# Coding Period Week 11

Organization : SymPy
Solvers: Completing Solveset

1 August 2016 - 7 August 2016

by Shekhar Prasad Rajak — Posted on August 7, 2016

eliminate() continue:

• PR : #11485

• Regarding issue #2720, It is something similar to eliminate present in wolfram.

• Right now it is working for real domain and not considering ImageSet, Intersection. Complement. If it find ImageSet, Intersection. Complement for the symbol to be eliminated, then just raises NotImaplementedError(in near future it can be implemented).

• It can take N nummber of equations and M number of symbols to be eliminated. It returns FiniteSet of equations which doesn’t contains these symbols.

Continue - Diophantine in Solveset :

PR 11234

• In commit : returning ConditionSet when it diophantine doesn’t the diophantine equation type and not able to solve.

Idea for improved _solve_trig in Solveset :

In [1]: solveset(sin(x) + cos(y), x, S.Reals)
Out[1]: {x | x ∊ ℝ ∧ sin(x) + cos(y) = 0}

In [2]: solve(sin(x) + cos(y), x)
Out[2]: [asin(cos(y)) + π, -asin(cos(y))]

• This above examples is enough to tell that _solve_trig is not using inverse trigonometric function. We can have something, which can solve trig equations by making free the symbol in lhs and in rhs inverse trig function.

• solveset(sin(2*x) - sqrt(3)*cos(2*x), x, S.Reals) for this right now _solve_trig is converting it into exp form and solving it. But it is can be simply solved using sin(x + y) == sin(x)*cos(y) + cos(x)*sin(y) formula.

• First divide both side with sqrt(a**2 + b**2) where a, b is coeff of sin(2*x) , cos(2*x).

• sin(2*x)/2 - (sqrt(3)/2)*cos(2*x) ==> sin(2*x)*cos(pi/3) - sin(pi/3)*cos(2*x) ==> sin(2*x - pi/3).

• Now sin(2*x - pi/3) is solvable using solve_decomposition.

Meanwhile :

• Some analysis about Abs solver :

In [1]: solveset(Abs(x) - 1,  x)
ValueError:
Absolute values cannot be inverted in the complex domain.

In [2]: solveset(Abs(x) - (1 + I), x)
ValueError:
Absolute values cannot be inverted in the complex domain.

In [3]: solveset(Abs(x) - y , x)
ValueError:

Absolute values cannot be inverted in the complex domain. - In 1st case (for complex domain) ans should be http://www.wolframalpha.com/input/?i=Abs(x)+-+(1+)+%3D0+for+x

• In 2nd case EmptySet. and in 3rd case (general solution when domain=S.Complexes) soln should be http://www.wolframalpha.com/input/?i=Abs(x)+-+y+%3D0+for+x

• In general( 3rd case) it should print ConditionSet(x, -Abs(re(y)) <= re(x) and re(x) <= Abs(re(y)) and re(y)>0, Eq(im(y), 0) , S.Complexes).

continue..