_Solver_min.ipynb

Kernel: Python 3 (system-wide)

import sympy as sp
import sympy.plotting as splt
x = sp.Symbol('x')

K = 10
eq1 = (2*x)**2/(0.1-x)**2-0.0753
res = sp.solve([eq1], [x], prec = 20)
print("Lösungen:")
res

Lösungen:

[(-0.0159022832155449,), (0.0120650472484646,)]

x1=res[1][0]
sp.re(x1)

$\displaystyle 0.0120650472484646$

c = 1.013E5 *0.21 / 8.314/(25+273.15)/1000
print("{:.06g} mol/L = {:.06g} mmol/L".format(c, c*1000))

0.00858191 mol/L = 8.58191 mmol/L

Grafische Lösung

plot1 = splt.plot(eq1)

plot2 = splt.plot(eq1, xlim=(-0.05,0.05), ylim=[-1,1], adaptive = False, nb_of_points=10000)

Gleichungssysteme aus mehreren Gleichungen

y = sp.Symbol('y')
eq1 = x**2 + y**2 -1
eq2 = x+y

res = sp.solve([eq1, eq2], [x,y], prec = 20)
print(res)

Man könnte die Resultate nun beispielsweise in Listen speichern (xx und yy) und und komplizierte Ausdrücke wie sqrt(2)/e in Fliesskommezahlen umzuwandeln (.evalf()).

xx = []
yy = []
for i in range(len(res)):
    xres = res[i][0]
    yres = res[i][1]
    xx.append(xres)
    yy.append(yres)
    print("Lösung ",i,":")
    print("x",i," = ",xres, " = ", xres.evalf())
    print("y",i,"= ",yres, " = ", yres.evalf())

print("alle Werte für x:",xx)
print("alle Werte für y:",yy)

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