Sympy: ask for help evaluate a^2 + b^2

[nifengcn]

if we know a + b = 4, ab = 2, we want to evaluate a^2 + b^2. Is there a common method in sympy to do the transform a^2 + b^2 = (a + b)^2 - 2ab to solve such problems. Thank you.

[smichr]

Maybe just this:

>>> var('a b c')
(a, b, c)
>>> solve((a+b-4,a*b-2,a**2+b**2-c))
[{a: 2 - sqrt(2), b: sqrt(2) + 2, c: 12}, {a: sqrt(2) + 2, b: 2 - sqrt(2), c: 12}]

[nifengcn]

Maybe just this:

>>> var('a b c')
(a, b, c)
>>> solve((a+b-4,a*b-2,a**2+b**2-c))
[{a: 2 - sqrt(2), b: sqrt(2) + 2, c: 12}, {a: sqrt(2) + 2, b: 2 - sqrt(2), c: 12}]

This is a method of solving the problem. Actually, I want to know whether this is a method to transfrom expression A in terms of expression B and C. In the problem, A is a^2 + b^2, B is a + b and C is ab. A = B^2 - 2C

[sylee957]

I'm not sure if this is a helpful answer, but the only structured way I'm aware of to solve the problem is using ratsimpmodprime with groebner basis as answered in #19064.

from sympy import *

a, b = symbols('a b')
ratsimpmodprime(a**2+b**2, groebner([a+b-4, a*b-2]).exprs)

[oscarbenjamin]

Maybe this is what you want:

In [28]: a, b, A, B, C = symbols('a, b, A, B, C')                                                                                              

In [29]: eq = [Eq(A, a**2 + b**2), Eq(B, a + b), Eq(C, a*b)]                                                                                   

In [30]: sol = solve(eq, [A, a, b], dict=True)                                                                                                 

In [31]: sol = {s[A] for s in sol}                                                                                                             

In [32]: sol                                                                                                                                   
Out[32]: 
⎧ 2      ⎫
⎨B  - 2⋅C⎬
⎩        ⎭

Ideally we would have an eliminate function rather than needing to solve for a and b as unknowns.

[nifengcn]

Maybe this is what you want:

In [28]: a, b, A, B, C = symbols('a, b, A, B, C')                                                                                              

In [29]: eq = [Eq(A, a**2 + b**2), Eq(B, a + b), Eq(C, a*b)]                                                                                   

In [30]: sol = solve(eq, [A, a, b], dict=True)                                                                                                 

In [31]: sol = {s[A] for s in sol}                                                                                                             

In [32]: sol                                                                                                                                   
Out[32]: 
⎧ 2      ⎫
⎨B  - 2⋅C⎬
⎩        ⎭

Ideally we would have an eliminate function rather than needing to solve for a and b as unknowns.

This is actually what I want. It is very smart to make use of the solve function. Look forward to the eliminate function.