multivars eq ?

multivariable

asked 2024-09-27 10:01:26 +0100

ortollj
1341 ●23 ●63 ●98

how do I get SageMath to give me both solutions?

# R.<theta_0,theta_1>=QQ[]
thetaVars=var('theta_0','theta_1')
aVars=var(['a_00', 'a_01', 'a_10', 'a_11'])
eqL=[]
eqL.append(3*theta_0^2 + 9*theta_0*theta_1 + 5*theta_1^2 == \
           a_00*theta_0^2 + a_01*theta_0*theta_1 + a_10*theta_0*theta_1 + a_11*theta_1^2)
eqL.append(-a_01*a_10 + a_00*a_11 == 1)

for eq in eqL :
    show(eq)
#how do I get SageMath to give me both solutions?    
# 2 solutions 
#s0=a_00==3,a_01==7,a_10==2,a_11==5
#s1=a_00==3,a_01==2,a_10==7,a_11==5

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Call solve(eqL,aVars) ?

Max Alekseyev ( 2024-09-27 12:50:16 +0100 )edit

W11,WSL UBUNTU SAGEMATH 10.2 solve(eqL,aVars) gives me something complicated, extract below:

[[a_00 == -1/2*((r1 + r2 - 9)*theta_0*theta_1 - 3*theta_0^2 - 5*theta_1^2 + sqrt(-6*(r1 + r2 - 9)*theta_0^3*theta_1 + (r1^2 - 2*(r1 + 9)*r2 + r2^2 - 18*r1 + 107)*theta_0^2*theta_1^2 - 10*(r1 + r2 - 9)*theta_0*theta_1^3 + 9*theta_0^4 + 25*theta_1^4))/theta_0^2, a_01 == r1, a_10 == r2, a_11 == -1/2*((r1 + r2 - 9)*theta_0*theta_1 - 3*theta_0^2 - 5*theta_1^2 - sqrt(-6*(r1 + r2 - 9)*theta_0^3*theta_1 + (r1^2 - 2*(r1 + 9)*r2 + r2^2 - 18*r1 + 107)*theta_0^2*theta_1^2 - 10*(r1 + r2 - 9)*theta_0*theta_1^3 + 9*theta_0^4 + 25*theta_1^4))/theta_1^2], [a_00 == -1/2*((r3 + r4 - 9)*theta_0*theta_1 - 3*theta_0^2 - 5*theta_1^2 - sqrt(-6*(r3 + r4 - 9)*theta_0^3*theta_1 + (r3^2 -

ortollj ( 2024-09-27 13:17:13 +0100 )edit

human can solve this 2 equations very easily for aVars

ortollj ( 2024-09-27 13:38:53 +0100 )edit

add a comment

R.<theta_0,theta_1> = SR[] aVars=var(['a_00', 'a_01', 'a_10', 'a_11']) eqL=[] eqL.extend( ( 3*theta_0^2 + 9*theta_0*theta_1 + 5*theta_1^2 - \ (a_00*theta_0^2 + a_01*theta_0*theta_1 + a_10*theta_0*theta_1 + a_11*theta_1^2) ).coefficients() ) eqL.append(-a_01*a_10 + a_00*a_11 == 1) show( solve(eqL,aVars) )

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