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remvalue

f(x):=x^3-x-2;

'f(0) = f(0);

' f(2) = f(2);

Calculate

remvalue

remvalue(b);

'b = b::3/2;

'(a+b)/2 = (a+b)/2;

Calculate

remvalue

x: 2*ironPlate+ironRi...

''(ironPlate: 2*ironB...

remvalue(ironPlate);

Calculate

remvalue

f(x):=x^3-x-2;

f(0);

f(2);

Calculate

remvalue

f(x):=x^3-x-2;

'f(0) = f(0);

' f(2) = f(2);

Calculate

remvalue

f(x):=x^3-x-2;

'f(0) = f(0);

' f(2) = f(2);

Calculate

remvalue

f(x):=x^3-x-2;

f(0);

f(2);

Calculate

remvalue

f(x):=x^3-x-2;

'f(0) = f(0);

' f(2) = f(2);

Calculate

remvalue

f(x):=x^3-x-2;

f(0);

f(2);

Calculate

remvalue

f(x) = f(x):=x^3-x-2;

'f(0) = f(0);

' f(2) = f(2);

Calculate

remvalue

Run Example
(%i1)remvalue(n,z);
(%o1)                           [false, false]
(%i2) matchdeclare(a,lambda([x],freeof(x,n)));
(%o2)                                done
(%i3) matchdeclare(b,lambda([x],freeof(x,n) and integerp(x) and x>
0));
(%o3)                                done
(%i4) matchdeclare(f,all);
(%o4)                                done
(%i5) matchdeclare(g,lambda([x],freeof(n-1,x)));
(%o5)                                done
(%i6) defrule(r1,zt(1,n,z),z/(z-1));
                                                 z
(%o6)                      r1 : zt(1, n, z) -> -----
                                               z - 1
(%i7) defrule(r2,zt(n,n,z),z/(z-1)^2);
                                                z
(%o7)                    r2 : zt(n, n, z) -> --------
                                                    2
                                             (z - 1)
(%i8) defrule(r3,zt(1/n,n,z),log(z/(z-1)));
                                1                 z
(%o8)                   r3 : zt(-, n, z) -> log(-----)
                                n               z - 1
(%i9) defrule(r4,zt(a^n,n,z),z/(z-a));
                                   n             z
(%o9)                     r4 : zt(a , n, z) -> -----
                                               z - a
(%i10) defrule(r5,zt(a^(n-1),n,z),1/(z-a));
                                 n - 1             1
(%o10)                  r5 : zt(a     , n, z) -> -----
                                                 z - a
(%i11) defrule(r6,zt(binomial(n,b),n,z),z/(z-1)^(b+1));
                                                       - b - 1
(%o11)         r6 : zt(binomial(n, b), n, z) -> (z - 1)        z
(%i12) defrule(r7,zt(n^b,n,z),block([tmp:z/(z-1)],  for i:1 thru b do tmp:-z*diff(tmp,z),  factor(tmp)));
                b                          z
(%o12) r7 : zt(n , n, z) -> block([tmp : -----], 
                                         z - 1
                           for i thru b do tmp : - diff(tmp, z) z, factor(tmp))
(%i13) defrule(r8,zt(sin(a*n),n,z),z*'sin(a)/((z^2-2*z*'cos(a)+1)));
                                                sin(a) z
(%o13)          r8 : zt(sin(a n), n, z) -> -------------------
                                            2
                                           z  - 2 cos(a) z + 1
(%i14) defrule(r9,zt(cos(a*n),n,z),z*(z-'cos(a))/(z^2-2*z*'cos(a)+1));
                                             z (z - cos(a))
(%o14)          r9 : zt(cos(a n), n, z) -> -------------------
                                            2
                                           z  - 2 cos(a) z + 1
(%i15) defrule(r10,zt(kron_delta(b,n),n,z),1/z^b);
                                                        1
(%o15)              r10 : zt(kron_delta(b, n), n, z) -> --
                                                         b
                                                        z
(%i16) defrule(r11,zt(a^n*f,n,z),'subst(z/a,z,ztrans(f,n,z)));
                     n                        z
(%o16)     r11 : zt(a  f, n, z) -> substitute(-, z, ztrans(f, n, z))
                                              a
(%i17) defrule(r12,zt(n^b*g,n,z),block([tmp:ztrans(g,n,z)],  for i:1 thru b do tmp:-z*'diff(tmp,z),  return(tmp)));
                   b
(%o17) r12 : zt(g n , n, z) -> block([tmp : ztrans(g, n, z)], 
                                                           dtmp
                                   for i thru b do tmp : - ---- z, return(tmp))
                                                            dz
(%i18) defrule(r13,zt(exp(-a*n),n,z),z/(z-exp(-a)));
                                - a n               z
(%o18)               r13 : zt(%e     , n, z) -> ---------
                                                      - a
                                                z - %e
(%i19) defrule(r14,zt(f(n-m),n,z),z^(-m)*ztrans(f(n),n,z));
                                            ztrans(f(n), n, z)
(%o19)          r14 : zt(f(n - m), n, z) -> ------------------
                                                     m
                                                    z
(%i20) declare(zt,linear);
(%o20)                               done
(%i21) ztrans1(e):=apply1(e,r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,r11,r12,r13,r14);
(%o21) ztrans1(e) := apply1(e, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, 
                                                                 r12, r13, r14)
(%i22) ztrans(f,n,z):=ev(ztrans1(zt(f,n,z)),diff,subst);
(%o22)     ztrans(f, n, z) := ev(ztrans1(zt(f, n, z)), diff, subst)
(%i23) defrule(ir1,izt(z/(z-a),z,n),a^n);
                                     z              n
(%o23)                   ir1 : izt(-----, z, n) -> a
                                   z - a
(%i24) defrule(ir2,izt(1/(z-a),z,n),a^(n-1));
                                   1              n - 1
(%o24)                 ir2 : izt(-----, z, n) -> a
                                 z - a
(%i25) declare(izt,linear);
(%o25)                               done
(%i26) invztrans1(e):=apply1(e,ir1,ir2);
(%o26)               invztrans1(e) := apply1(e, ir1, ir2)
(%i27) invztrans(f,z,n):=invztrans1(izt(f,z,n));
(%o27)          invztrans(f, z, n) := invztrans1(izt(f, z, n))
(%i28) ztrans(1,n,z);
                                       z
(%o28)                               -----
                                     z - 1
(%i29) ztrans(a,n,z);
                                      a z
(%o29)                               -----
                                     z - 1
(%i30) expand(ztrans((-1)^n,n,z));
                                       z
(%o30)                               -----
                                     z + 1
(%i31) ztrans(n,n,z);
                                      z
(%o31)                             --------
                                          2
                                   (z - 1)
(%i32) ztrans(n^2,n,z);
                                   z (z + 1)
(%o32)                             ---------
                                          3
                                   (z - 1)
(%i33) ztrans(a^(n-1),n,z);
                                       1
(%o33)                               -----
                                     z - a
(%i34) factor(ztrans(a^(n-1)+n^2,n,z));
                         3      2      2
                      2 z  - a z  - 2 z  - a z + 3 z - 1
(%o34)                ----------------------------------
                                      3
                               (z - 1)  (z - a)
(%i35) 
Run Example
f(x) = f(x):=x^3-x-2;
                                           3
(%o1)                      f(x) = f(x) := x  - x - 2
(%i2) 'f(0) = f(0);
(%o2)                             f(0) = - 2
(%i3) ' f(2) = f(2);
(%o3)                              f(2) = 4
(%i4) 'a = a::0;
(%o4)                                a = 0
(%i5) 'b = b::2;
(%o5)                                b = 2
(%i6) '(a+b)/2 = (a+b)/2;
                                   b + a
(%o6)                              ----- = 1
                                     2
(%i7) 'f((a+b)/2) = f((a+b)/2);
(%o7)                             f(1) = - 2
(%i8) remvalue(a);
(%o8)                                 [a]
(%i9) 'a = a::1;
(%o9)                                a = 1
(%i10) '(a+b)/2 = (a+b)/2;
                                   b + a   3
(%o10)                             ----- = -
                                     2     2
(%i11) 'f((a+b)/2) = f((a+b)/2);
                                    3      1
(%o11)                            f(-) = - -
                                    2      8
(%i12) remvalue(a);
(%o12)                                [a]
(%i13) 'a = a::1/2;
                                         1
(%o13)                               a = -
                                         2
(%i14) '(a+b)/2 = (a+b)/2;
                                   b + a   5
(%o14)                             ----- = -
                                     2     4
(%i15) 'f((a+b)/2) = f((a+b)/2);
                                    5      83
(%o15)                            f(-) = - --
                                    4      64
(%i16) remvalue(a);
(%o16)                                [a]
(%i17) 'a = a::5/4;
                                         5
(%o17)                               a = -
                                         4
(%i18) a;
                                       5
(%o18)                                 -
                                       4
(%i19) b;
(%o19)                                 2
(%i20) '(a+b)/2 = (a+b)/2;
                                  b + a   13
(%o20)                            ----- = --
                                    2     8
(%i21) 'f((a+b)/2) = f((a+b)/2);
                                    13    341
(%o21)                            f(--) = ---
                                    8     512
(%i22) 
Run Example
remvalue(all);
(%o1)                                 []
(%i2) remfunction(all);
(%o2)                                 []
(%i3) e1: T(s) = B1*W1(s) + J*s*W1(s) + (N1/N2)*(2*Jc*s*W(s) + B2*W(s));
                  (W(s) B2 + 2 Jc s W(s)) N1
(%o3)      T(s) = -------------------------- + s W1(s) J + W1(s) B1
                              N2
(%i4) e2: N1*W1(s) = N2*W(s);
(%o4)                         W1(s) N1 = W(s) N2
(%i5) e3: I1(s) = I2(s) + I3(s);
(%o5)                        I1(s) = I3(s) + I2(s)
(%i6) e4: Vr(s) = R*I1(s) + I3(s)/(C*s);
                                              I3(s)
(%o6)                       Vr(s) = I1(s) R + -----
                                               s C
(%i7) e5: I3(s)/(C*s) = L*s*I2(s) + Ve(s);
                           I3(s)
(%o7)                      ----- = s I2(s) L + Ve(s)
                            s C
(%i8) e6: T(s) = Ki*I2(s);
(%o8)                           T(s) = Ki I2(s)
(%i9) e7: Ve(s) = Ke*W1(s);
(%o9)                          Ve(s) = Ke W1(s)
(%i10) fullratsimp(solve([e1,e2,e3,e4,e5,e6,e7], [I1(s),I2(s),I3(s),Ve(s),W(s),W1(s),T(s)]),Vr(s))/Vr(s);
         I1(s)       3        2                                   2
(%o10) [[----- = (((s  C J + s  B1 C) L + s J + Ke Ki s C + B1) N2
         Vr(s)
      2            3                       2
 + ((s  B2 + 2 Jc s ) C L + B2 + 2 Jc s) N1 )
      3        2                                   2
/((((s  C J + s  B1 C) L + s J + Ke Ki s C + B1) N2
      2            3                       2         2                        2
 + ((s  B2 + 2 Jc s ) C L + B2 + 2 Jc s) N1 ) R + ((s  J + s B1) L + Ke Ki) N2
                 2      2   I2(s)                 2                   2
 + (s B2 + 2 Jc s ) L N1 ), ----- = ((s J + B1) N2  + (B2 + 2 Jc s) N1 )
                            Vr(s)
      3        2                                   2
/((((s  C J + s  B1 C) L + s J + Ke Ki s C + B1) N2
      2            3                       2         2                        2
 + ((s  B2 + 2 Jc s ) C L + B2 + 2 Jc s) N1 ) R + ((s  J + s B1) L + Ke Ki) N2
                 2      2   I3(s)       3        2                        2
 + (s B2 + 2 Jc s ) L N1 ), ----- = (((s  C J + s  B1 C) L + Ke Ki s C) N2
                            Vr(s)
     2            3        2       3        2
 + (s  B2 + 2 Jc s ) C L N1 )/((((s  C J + s  B1 C) L + s J + Ke Ki s C + B1)
   2      2            3                       2
 N2  + ((s  B2 + 2 Jc s ) C L + B2 + 2 Jc s) N1 ) R
      2                        2                 2      2
 + ((s  J + s B1) L + Ke Ki) N2  + (s B2 + 2 Jc s ) L N1 ), 
Ve(s)            2       3        2                                   2
----- = (Ke Ki N2 )/((((s  C J + s  B1 C) L + s J + Ke Ki s C + B1) N2
Vr(s)
      2            3                       2         2                        2
 + ((s  B2 + 2 Jc s ) C L + B2 + 2 Jc s) N1 ) R + ((s  J + s B1) L + Ke Ki) N2
                 2      2   W(s)
 + (s B2 + 2 Jc s ) L N1 ), ----- = (Ki N1 N2)
                            Vr(s)
      3        2                                   2
/((((s  C J + s  B1 C) L + s J + Ke Ki s C + B1) N2
      2            3                       2         2                        2
 + ((s  B2 + 2 Jc s ) C L + B2 + 2 Jc s) N1 ) R + ((s  J + s B1) L + Ke Ki) N2
                 2      2   W1(s)         2
 + (s B2 + 2 Jc s ) L N1 ), ----- = (Ki N2 )
                            Vr(s)
      3        2                                   2
/((((s  C J + s  B1 C) L + s J + Ke Ki s C + B1) N2
      2            3                       2         2                        2
 + ((s  B2 + 2 Jc s ) C L + B2 + 2 Jc s) N1 ) R + ((s  J + s B1) L + Ke Ki) N2
                 2      2   T(s)                        2
 + (s B2 + 2 Jc s ) L N1 ), ----- = ((Ki s J + Ki B1) N2
                            Vr(s)
                         2       3        2                                   2
 + (Ki B2 + 2 Jc Ki s) N1 )/((((s  C J + s  B1 C) L + s J + Ke Ki s C + B1) N2
      2            3                       2         2                        2
 + ((s  B2 + 2 Jc s ) C L + B2 + 2 Jc s) N1 ) R + ((s  J + s B1) L + Ke Ki) N2
                 2      2
 + (s B2 + 2 Jc s ) L N1 )]]
(%i11) 

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