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backsubst-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: I0=I+EI+EIS;

Calculate

backsubst-linsolve

eq_x: px + lambda * u...

eq_y: py + lambda * u...

eq_z: pz + lambda * u...

Calculate

backsubst-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: k1*E*S-k11*ES-kc...

Calculate

backsubst-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: k1*E*S-k11*ES-kc...

Calculate

backsubst-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: k1*E*S-k11*ES-kc...

Calculate

backsubst-false-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: I0=I+EI+EIS;

Calculate

backsubst-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: I0=I+EI+EIS;

Calculate

backsubst-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: k1*E*S-k11*ES-kc...

Calculate

backsubst-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: I0=I+EI+EIS;

Calculate

backsubst-linsolve_params-linsolvewarn-true

eq1: v=kcat*ES+k2*EIS;

eq2: E0=E+ES+EI+EIS;

eq3: I0=I+EI+EIS;

Calculate

backsubst

Run Example
(%i1)eq_x: px + lambda * ux = qx + mi * vx;
(%o1)                     ux lambda + px = mi vx + qx
(%i2) eq_y: py + lambda * uy = qy + mi * vy;
(%o2)                     uy lambda + py = mi vy + qy
(%i3) eq_z: pz + lambda * uz = qz + ni * wz;
(%o3)                     uz lambda + pz = ni wz + qz
(%i4) [backsubst: false];
(%o4)                               [false]
(%i5) linsolve([eq_y, eq_z, eq_x], [mi, ni, lambda]);
            uy lambda - qy + py       uz lambda - qz + pz
(%o5) [mi = -------------------, ni = -------------------, 
                    vy                        wz
                                                  (qx - px) vy - qy vx + py vx
                                         lambda = ----------------------------]
                                                         ux vy - uy vx
(%i6) 
Run Example
eq1: v=kcat*ES+k2*EIS;
(%o1)                        v = kcat ES + k2 EIS
(%i2) eq2: E0=E+ES+EI+EIS;
(%o2)                       E0 = ES + EIS + EI + E
(%i3) eq3: I0=I+EI+EIS;
(%o3)                          I0 = I + EIS + EI
(%i4) eq4: S0=S+ES+EIS;
(%o4)                          S0 = S + ES + EIS
(%i5) eq5: k1*E*S-k11*ES-kcat*ES-k4*ES*I+k44*EIS=0;
(%o5)          k1 E S - k4 ES I - kcat ES - k11 ES + k44 EIS = 0
(%i6) eq6: k5*EI*S-k55*EIS+k4*ES*I-k44*EIS-k2*EIS=0;
(%o6)         k5 EI S + k4 ES I - k55 EIS - k44 EIS - k2 EIS = 0
(%i7) eg7: -k33*EI+k3*E*I+k55*EIS+k2*EIS-k5*EI*S=0;
(%o7)         - k5 EI S + k3 E I + k55 EIS + k2 EIS - k33 EI = 0
(%i8) eq8: k33*EI-k3*E*S+k11*ES-k1*E*S+kcat*ES=0;
(%o8)          - k3 E S - k1 E S + kcat ES + k11 ES + k33 EI = 0
(%i9) backsubst:true;
(%o9)                                true
(%i10) linsolve_params:true;
(%o10)                               true
(%i11) linsolvewarn:true;
(%o11)                               true
(%i12) eliminate([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8],[E,S,ES,EIS,EI,I]);

Unrecoverable error: Can't allocate.  Good-bye!.
Run Example
eq1: v=kcat*ES+k2*EIS;
(%o1)                        v = kcat ES + k2 EIS
(%i2) eq2: E0=E+ES+EI+EIS;
(%o2)                       E0 = ES + EIS + EI + E
(%i3) eq3: k1*E*S-k11*ES-kcat*ES-k4*ES*I+k44*EIS=0;
(%o3)          k1 E S - k4 ES I - kcat ES - k11 ES + k44 EIS = 0
(%i4) eq4: k5*EI*S-k55*EIS+k4*ES*I-k44*EIS-k2*EIS=0;
(%o4)         k5 EI S + k4 ES I - k55 EIS - k44 EIS - k2 EIS = 0
(%i5) eg5: -k33*EI+k3*E*I+k55*EIS+k2*EIS-k5*EI*S=0;
(%o5)         - k5 EI S + k3 E I + k55 EIS + k2 EIS - k33 EI = 0
(%i6) eq6: k33*EI-k3*E*S+k11*ES-k1*E*S+kcat*ES=0;
(%o6)          - k3 E S - k1 E S + kcat ES + k11 ES + k33 EI = 0
(%i7) backsubst:true;
(%o7)                                true
(%i8) linsolve_params:true;
(%o8)                                true
(%i9) linsolvewarn:true;
(%o9)                                true
(%i10) linsolve([eq1,eq2,eq3],[E0,v,I,S,kcat,k2,k1,k11,k2,k22,k3,k33,k4,k44,k5,k55]);
(%o10) [E0 = ES + EIS + EI + E, v = %r9 E S - %r4 ES I - %r11 k4 ES - %r8 ES
 + (%r3 + %r10) EIS + %r12 k1 E, I = %r11, S = %r12, 
         - %r9 E S + %r4 ES I + %r11 k4 ES + %r8 ES - %r3 EIS - %r12 k1 E
kcat = - ----------------------------------------------------------------, 
                                        ES
k2 = %r10, k1 = %r9, k11 = %r8, k22 = %r7, k3 = %r6, k33 = %r5, k4 = %r4, 
k44 = %r3, k5 = %r2, k55 = %r1]
(%i11) 

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