Software for long and repetitive algebra

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A user is seeking software recommendations to assist with a Chemical Engineering problem involving the design of a reactor characterized by a 5th order polynomial equation. The user finds deriving the equation from first principles time-consuming due to the complexity of multiplying various constants. They are looking for a program that allows them to define groups of constants and perform manipulations on these groups, such as calculating products or powers, to streamline their calculations. A suggestion is made to explore general-purpose numerical analysis software, with a reference to a Wikipedia list of such tools as a potential resource for finding suitable options.
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I hope this is the correct forum, I have read most of the rules and it seemed the best place for this post!

I have a Chemical Engineering problem, in the design of a reactor which has a design equation which I know to be a 5th order polynomial. Deriving this from first principles takes a lot of time, with multiplication of a long list of constants in varying orders to find the coefficients of the quintic equation.

Is there any program anyone can recommend where I can specify groups of constants for example J= k1*k2*k3 and M= k4*k5*k6 then ask it to produce the result of some manipulation on J and M, J*M or JM^5? I have simplified this down to explain but I have a long list of these groupings and if such software existed it would save a lot of time!

Thanks
 
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