Coding Period Week 8

Continue - Diophantine in Solveset :

PR 11234

• For general Pythagorean diop_type (Diophantine eq type), it seems diophantine always returns parameterized solution so I did some changes in the PR. commit

• You can refer this comment.

Continue Simplified Trig soln

PR #11188

• After some changes, the PR is ready for review.

Continue nonlinsolve :

PR #11111

• Added some XFAIL test-cases of system of Trigonometric equations. solveset trig solver (solve_trig) is not smart enough(solveset returns ConditionSet, where soln can be simply inverse trig functions using _invert or inverse Trigonometric functions). So solveset returns ConditionSet that means substitution is not getting soln.

• It is better to replace trigonometric functions or other Function with symbols

(e.g. sin(x) –> u, sin(y)–> v, f(x)–> f_x, g(x) –> g_x)

and then solve for the symbols. After getting solution from nonlinsolve user can invert or do solveset

(e.g. solveset(Eq(sin(x), soln_u), x, domain) to get value of x).

• Ready for review.

Meanwhile :

• We already know that solveset need improved invert_real , invert_complex and Imageset Intersections.

• previous work is in this PR 10971. Trying to improve them.

Some cases is here :

# In 2, 4, 5 intersection is not needed.

In [1]: img = ImageSet(Lambda(n, x/n), S.Complexes)

In [2]: Intersection(img, S.Complexes)
Out[2]:
    ⎧x        ⎫
ℂ ∩ ⎨─ | n ∊ ℂ⎬
    ⎩n        ⎭

In [3]: img = ImageSet(Lambda(n, x/n), S.Integers)

In [4]: Intersection(img, S.Complexes)
Out[4]:
⎧x        ⎫
⎨─ | n ∊ ℤ⎬ ∩ ℂ
⎩n        ⎭

In [5]: Intersection(ImageSet(Lambda(n, 2*n*I*pi), S.Integers), S.Complexes)
Out[5]: {2⋅ⅈ⋅π⋅n | n ∊ ℤ} ∩ ℂ

# ImageSet Intersection is not implemented when inverter returns multiple values.
# here ans should be {0, 1}
In [6]: img1 = ImageSet(Lambda(n, n**2), S.Integers)

In [7]: Intersection(img1, Interval(0,2))
Out[7]:
         ⎧ 2        ⎫
[0, 2] ∩ ⎨n  | n ∊ ℤ⎬
         ⎩          ⎭

continue..