Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

extended solveset for polynomial congruence #18402

Open
wants to merge 6 commits into
base: master
Choose a base branch
from
Open

extended solveset for polynomial congruence #18402

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
6 commits
Select commit Hold shift + click to select a range
0914842
extended solveset for polynomial congruence
abhinav-anand-addepar Jan 19, 2020
4685047
minor changes
abhinav-anand-addepar Jan 20, 2020
4bca2f3
corrected minor mistakes
abhinav-anand-addepar Jan 21, 2020
dfb13a7
fixed doc test
abhinav-anand-addepar Jan 21, 2020
b258cea
made changes in solve_modular function
abhinav-anand-addepar Jan 21, 2020
be6cf13
changed doc test
abhinav-anand-addepar Jan 21, 2020
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Jump to
Jump to file
Failed to load files.
Diff view
Diff view
18 changes: 15 additions & 3 deletions sympy/solvers/solveset.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -40,7 +40,7 @@
from sympy.matrices import Matrix, MatrixBase
from sympy.ntheory import totient
from sympy.ntheory.factor_ import divisors
from sympy.ntheory.residue_ntheory import discrete_log, nthroot_mod
from sympy.ntheory.residue_ntheory import discrete_log, nthroot_mod, polynomial_congruence
from sympy.polys import (roots, Poly, degree, together, PolynomialError,
RootOf, factor)
from sympy.polys.polyerrors import CoercionFailed
Expand Down Expand Up @@ -1175,7 +1175,6 @@ def _invert_modular(modterm, rhs, n, symbol):
if g is not S.One:
x_indep_term = rhs*invert(g, m)
return _invert_modular(Mod(h, m), Mod(x_indep_term, m), n, symbol)

if a.is_Pow:
# base**expo = a
base, expo = a.args
Expand Down Expand Up @@ -1280,7 +1279,20 @@ def _solve_modular(f, symbol, domain):
return unsolved_result

n = Dummy('n', integer=True)
f_x, g_n = _invert_modular(modterm, rhs, n, symbol)

if modterm.args[0].is_polynomial():
a, m = modterm.args
f_x = symbol
g_n = EmptySet
if abs(rhs) < abs(m):
try:
remainder_list = polynomial_congruence(a - rhs, int(m))
for rem in remainder_list:
g_n += ImageSet(Lambda(n, m*n + rem), S.Integers)
except (ValueError, NotImplementedError):
return unsolved_result
else:
f_x, g_n = _invert_modular(modterm, rhs, n, symbol)

if f_x is modterm and g_n is rhs:
return unsolved_result
Expand Down
8 changes: 8 additions & 0 deletions sympy/solvers/tests/test_solveset.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -2253,6 +2253,14 @@ def test_solve_modular():
# domain intersection
assert solveset(3 - Mod(5*x - 8, 7), x, S.Naturals0) == \
Intersection(ImageSet(Lambda(n, 7*n + 5), S.Integers), S.Naturals0)

assert solveset(Mod(x**16 - 7, 36) - 2, x, S.Integers) == \
Union(ImageSet(Lambda(n, 36*n + 3), S.Integers),
ImageSet(Lambda(n, 36*n + 9), S.Integers),
ImageSet(Lambda(n, 36*n + 15), S.Integers),
ImageSet(Lambda(n, 36*n + 21), S.Integers),
ImageSet(Lambda(n, 36*n + 27), S.Integers),
ImageSet(Lambda(n, 36*n + 33), S.Integers))
# Complex args
assert solveset(Mod(x, 3) - I, x, S.Integers) == \
EmptySet()
Expand Down