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Solve a parametric system of linear equations in Wolfram|Alpha?

Posted 1 month ago
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Hi everyone, I'd like to solve a (symbolic) system of linear equations in Wolfram Alpha in 4 variables (A,B,C,D), with 3 additional parameters (Y,V,T). I gave this command, but Wolfram Alpha doesn't understand what to do:

solve A*T^5+B*T^4+C*T^3+D*T^2=0, 5*A*T^4+4*B*T^3+3*C*T^2+2*D*T=0, A/6*T^6+B/5*T^5+C/4*T^4+D/3*T^3=-V, 1/42*A*T^7+1/30*B*T^6+1/20*C*T^5+1/12*D*T^4=Y for A,B,C,D

Instead, if I type a similar command for a similar system but with 3 variables A,B,C, for example

solve A*T^5+B*T^4+C*T^3=Y,5*A*T^4+4*B*T^3+3*C*T^2=V,20*A*T^3+12*B*T^2+6*C*T=0 for A,B,C

Wolphram Alpha understands and provides a parametric solution.

Do you know where the problem is? I think the two commands are similar, so I cannot understan why it doesn't work.

Please let me know if you have any ideas. Cheers,

E.

4 Replies
Posted 1 month ago

In Mathematica can be solved if formulated as: Solve[{AT^5+BT^4+CT^3+DT^2==0, 5AT^4+4BT^3+3CT^2+2DT==0, A/6T^6+B/5T^5+C/4T^4+D/3T^3==-V, 1/42AT^7+1/30BT^6+1/20CT^5+1/12DT^4==Y}, {A,B,C,D }]

Note that AT^5 could reference a variable AT instead of referring to A and T.

Between A and T, B and T etc. there is a * which has not been copied here, I need to insert a space here to make it appear.

In any case I don't have Mathematica ... Is there a way to solve it with Wolfram Alpha?

Does Mathematica find a solution?

solve A* T^5+B* T^4+C* T^3+D* T^2=0, 5* A* T^4+4* B* T^3+3* C* T^2+2* D* T=0, A/6* T^6+B/5* T^5+C/4* T^4+D/3* T^3=-V, 1/42* A* T^7+1/30* B* T^6+1/20* C* T^5+1/12* D* T^4=Y for A,B,C,D

Thanks

E.

Posted 1 month ago

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That is what I get. I assume there is a minor error in your Alpha command, as I don't have access to Alpha I can't figure out in more detail.

Ok, thanks, I'll verify if it works. It seems very strange to me that I cannot use Wolfram Alpha to solve it.

Thanks,

E.

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