Symbolic calculation with solve command

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Ali Kiral
Ali Kiral 2025-5-30
评论： Ali Kiral 2025-6-1
Ran in:
I want MATLAB to express k1 k2 and k3 in terms of r through the following code but I can't get any useful result. The equations are pretty nonlinear. Is that the reason?
syms k1 k2 k3 r
eqns = [2*r*k3 + r*k2+r*k1 == 6, 7*r*k1 + 6*r*k2+2*r^2*k2*k3-r*k3 == 48, 8*r*k1-r*k2-r*k3-2*r^2*k1*k2+5*r^2*k1*k3+2*r^3*k1*k2*k3==63];
S = solve(eqns,[k1 k2 k3])
S = struct with fields:
k1: [4×1 sym] k2: [4×1 sym] k3: [4×1 sym]
S.k1
ans = 
S.k2
ans = 
S.k3
ans = 
[SL: formatted code as code and executed it. I also displayed each field of S.]

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采纳的回答

Torsten
Torsten 2025-5-30
Use
S = solve(eqns,[k1 k2 k3],'MaxDegree',4)
instead of
S = solve(eqns,[k1 k2 k3])
  1 个评论
Walter Roberson
Walter Roberson 2025-5-30
编辑：Walter Roberson 2025-5-30
Ran in:
Be warned that the form without the root() expression is pretty long.
syms k1 k2 k3 r
eqns = [2*r*k3 + r*k2+r*k1 == 6, 7*r*k1 + 6*r*k2+2*r^2*k2*k3-r*k3 == 48, 8*r*k1-r*k2-r*k3-2*r^2*k1*k2+5*r^2*k1*k3+2*r^3*k1*k2*k3==63];
S = solve(eqns, [k1 k2 k3], 'maxdegree', 4)
S = struct with fields:
k1: [4×1 sym] k2: [4×1 sym] k3: [4×1 sym]
S.k1
ans = 
char(S.k1(1))
ans = '-(96*r^2*(1/(40*r) + (9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2)/(6*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/6)) + (- (23213*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2))/(5120*r^4) - 9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2))/(25*r^2) - (117459*6^(1/2)*(3*3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2) + 1302896879/(2048000*r^6))^(1/2))/(16000*r^3))^(1/2)/(6*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/6)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/4)))^2 - 160*r^3*(1/(40*r) + (9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2)/(6*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/6)) + (- (23213*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2))/(5120*r^4) - 9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2))/(25*r^2) - (117459*6^(1/2)*(3*3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2) + 1302896879/(2048000*r^6))^(1/2))/(16000*r^3))^(1/2)/(6*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/6)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/4)))^3 - 773*r*(1/(40*r) + (9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2)/(6*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/6)) + (- (23213*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2))/(5120*r^4) - 9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/2))/(25*r^2) - (117459*6^(1/2)*(3*3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2) + 1302896879/(2048000*r^6))^(1/2))/(16000*r^3))^(1/2)/(6*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/6)*(9*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(2/3) - (1257*((3^(1/2)*(245367007511193/(16384000000*r^12))^(1/2))/18 + 1302896879/(110592000*r^6))^(1/3))/(50*r^2) + 23213/(5120*r^4))^(1/4))) + 42)/(27*r)'

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更多回答（1 个）

Steven Lord
Steven Lord 2025-5-30
Ran in:
If you object to the presence of root() in the solutions, since you're using release R2023a or later you can use the rewrite function with the "expandroot" option. You could also try using vpa on that result to try to make it a little easier to read, but the expressions are long and complicated enough that it doesn't help that much IMO.
syms k1 k2 k3 r
eqns = [2*r*k3 + r*k2+r*k1 == 6, 7*r*k1 + 6*r*k2+2*r^2*k2*k3-r*k3 == 48, 8*r*k1-r*k2-r*k3-2*r^2*k1*k2+5*r^2*k1*k3+2*r^3*k1*k2*k3==63];
S = solve(eqns,[k1 k2 k3]);
rewrittenExpression = rewrite(S.k1, "expandroot")
rewrittenExpression = 
vpa(rewrittenExpression, 4)
ans = 
●
If you don't want to have it written in terms of those intermediate sub-expressions you can change one of the preferences, but again that makes the expression look even more complicated.
previousValue = sympref('AbbreviateOutput',false);
vpa(rewrittenExpression, 4)
ans = 
sympref('AbbreviateOutput',previousValue); % reset the preference
  1 个评论
Ali Kiral
Ali Kiral 2025-6-1
Thank you Steve! Equations are already horribly non-linear and I wasn't expecting a simple expression anyway

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