details: http://hg.sympy.org/sympy/rev/17b95f9f1d9d
changeset: 1794:17b95f9f1d9d
user: Mateusz Paprocki <[EMAIL PROTECTED]>
date: Wed Oct 15 12:12:54 2008 +0200
description:
Fixed issue #1123
The problem was in new roots() function - it was
checking not enough trivial cases and used functional
and square-free decomposition unnecessarily, making
the results overcomplicated (so that simplify hanged
on multivariate gcd computation).
diffs (98 lines):
diff -r 6bfb268ef808 -r 17b95f9f1d9d sympy/polys/rootfinding.py
--- a/sympy/polys/rootfinding.py Mon Oct 13 22:45:28 2008 +0200
+++ b/sympy/polys/rootfinding.py Wed Oct 15 12:12:54 2008 +0200
@@ -238,43 +238,43 @@
else:
return {}
else:
- if multiple:
- return [S.Zero] * f.degree
- else:
- return { S.Zero : f.degree }
+ result = { S.Zero : f.degree }
+ else:
+ (k,), f = f.as_reduced()
- (k,), f = f.as_reduced()
+ if k == 0:
+ result = {}
+ else:
+ result = { S.Zero : k }
- if k == 0:
- result = {}
- else:
- result = { S.Zero : k }
+ if f.degree == 1:
+ result[roots_linear(f)[0]] = 1
+ else:
+ factors = poly_decompose(f)
- factors = poly_decompose(f)
+ zeros, g = {}, factors[0]
- zeros, g = {}, factors[0]
-
- for i, h in enumerate(poly_sqf(g)):
- for zero in roots_trivial(h):
- if zeros.has_key(zero):
- zeros[zero] += i+1
- else:
- zeros[zero] = i+1
-
- for factor in factors[1:]:
- previous, zeros = zeros.copy(), {}
-
- for zero, i in previous.iteritems():
- g = factor.sub_term(zero, (0,))
-
- for j, h in enumerate(poly_sqf(g)):
+ for i, h in enumerate(poly_sqf(g)):
for zero in roots_trivial(h):
if zeros.has_key(zero):
- zeros[zero] += i*(j+1)
+ zeros[zero] += i+1
else:
- zeros[zero] = i*(j+1)
+ zeros[zero] = i+1
- result.update(zeros)
+ for factor in factors[1:]:
+ previous, zeros = zeros.copy(), {}
+
+ for zero, i in previous.iteritems():
+ g = factor.sub_term(zero, (0,))
+
+ for j, h in enumerate(poly_sqf(g)):
+ for zero in roots_trivial(h):
+ if zeros.has_key(zero):
+ zeros[zero] += i*(j+1)
+ else:
+ zeros[zero] = i*(j+1)
+
+ result.update(zeros)
domain = flags.get('domain', None)
diff -r 6bfb268ef808 -r 17b95f9f1d9d sympy/polys/tests/test_polynomial.py
--- a/sympy/polys/tests/test_polynomial.py Mon Oct 13 22:45:28 2008 +0200
+++ b/sympy/polys/tests/test_polynomial.py Wed Oct 15 12:12:54 2008 +0200
@@ -6,7 +6,7 @@
from sympy.polys.algorithms import *
from sympy.polys.rootfinding import *
-a,b,c,x,y,z,u,v,t = symbols('abcxyzuvt')
+a,b,c,d,x,y,z,u,v,t = symbols('abcdxyzuvt')
def test_monomial_cmp():
assert monomial_lex_cmp((3,2,1), (1,2,4)) == 1
@@ -997,6 +997,9 @@
S.One: 1, -S.One: 1, I: 1, -I: 1
}
+ assert roots((a+b+c)*x + a+b+c+d, x) == \
+ { (-a-b-c-d) / (a+b+c) : 1 }
+
assert roots(x**3+x**2-x+1, x, cubics=False) == {}
r1_2, r1_3, r1_9, r4_9, r19_27 = [ Rational(*r) \
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