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What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For instance, let

f[e_] := df*(e^1 + Subscript[C, 2]*e^2 + Subscript[C, 3]*e^3 + 
 Subscript[C, 4]*e^4 + Subscript[C, 5]*e^5 + Subscript[C, 6]*e^6);

and

fe = f[e]; f1e = f'[e];
u = Simplify[e - (2/3) Series[fe/f1e, {e, 0, 4}]];
f1u = f'[u]; J = (3 f1u + f1e)/(6 f1u - 2 f1e);
v = Simplify[e - J*(f[e]/f'[e])]

In fact, when I call Simplify[] in the above piece of code, Subscript[C, 2], ..., Subscript[C, 6] must be considered as matrices. I mean, Simplify[], assume that all muliplications are Commutative, while there is no such thing for matrices. To tackle this, I also added

NonCommutativeMultiply[Subscript[C, 2], Subscript[C, 3], Subscript[C, 4], Subscript[C, 5], Subscript[C, 6]]

at the beggining of my code, but once again I could not obtain reliable outputs! For example, we must have $C_2C_3\neq C_3C_2$, or the code must not simplify $C_2C_3C_2$ to $C_2^2C_3$. I also used the way described by Mr.Wizard in http://mathematica.stackexchange.com/questions/17926/why-does-simplify-ignore-an-assumption?newsletter=1&nlcode=83941%7cfd18https://mathematica.stackexchange.com/questions/17926/why-does-simplify-ignore-an-assumption?newsletter=1&nlcode=83941%7cfd18, but once again the matrix products are commutative? So, is there any way to use Simplify or FullSimplify on matrix expressions involving matrix products to have reliable output simplified expression? Any tips or help will be fully appreciated.

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For instance, let

f[e_] := df*(e^1 + Subscript[C, 2]*e^2 + Subscript[C, 3]*e^3 + 
 Subscript[C, 4]*e^4 + Subscript[C, 5]*e^5 + Subscript[C, 6]*e^6);

and

fe = f[e]; f1e = f'[e];
u = Simplify[e - (2/3) Series[fe/f1e, {e, 0, 4}]];
f1u = f'[u]; J = (3 f1u + f1e)/(6 f1u - 2 f1e);
v = Simplify[e - J*(f[e]/f'[e])]

In fact, when I call Simplify[] in the above piece of code, Subscript[C, 2], ..., Subscript[C, 6] must be considered as matrices. I mean, Simplify[], assume that all muliplications are Commutative, while there is no such thing for matrices. To tackle this, I also added

NonCommutativeMultiply[Subscript[C, 2], Subscript[C, 3], Subscript[C, 4], Subscript[C, 5], Subscript[C, 6]]

at the beggining of my code, but once again I could not obtain reliable outputs! For example, we must have $C_2C_3\neq C_3C_2$, or the code must not simplify $C_2C_3C_2$ to $C_2^2C_3$. I also used the way described by Mr.Wizard in http://mathematica.stackexchange.com/questions/17926/why-does-simplify-ignore-an-assumption?newsletter=1&nlcode=83941%7cfd18, but once again the matrix products are commutative? So, is there any way to use Simplify or FullSimplify on matrix expressions involving matrix products to have reliable output simplified expression? Any tips or help will be fully appreciated.

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For instance, let

f[e_] := df*(e^1 + Subscript[C, 2]*e^2 + Subscript[C, 3]*e^3 + 
 Subscript[C, 4]*e^4 + Subscript[C, 5]*e^5 + Subscript[C, 6]*e^6);

and

fe = f[e]; f1e = f'[e];
u = Simplify[e - (2/3) Series[fe/f1e, {e, 0, 4}]];
f1u = f'[u]; J = (3 f1u + f1e)/(6 f1u - 2 f1e);
v = Simplify[e - J*(f[e]/f'[e])]

In fact, when I call Simplify[] in the above piece of code, Subscript[C, 2], ..., Subscript[C, 6] must be considered as matrices. I mean, Simplify[], assume that all muliplications are Commutative, while there is no such thing for matrices. To tackle this, I also added

NonCommutativeMultiply[Subscript[C, 2], Subscript[C, 3], Subscript[C, 4], Subscript[C, 5], Subscript[C, 6]]

at the beggining of my code, but once again I could not obtain reliable outputs! For example, we must have $C_2C_3\neq C_3C_2$, or the code must not simplify $C_2C_3C_2$ to $C_2^2C_3$. I also used the way described by Mr.Wizard in https://mathematica.stackexchange.com/questions/17926/why-does-simplify-ignore-an-assumption?newsletter=1&nlcode=83941%7cfd18, but once again the matrix products are commutative? So, is there any way to use Simplify or FullSimplify on matrix expressions involving matrix products to have reliable output simplified expression? Any tips or help will be fully appreciated.

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What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For instance, let

f[e_] := df*(e^1 + Subscript[C, 2]*e^2 + Subscript[C, 3]*e^3 + 
 Subscript[C, 4]*e^4 + Subscript[C, 5]*e^5 + Subscript[C, 6]*e^6);

and

fe = f[e]; f1e = f'[e];
u = Simplify[e - (2/3) Series[fe/f1e, {e, 0, 4}]];
f1u = f'[u]; J = (3 f1u + f1e)/(6 f1u - 2 f1e);
v = Simplify[e - J*(f[e]/f'[e])]

In fact, when I call Simplify[] in the above piece of code, Subscript[C, 2], ..., Subscript[C, 6] must be considered as matrices. I mean, Simplify[], assume that all muliplications are Commutative, while there is no such thing for matrices. To tackle this, I also added

NonCommutativeMultiply[Subscript[C, 2], Subscript[C, 3], Subscript[C, 4], Subscript[C, 5], Subscript[C, 6]]

at the beggining of my code, but once again I could not obtain reliable outputs! For example, we must have $C_2C_3\neq C_3C_2$, or the code must not simplify $C_2C_3C_2$ to $C_2^2C_3$. I also used the way described by Mr.Wizard in http://mathematica.stackexchange.com/questions/17926/why-does-simplify-ignore-an-assumption?newsletter=1&nlcode=83941%7cfd18, but once again the mtrixmatrix products are commutative? So, is there any way to use Simplify or FullSimplify on matrix expressions involving matrix products to have reliable output simpliedsimplified expression? Any tips or help will be fully appreciated.

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For instance, let

f[e_] := df*(e^1 + Subscript[C, 2]*e^2 + Subscript[C, 3]*e^3 + 
 Subscript[C, 4]*e^4 + Subscript[C, 5]*e^5 + Subscript[C, 6]*e^6);

and

fe = f[e]; f1e = f'[e];
u = Simplify[e - (2/3) Series[fe/f1e, {e, 0, 4}]];
f1u = f'[u]; J = (3 f1u + f1e)/(6 f1u - 2 f1e);
v = Simplify[e - J*(f[e]/f'[e])]

In fact, when I call Simplify[] in the above piece of code, Subscript[C, 2], ..., Subscript[C, 6] must be considered as matrices. I mean, Simplify[], assume that all muliplications are Commutative, while there is no such thing for matrices. To tackle this, I also added

NonCommutativeMultiply[Subscript[C, 2], Subscript[C, 3], Subscript[C, 4], Subscript[C, 5], Subscript[C, 6]]

at the beggining of my code, but once again I could not obtain reliable outputs! For example, we must have $C_2C_3\neq C_3C_2$, or the code must not simplify $C_2C_3C_2$ to $C_2^2C_3$. I also used the way described by Mr.Wizard in http://mathematica.stackexchange.com/questions/17926/why-does-simplify-ignore-an-assumption?newsletter=1&nlcode=83941%7cfd18, but once again the mtrix products are commutative? So, is there any way to use Simplify or FullSimplify on matrix expressions involving matrix products to have reliable output simplied expression? Any tips or help will be fully appreciated.

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For instance, let

f[e_] := df*(e^1 + Subscript[C, 2]*e^2 + Subscript[C, 3]*e^3 + 
 Subscript[C, 4]*e^4 + Subscript[C, 5]*e^5 + Subscript[C, 6]*e^6);

and

fe = f[e]; f1e = f'[e];
u = Simplify[e - (2/3) Series[fe/f1e, {e, 0, 4}]];
f1u = f'[u]; J = (3 f1u + f1e)/(6 f1u - 2 f1e);
v = Simplify[e - J*(f[e]/f'[e])]

In fact, when I call Simplify[] in the above piece of code, Subscript[C, 2], ..., Subscript[C, 6] must be considered as matrices. I mean, Simplify[], assume that all muliplications are Commutative, while there is no such thing for matrices. To tackle this, I also added

NonCommutativeMultiply[Subscript[C, 2], Subscript[C, 3], Subscript[C, 4], Subscript[C, 5], Subscript[C, 6]]

at the beggining of my code, but once again I could not obtain reliable outputs! For example, we must have $C_2C_3\neq C_3C_2$, or the code must not simplify $C_2C_3C_2$ to $C_2^2C_3$. I also used the way described by Mr.Wizard in http://mathematica.stackexchange.com/questions/17926/why-does-simplify-ignore-an-assumption?newsletter=1&nlcode=83941%7cfd18, but once again the matrix products are commutative? So, is there any way to use Simplify or FullSimplify on matrix expressions involving matrix products to have reliable output simplified expression? Any tips or help will be fully appreciated.

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How Simplify and Assume can be combined on matrix products?

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For instance, let

f[e_] := df*(e^1 + Subscript[C, 2]*e^2 + Subscript[C, 3]*e^3 + 
 Subscript[C, 4]*e^4 + Subscript[C, 5]*e^5 + Subscript[C, 6]*e^6);

and

fe = f[e]; f1e = f'[e];
u = Simplify[e - (2/3) Series[fe/f1e, {e, 0, 4}]];
f1u = f'[u]; J = (3 f1u + f1e)/(6 f1u - 2 f1e);
v = Simplify[e - J*(f[e]/f'[e])]

In fact, when I call Simplify[] in the above piece of code, Subscript[C, 2], ..., Subscript[C, 6] must be considered as matrices. I mean, Simplify[], assume that all muliplications are Commutative, while there is no such thing for matrices. To tackle this, I also added

NonCommutativeMultiply[Subscript[C, 2], Subscript[C, 3], Subscript[C, 4], Subscript[C, 5], Subscript[C, 6]]

at the beggining of my code, but once again I could not obtain reliable outputs! For example, we must have $C_2C_3\neq C_3C_2$, or the code must not simplify $C_2C_3C_2$ to $C_2^2C_3$. I also used the way described by Mr.Wizard in http://mathematica.stackexchange.com/questions/17926/why-does-simplify-ignore-an-assumption?newsletter=1&nlcode=83941%7cfd18, but once again the mtrix products are commutative? So, is there any way to use Simplify or FullSimplify on matrix expressions involving matrix products to have reliable output simplied expression? Any tips or help will be fully appreciated.