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Mathematics Algebra Calculus Wolfram Language

How to realize this simplification canceling each term by a factor

Jacques Ou

Posted 3 years ago

eq1 = 1/(2 (-1 + A3) A4 v0) ((-1 + 2 A3 - A4) v0 SuperStar[(Subscript[c, m])] - (-1 + A4) (-A1 A3 + Imax + Sqrt[(-A1 A3 + Imax)^2 + 2 (A2 A3 - Imax) v0 SuperStar[(Subscript[c, m])] + v0^2 (SuperStar[(Subscript[c, m])])^2])) cancel each term in eq1 with v0 c_m^*

eq1 = 1/(2 (-1 + 
             A3) A4 v0) ((-1 + 2 A3 - A4) v0 SuperStar[(Subscript[c, 
              m])] - (-1 + A4) (-A1 A3 + Imax + 
               Sqrt[(-A1 A3 + Imax)^2 + 
                2 (A2 A3 - Imax) v0 SuperStar[(Subscript[c, m])] + 
                v0^2 (SuperStar[(Subscript[c, m])])^2]))

cancel each term in eq1 with

 v0 c_m^*

POSTED BY: Jacques Ou

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Bill Nelson

Posted 3 years ago

I am sorry that I did not understand what you expected. If I look at eq1 then the denominator is 2 (-1+A3) A4 v0 and that does not contain v0 c_m* Can you show what the result should be after cancelling? Perhaps that will help me understand.

POSTED BY: Bill Nelson

Bill Nelson

Posted 3 years ago

Does this do what you want? Simplify[eq1,v0 (SuperStar[(Subscript[c, m])])==1] which returns -(1 - 2A3 + A1A3 + A4 - A1A3A4 - Imax + A4Imax + (-1 + A4)Sqrt[2A2A3 + A1^2A3^2 + (-1 + Imax)^2 - 2A1A3Imax])/(2(-1 + A3)A4v0) Or this eq1/.{v0 (SuperStar[(Subscript[c, m])])->1,v0^2 (SuperStar[(Subscript[c, m])])^2->1} which returns this (-1 + 2A3 - A4 - (-1 + A4)(-(A1A3) + Imax + Sqrt[1 + 2(A2A3 - Imax) + (-(A1A3) + Imax)^2]))/(2(-1 + A3)A4v0)

Does this do what you want?

Simplify[eq1,v0 (SuperStar[(Subscript[c, m])])==1]

which returns

-(1 - 2*A3 + A1*A3 + A4 - A1*A3*A4 - Imax + A4*Imax + (-1 + A4)*Sqrt[2*A2*A3 +
A1^2*A3^2 + (-1 + Imax)^2 - 2*A1*A3*Imax])/(2*(-1 + A3)*A4*v0)

Or this

eq1/.{v0 (SuperStar[(Subscript[c, m])])->1,v0^2 (SuperStar[(Subscript[c, m])])^2->1}

which returns this

(-1 + 2*A3 - A4 - (-1 + A4)*(-(A1*A3) + Imax + Sqrt[1 + 2*(A2*A3 - Imax) +
(-(A1*A3) + Imax)^2]))/(2*(-1 + A3)*A4*v0)

POSTED BY: Bill Nelson

Jacques Ou

Posted 3 years ago

This is not expected. My expectation is Canceling v0 c_m^* from the numerator and the denominator of eq1.

POSTED BY: Jacques Ou

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