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Question: 95% of memory occupied and several hours

Question:95% of memory occupied and several hours

Gabriel Barcellos 80 Maple 2023
performance fsolve
March 13 2026
0

Objective: Solve a system of two equations.

Obstacle: Generating these two equations depends on millions of previous combinations as well as derivatives.

In other words, we've reached the maximum limit that Maple on my computer can handle.

What would be better, to leave the equations aside or to upgrade my computer?

> 

restart
> 

with(plots)
> 

with(linalg)
> 

H01 := -gamma11*S11-gamma12*S12-gamma13*S13-gamma14*S14-gamma15*S15-gamma16*S16-gamma17*S17-gamma18*S18-gamma19*S19-gamma110*S110-gamma111*S111-gamma112*S112-eta1*(S11^2+S110^2+S111^2+S112^2+S12^2+S13^2+S14^2+S15^2+S16^2+S17^2+S18^2+S19^2)-J1*(S11*S12+S12*S13+S13*S14+S14*S18+S18*S112+S112*S111+S111*S110+S110*S19+S19*S15+S15*S11+S16*(S12+S110+S15+S17)+S17*(S113+S111+S18))
> 

H02 := -gamma21*S21-gamma22*S22-gamma23*S23-gamma24*S24-gamma25*S25-gamma26*S26-gamma27*S27-gamma28*S28-gamma29*S29-gamma210*S210-gamma211*S211-gamma212*S212-eta2*(S21^2+S210^2+S211^2+S212^2+S22^2+S23^2+S24^2+S25^2+S26^2+S27^2+S28^2+S29^2)-J1*(S21*S22+S22*S23+S23*S24+S24*S28+S28*S212+S212*S211+S211*S210+S210*S29+S29*S25+S25*S21+S26*(S22+S210+S25+S27)+S27*(S213+S211+S28))
> 

Z01 := exp(-beta*H01)
> 

Z01 := add(add(add(add(add(add(add(add(add(add(add(add(Z01, S11 = [-2, -1, 0, 1, 2]), S12 = [-2, -1, 0, 1, 2]), S13 = [-2, -1, 0, 1, 2]), S14 = [-2, -1, 0, 1, 2]), S15 = [-2, -1, 0, 1, 2]), S16 = [-2, -1, 0, 1, 2]), S17 = [-2, -1, 0, 1, 2]), S18 = [-2, -1, 0, 1, 2]), S19 = [-2, -1, 0, 1, 2]), S110 = [-2, -1, 0, 1, 2]), S111 = [-2, -1, 0, 1, 2]), S112 = [-2, -1, 0, 1, 2])
> 

NULL
> 

Z02 := exp(-beta*H02)
> 

Z02 := add(add(add(add(add(add(add(add(add(add(add(add(Z02, S21 = [-2, -1, 0, 1, 2]), S22 = [-2, -1, 0, 1, 2]), S23 = [-2, -1, 0, 1, 2]), S24 = [-2, -1, 0, 1, 2]), S25 = [-2, -1, 0, 1, 2]), S26 = [-2, -1, 0, 1, 2]), S27 = [-2, -1, 0, 1, 2]), S28 = [-2, -1, 0, 1, 2]), S29 = [-2, -1, 0, 1, 2]), S210 = [-2, -1, 0, 1, 2]), S211 = [-2, -1, 0, 1, 2]), S212 = [-2, -1, 0, 1, 2])
> 

NULL
> 

G0 := -(1/24)*N*ln(Z01*Z02)/beta
> 

NULL
> 

m01 := -24*(diff(G0, gamma11))/N
> 

m02 := -24*(diff(G0, gamma21))/N
> 

NULL
> 

beta := 11.605/T; gamma11 := 2*J1*m1+2*J2*m2; eta1 := Delta; gamma21 := 2*J1*m2+2*J2*m1; eta2 := Delta; gamma12 := J1*m1+2*J2*m2; gamma22 := J1*m2+2*J2*m1; gamma13 := J1*m1+2*J2*m2; gamma23 := J1*m2+2*J2*m1; gamma14 := 2*J1*m1+2*J2*m2; gamma24 := 2*J1*m2+2*J2*m1; gamma15 := J1*m1+2*J2*m2; gamma25 := J1*m2+2*J2*m1; gamma16 := 2*J2*m2; gamma26 := 2*J2*m1; gamma17 := 2*J2*m2; gamma27 := 2*J2*m1; gamma18 := J1*m1+2*J2*m2; gamma28 := J1*m2+2*J2*m1; gamma19 := 2*J1*m1+2*J2*m2; gamma29 := 2*J1*m2+2*J2*m1; gamma110 := J1*m1+2*J2*m2; gamma210 := J1*m2+2*J2*m1; gamma111 := J1*m1+2*J2*m2; gamma211 := J1*m2+2*J2*m1; gamma112 := 2*J1*m1+2*J2*m2; gamma212 := 2*J1*m2+2*J2*m1
> 

NULL
> 

eq1 := m1 = m01
> 

eq2 := m2 = m02
> 

fsolve(subs(J1 = 2*.83, N = 1, J2 = -2*.58, Delta = 0, m1 = 0.1e-1, {eq1, eq2}), {T, m2}, T = 0 .. 220, m2 = -.1 .. .1)
> 

fsolve(subs(J1 = 2*.83, N = 1, J2 = -2*.58, T = 1, Delta = 0, {eq1, eq2}), {m1, m2}, m1 = -5 .. 5, m2 = -5 .. 5)

{m1 = 2.000000000, m2 = -2.000000000}

 (1)

NULL

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