The substitutions that I have posted above work as desired only sequentially. And I find easier to write them sequentially. I.e. adding one substitution at a time,  and find from the result which is the next syntactic unit suitable for substitution trying to approach the expected result, and avoid any undo of the the previous substitution steps.

The substitutions that I have posted above work as desired only sequentially. And I find easier to write them sequentially. I.e. adding one substitution at a time,  and find from the result which is the next syntactic unit suitable for substitution trying to approach the expected result, and avoid any undo of the the previous substitution steps.

I do not need pictures and ccs' files, and it would be a waste of space.

In fact, long time ago I have asked to Will that full thread contents could be saved in text form. Or at least, in print friendly form. I am still waiting...

Thanks to you it was done. But it is basically a consequence of the pass of time. Nevertheless, 999 is also a nice number.

M := matrix(2,2,[(q-b)*f[x,x]*eta(c)/(f(x)-c)-(q-b)*(f[x]-q)*
eta(c)/(f(x)-c)^2*f[x],(q-b)*(f[x]-q)*eta[c]/(f(x)-c)+(q-b)*
(f[x]-q)*eta(c)/(f(x)-c)^2,1+(f[x]-q)*eta(c)/(f(x)-c)-(q-b)*
eta(c)/(f(x)-c),0]):

subs(q-b=-mu*(f(x)-c),eta(c)=lambda*(f(x)-c)/(f[x]-q),
f(x)-c=eta*(f[x]-q),eval(M));
  
        [-mu eta f[x, x] lambda + mu lambda f[x] ,

        -mu (f[x] - q) eta[c] - lambda mu]

        [1 + lambda + mu eta lambda , 0]

with a factor lambda of difference with your handwritten matrix. May be a typo somewhere.

In fact, my available time runs out much earlier than my patience...

M := matrix(2,2,[(q-b)*f[x,x]*eta(c)/(f(x)-c)-(q-b)*(f[x]-q)*
eta(c)/(f(x)-c)^2*f[x],(q-b)*(f[x]-q)*eta[c]/(f(x)-c)+(q-b)*
(f[x]-q)*eta(c)/(f(x)-c)^2,1+(f[x]-q)*eta(c)/(f(x)-c)-(q-b)*
eta(c)/(f(x)-c),0]):

subs(q-b=-mu*(f(x)-c),eta(c)=lambda*(f(x)-c)/(f[x]-q),
f(x)-c=eta*(f[x]-q),eval(M));
  
        [-mu eta f[x, x] lambda + mu lambda f[x] ,

        -mu (f[x] - q) eta[c] - lambda mu]

        [1 + lambda + mu eta lambda , 0]

with a factor lambda of difference with your handwritten matrix. May be a typo somewhere.

In fact, my available time runs out much earlier than my patience...

It is hidden as the algoritms and the code are mostly undocumented. But tracing what Maple does provides a further close up to where the problem may lay:

infolevel[all]:=5:
trace(solve):
trace(`factor/polynom`):
trace(radnormal):
trace(SolveTools:-Transformers:-LinearRational):
printlevel:=10:solve( -a + sqrt(a^2 - 4*x) < 0, x) assuming a>0;
...

                2       1/2
      [[{-a + (a  - 4 x)   }, {}, {x}, {}, true, false, 1, {x}]]

<-- exit SolveTools:-Transformers:-LinearRational:-ModuleApply (now in solve/rec2) = [[{-a+(a^2-4*x)^(1/2)}, {}, {x}, {}, true, false, 1, {x}]]}
{--> enter SolveTools:-Transformers:-LinearRational:-ModuleApply, args = [[{-a+_S000001, a^2-4*x-_S000001^2}, {1 <> 0}, {x, _S000001}, [], true, false, 1, {x}]]

                         SS := table([0 = 0])


                           2                 2
  sys := [{-a + _S000001, a  - 4 x - _S000001 }, {1 <> 0},

        {x, _S000001}, [], true, false, 1, {x}]

LinearRational:   solving for linear equation in   _S000001
LinearRational:   solving for linear equation in   x

      [{}, {}, {}, [{x = 0, _S000001 = a}], true, false, 1, {x}]


     [[{}, {}, {}, [{x = 0, _S000001 = a}], true, false, 1, {x}]]

<-- exit SolveTools:-Transformers:-LinearRational:-ModuleApply (now in solve/rec/radical) = [[{}, {}, {}, [{x = 0, _S000001 = a}], true, false, 1, {x}]]}
{--> enter factor/polynom, args = a-1/63245986*O*O*a
factor/polynom:   polynomial factorization: number of terms   2

                           c := 1/63245986

                                 true

                            v := {O, O, a}

                                a := O

                                l := 0

                                v := a

<-- exit factor/polynom (now in factor/factor) = 1/63245986*a*(63245986-O*O)}

                                       2
                                      a
                       r := [{x < 0, ---- < x}]
                                      4

...

I.e. sounds to me that the problem is somehow related to 'factor/polynom' (may lay in a routine it calls). But I have no idea on the factorization algorithm for further digging into this stuff. E.g. I wonder from where this number 1/63245986 arise.

It is hidden as the algoritms and the code are mostly undocumented. But tracing what Maple does provides a further close up to where the problem may lay:

infolevel[all]:=5:
trace(solve):
trace(`factor/polynom`):
trace(radnormal):
trace(SolveTools:-Transformers:-LinearRational):
printlevel:=10:solve( -a + sqrt(a^2 - 4*x) < 0, x) assuming a>0;
...

                2       1/2
      [[{-a + (a  - 4 x)   }, {}, {x}, {}, true, false, 1, {x}]]

<-- exit SolveTools:-Transformers:-LinearRational:-ModuleApply (now in solve/rec2) = [[{-a+(a^2-4*x)^(1/2)}, {}, {x}, {}, true, false, 1, {x}]]}
{--> enter SolveTools:-Transformers:-LinearRational:-ModuleApply, args = [[{-a+_S000001, a^2-4*x-_S000001^2}, {1 <> 0}, {x, _S000001}, [], true, false, 1, {x}]]

                         SS := table([0 = 0])


                           2                 2
  sys := [{-a + _S000001, a  - 4 x - _S000001 }, {1 <> 0},

        {x, _S000001}, [], true, false, 1, {x}]

LinearRational:   solving for linear equation in   _S000001
LinearRational:   solving for linear equation in   x

      [{}, {}, {}, [{x = 0, _S000001 = a}], true, false, 1, {x}]


     [[{}, {}, {}, [{x = 0, _S000001 = a}], true, false, 1, {x}]]

<-- exit SolveTools:-Transformers:-LinearRational:-ModuleApply (now in solve/rec/radical) = [[{}, {}, {}, [{x = 0, _S000001 = a}], true, false, 1, {x}]]}
{--> enter factor/polynom, args = a-1/63245986*O*O*a
factor/polynom:   polynomial factorization: number of terms   2

                           c := 1/63245986

                                 true

                            v := {O, O, a}

                                a := O

                                l := 0

                                v := a

<-- exit factor/polynom (now in factor/factor) = 1/63245986*a*(63245986-O*O)}

                                       2
                                      a
                       r := [{x < 0, ---- < x}]
                                      4

...

I.e. sounds to me that the problem is somehow related to 'factor/polynom' (may lay in a routine it calls). But I have no idea on the factorization algorithm for further digging into this stuff. E.g. I wonder from where this number 1/63245986 arise.

Exactly, in my own disk. Google advanced search could also be used but, as far as I know it, it is not as efficient in selecting links by date as my file manager at ordering by date stored thread files. 

Nevertheless, I agree. A google search box would help a lot.

It is the same, just with changed names, if you want a similar substitution.

It is the same, just with changed names, if you want a similar substitution.

I think that the assumption makes no difference here:

solve(ineq2,x);
                     RealRange(Open(0), infinity)

I think that the assumption makes no difference here:

solve(ineq2,x);
                     RealRange(Open(0), infinity)

It depends on what each user needs. E.g. for numerical, concrete computations, 'LinearAlgebra' is probably superior to 'linalg'. But for some symbolic manipulations 'linalg' may still be better (or less bad).

It depends on what each user needs. E.g. for numerical, concrete computations, 'LinearAlgebra' is probably superior to 'linalg'. But for some symbolic manipulations 'linalg' may still be better (or less bad).

The pre, code, and maple tags

I do not know of a useful list-by-date like option in Mapleprimes' search.

I find it much simpler to store and search  threads locally.