1_v))))
 + ka ((sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v) . (del(p2_v) - del(p1_v)))
 . ksi_v) Ak - A0tot ka ((sk(a21_v) . (del(p3_v) - del(p1_v))
 - sk(a31_v) . (del(p2_v) - del(p1_v))) . ksi_v))/(8 A0tot Ak)
(%i46) Vst_expr: assoc(del('Vst), sb_ak);
            - q - 2
(%o46) - (Ak        (Cq q (ksi_v . (sk(a21_v) . (del(p3_v) - del(p1_v))
 - sk(a31_v) . (del(p2_v) - del(p1_v))))
 + Cq q ((sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v) . (del(p2_v) - del(p1_v)))
 . ksi_v)))/8
(%i47) Vb_expr : assoc(del('Vb), sb_ak);
                 <2>
(%o47) ((kb ksi_v    (ksi_v . sig_v) (sig_v . (sk(a34_v) . (del(p2_v) - del(p4_v))
 - sk(a24_v) . (del(p3_v) - del(p4_v))))
                <2>
 + (- 2 kb ksi_v    (ksi_v . (sk(a34_v) . (del(p2_v) - del(p4_v))
 - sk(a24_v) . (del(p3_v) - del(p4_v))))
 - 2 kb ((sk(a21_v) . (del(p3_v) - del(p1_v)) - sk(a31_v) . (del(p2_v) - del(p1_v)))
               <2>       <2>
 . sig_v) ksi_v   ) sig_v    + kb ((sk(a34_v) . (del(p2_v) - del(p4_v))
                                                      <2>
 - sk(a24_v) . (del(p3_v) - del(p4_v))) . sig_v) ksi_v    (ksi_v . sig_v))
 sin(theta - theta0) + kb (ksi_v . (sk(a21_v) . (del(p3_v) - del(p1_v))
                                                              <2>
 - sk(a31_v) . (del(p2_v) - del(p1_v)))) (ksi_v . sig_v) sig_v
 sin(theta - theta0) + kb ((sk(a21_v) . (del(p3_v) - del(p1_v))
                                                                      <2>
 - sk(a31_v) . (del(p2_v) - del(p1_v))) . ksi_v) (ksi_v . sig_v) sig_v
                               <2> 3/2       <2> 3/2
 sin(theta - theta0))/(2 (ksi_v   )    (sig_v   )    sin(theta))
(%i48) FOO(e):=gcfac(trigexpand(nc_factor(expand(e, 0, 0))));
(%o48)      FOO(e) := gcfac(trigexpand(nc_factor(expand(e, 0, 0))))
(%i49) fVarea1: FOO(diff(Vrea_expr, del(p1_v)));
             ka (cp(a31_v, ksi_v) - cp(a21_v, ksi_v)) (Ak - A0tot)
(%o49)       -----------------------------------------------------
                                  4 A0tot Ak
(%i50) fVarea2: FOO(diff(Vrea_expr, del(p2_v)));
                        ka cp(a31_v, ksi_v) (Ak - A0tot)
(%o50)                - --------------------------------
                                   4 A0tot Ak
(%i51) fVarea3: FOO(diff(Vrea_expr, del(p3_v)));
                       ka cp(a21_v, ksi_v) (Ak - A0tot)
(%o51)                 --------------------------------
                                  4 A0tot Ak
(%i52) fVst1: FOO(diff(Vst_expr, del(p1_v)));
                   Cq q (cp(a31_v, ksi_v) - cp(a21_v, ksi_v))
(%o52)           - ------------------------------------------
                                       q + 2
                                   4 Ak
(%i53) fVst2: FOO(diff(Vst_expr, del(p2_v)));
                             Cq q cp(a31_v, ksi_v)
(%o53)                       ---------------------
                                       q + 2
                                   4 Ak
(%i54) fVst3: FOO(diff(Vst_expr, del(p3_v)));
                              Cq q cp(a21_v, ksi_v)
(%o54)                      - ---------------------
                                        q + 2
                                    4 Ak
(%i55) fVk1: FOO(diff(Vk_expr, del(p1_v)));
                 ksi_v + 3 (cp(a31_v, tc_v) - cp(a21_v, tc_v))
(%o55)           ---------------------------------------------
                                      18
(%i56) fVk2: FOO(diff(Vk_expr, del(p2_v)));
                           ksi_v - 3 cp(a31_v, tc_v)
(%o56)                     -------------------------
                                      18
(%i57) fVk3: FOO(diff(Vk_expr, del(p3_v)));
                           ksi_v + 3 cp(a21_v, tc_v)
(%o57)                     -------------------------
                                      18
(%i58) fVb1: FOO(diff(Vb_expr, del(p1_v)));
(%o58) (kb ((cp(a31_v, ksi_v) - cp(a21_v, ksi_v)) ksi_dot_sig
                                            2
 + (cp(a21_v, sig_v) - cp(a31_v, sig_v)) ksi )
                                                        4
 (cos(theta0) sin(theta) - sin(theta0) cos(theta)))/(ksi  sin(theta))
(%i59) fVb2: FOO(diff(Vb_expr, del(p2_v)));
(%o59) (kb ((cp(a34_v, sig_v) - cp(a31_v, ksi_v)) ksi_dot_sig
                                            2
 + (cp(a31_v, sig_v) - cp(a34_v, ksi_v)) ksi )
                                                        4
 (cos(theta0) sin(theta) - sin(theta0) cos(theta)))/(ksi  sin(theta))
(%i60) fVb3: FOO(diff(Vb_expr, del(p3_v)));
(%o60) - (kb ((cp(a24_v, sig_v) - cp(a21_v, ksi_v)) ksi_dot_sig
                                            2
 + (cp(a21_v, sig_v) - cp(a24_v, ksi_v)) ksi )
                                                        4
 (cos(theta0) sin(theta) - sin(theta0) cos(theta)))/(ksi  sin(theta))
(%i61) fVb4: FOO(diff(Vb_expr, del(p4_v)));
(%o61) - (kb ((cp(a34_v, sig_v) - cp(a24_v, sig_v)) ksi_dot_sig
                                            2
 + (cp(a24_v, ksi_v) - cp(a34_v, ksi_v)) ksi )
                                                        4
 (cos(theta0) sin(theta) - sin(theta0) cos(theta)))/(ksi  sin(theta))
(%i62) 

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