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Comments on How to apply a unit constraint in SymPy
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How to apply a unit constraint in SymPy
The solution to this is probably easy, but I haven't been able to find it. Using SymPy, I am trying to solve this equation: $$ {x_1}^2 + {x_2}^2 + {x_3}^2 + 3 = a $$ with this constraint: $$ {x_1}^2 + {x_2}^2 + {x_3}^2 = 1 $$ It is obvious that $a=4$. So, I wrote this code:
import sympy as sp
a, x1, x2, x3 = sp.symbols('a x1 x2 x3')
eq1 = x1**2 + x2**2 + x3**2 + 3 - a
eq2 = x1**2 + x2**2 + x3**2 - 1
sol = sp.solve([eq1, eq2], a)
print(sol)
Which returns:
{a: x1**2 + x2**2 + x3**2 + 3}
The unit-norm constraint on x is not applied.
How can I get SymPy to apply the unit-norm constraint, which results in $a=4$?
Post
Are the coefficients of eq1 always 1? If so, you can simply subtract one equation from the other.
>>> sp.solve(eq1-eq2, a)
[4]
P.S. I don't have much experience with SymPy, so LMK if I missed some subtlety.
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