Advanced Search

Ronan

1506 Reputation

16 Badges

14 years, 224 days
East Grinstead, United Kingdom
Contact Ronan

MaplePrimes Activity


These are answers submitted by Ronan

Sylvester Matrix...

Ronan 1506
October 13 2012
0 1

These 2 equations can be solved using the Sylvester Maxtrx technique. Have annotated the worhsheet to try and explain.

Would be interesting to see other techniques for solving them.
 

restart

with(LinearAlgebra)

 

eq1 := (1/4)*p*g*A*B+(1/2)*g^2*A*B*h-(7/12)*p*g*A*h+(5/6)*A^2*h^2+(13/12)*A^2*h-(1/3)*p*A^2+(5/12)*g*A-(3/2)*g^2*A-(1/4)*p*A^2*h*c*g^2+(1/4)*p*g*A*d*h-(1/12)*p*g^2+(3/2)*A^3*h^3+(1/4)*p*A^2*h^2*d+(1/4)*p*A^2*h^2*B+(1/4)*p*A^2*h*B+(1/4)*A^2*h*c*g^2-(1/4)*p*A*c*g^3-(1/4)*g*A*B*h+(1/4)*g*A*d*h+(1/3)*A^2-(13/12)*p*A^2*h+(1/4)*p*g*A*B*h-(5/12)*p*g*A-(1/4)*g*A*B-(1/2)*g^2*A*B+(1/4)*A*c*g^3-(5/6)*p*A^2*h^2+(7/12)*g*A*h-(1/4)*A^2*h^2*d-(1/4)*A^2*h*B+(1/2)*g^2*A*B+(1/12)*g^2+(1/2)*g*A^2*h^2-(1/2)*g^4*A*c-2*g*A^2*h+(1/2)*A*d*h-(1/4)*A^2*h^2*B

NULL

NULL

eq2 := -(5/6)*A*c*g*h^3*B*d-4*h^3*c*g*A-(11/3)*c^2*g^4*h-9*A*c*g*h^2+7*h*B*c*g^2-6*A*c*g*h+(10/3)*c^2*g^4*h*B+(1/6)*h^2*B^4-(10/3)*c^2*g^3*h^2*A+(7/6)*B^2*h^3*d+3*B*c*g^2-A*c*g-2*h^2*c*g^2-(7/6)*d^2*h+(7/3)*B^2*h^3*d+(29/12)*d^2*h^3*B-h^4*c*A^2-c*A^2*h^2-B*h^3*d+(3/2)*c*d*g^2-B^2*c*g^2-3*d*h*B-3*d*h^2*B+(1/6)*B^3*h^2*d+(7/6)*d*B^2*h+(29/12)*d^2*h^2*B-4*h*c*g^2-(5/6)*B^2*h^3*A*c*g-(1/6)*B^2*c*g^2*d*h^2-(5/6)*B^2*h^2*A*c*g+(5/6)*B*c^2*g^3*A*h^2-(23/4)*d*h^2*B*c*g^2+(14/3)*d*h^3*A*c*g-(59/12)*d*h*B*c*g^2+(19/6)*d*h^2*A*c*g+(7/2)*B*A*c*g*h+(17/2)*B*A*c*g*h^2+5*B*h^3*A*c*g+(1/12)*B^4*h+(5/4)*d^3*h^3-(3/2)*c^3*g^6+(1/12)*h^3*B^4-(7/6)*h^3*d^2-(7/3)*d^2*h^2-B*d-2*c*g^2-4*c^2*g^4+(1/2)*d*h^4*c*A^2+(1/2)*B*h^4*c*A^2+(1/2)*B*h^3*c*A^2+(5/6)*A^2*c^2*g^2*h^3-(1/6)*B^3*c*g^2*h^2+(1/12)*h*c^2*g^4*B^2-(1/6)*B^3*c*g^2*h+(17/4)*d*h*c^2*g^4-4*d^2*h^2*c*g^2+(31/6)*d*h^2*c*g^2-(9/2)*c^2*g^3*A*h+(17/3)*d*h*c*g^2+4*B*h^2*c*g^2-(17/6)*h*B^2*c*g^2-(11/6)*B^2*h^2*c*g^2+(5/2)*c^2*g^4*B+(1/12)*d^2*h^3*B^2+(1/6)*B^3*h^3*d-2*c*A^2*h^3

NULL

NULL

Sylvesterg := SylvesterMatrix(eq1, eq2, h);

PolySylg := sort(LinearAlgebra:-Determinant(Sylvesterg), g);

``

Alternatively a Polynomial in h can be made

 

NULL

You need Numerical values for A,B,c,d,p to solve the polynomial

Then back substitute the roots into one of the equations to get the corresponding values of g or h.

 

Test Values

A := 3/2; 1; B := 6/5; 1; c := 9/7; 1; d := 4/3; -1; p := 1/2

Digits := 20;

sort(PolySylg, g)

G := [fsolve(PolySylg, g)];

NULL

Back Substitution

NULL

for i to nops(G) do g := G[i]; H1[i] := fsolve(eq1, h) end do

 

for i to nops(G) do g := G[i]; H2[i] := fsolve(eq2, h) end do

NULL


Download 2_non-linear_equatio.mw

I would suggest you contact your supplie...

Ronan 1506
October 08 2012
0 0

I would suggest you contact your supplier. I purchased a home use license of maple 15 early march and got a free upgrade to maple 16 when it was released. I just purchesed the home user license for maple 16 last week. I suppose by the time maple 17 and sim 7 are released I will need to pay something to get an upgrade.

assign works now...

Ronan 1506
May 22 2012
0 0

Thank you all for replys and comments. I did get assign to work. there was a duplicate entry ie 2 rows the same which caused the problem. To clarify a some of the ponts raised. The rows are dependant on the previous rows. I choose a matrix because in a previous post Iwas told lists can be inefficant. Also athe matrix is visually easy to read I find. What I posed was just a short made up example. Thr algsubs on the equations is to shorten them as the can go on for screenful after screenfull. At the end of the assembling the equations I end uo with a 4x4 matrix whose determinant multiplies out to a 20th order polynomial. It is at this point I am using the assign to the valuse saved in the store matrix. I shall experiment with the

"#If you prefer assignment then you can use the two elementwise operations assign~ and  =~  : assign~(store[..,1]=~store[..,2]): a1,CX3,S1; "

At present I am using a for i to 100 do loop.

First 7 8 9 Page 9 of 9