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Question: How to re-write an expression based on two other expressions?

Question:How to re-write an expression based on two other expressions?

Katatonia 65 Maple
linear-combination
June 24 2021
1

Suppose I have an expression denoted by Q3. I also have two other expressions such as Q1, Q2. I wanna write Q3 as a convex combination of Q1 and Q2, for example, Q3 = gamma*Q1 + (1-gamma)*Q2 where 0<gamma<1. How is it possible?

Q3 = 1/(v)*(    v*pi-  (   (1-alpha*gamma) *pi * r[0]  - (1-pi)*B*alpha  + (gamma*pi + (1-pi)*h)    )   )

 

Q2 = 1/v *(  v*pi    -  (   h - (1-pi)*B   )      )

 

Q1 = 1/v*(   v*pi     - (   pi*r[0]+ (1-pi)*h  )   )

 

I am not sure if is possible to write Q3 = gamma*Q1 + (1-gamma)*Q2 and it might be something like Q3 = gamma*Q1 + (1-gamma)*Q2 + constant

 

Thanks
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