1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
|
diff --git a/src/sage/interfaces/singular.py b/src/sage/interfaces/singular.py
index 9d65c9f..a028bbe 100644
--- a/src/sage/interfaces/singular.py
+++ b/src/sage/interfaces/singular.py
@@ -654,7 +654,7 @@ class Singular(ExtraTabCompletion, Expect):
s = Expect.eval(self, x, **kwds)
- if s.find("error") != -1 or s.find("Segment fault") != -1:
+ if s.find("error occurred") != -1 or s.find("Segment fault") != -1:
raise SingularError('Singular error:\n%s'%s)
if get_verbose() > 0:
@@ -1079,7 +1079,7 @@ class Singular(ExtraTabCompletion, Expect):
sage: S = singular.ring('real', '(a,b)', 'lp')
sage: singular.current_ring()
polynomial ring, over a field, global ordering
- // coefficients: float
+ // coefficients: Float()
// number of vars : 2
// block 1 : ordering lp
// : names a b
@@ -1157,7 +1157,7 @@ class Singular(ExtraTabCompletion, Expect):
sage: singular._tab_completion()
['exteriorPower',
...
- 'flintZ']
+ 'crossprod']
"""
p = re.compile("// *([a-z0-9A-Z_]*).*") #compiles regular expression
proclist = self.eval("listvar(proc)").splitlines()
@@ -1183,7 +1183,7 @@ class Singular(ExtraTabCompletion, Expect):
EXAMPLES::
sage: singular.version()
- "Singular ... version 4.1.0 ...
+ "Singular ... version 4...
"""
return singular_version()
@@ -1562,7 +1562,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
elif charstr[0] in ['0', 'QQ']:
from sage.all import QQ
br = QQ
- elif charstr[0]=='real':
+ elif charstr[0].startswith('Float'):
from sage.all import RealField, ceil, log
prec = singular.eval('ringlist(basering)[1][2][1]')
br = RealField(ceil((ZZ(prec)+1)/log(2,10)))
@@ -1750,7 +1750,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
# Singular 4 puts parentheses around floats and sign outside them
charstr = self.parent().eval('charstr(basering)').split(',',1)
- if charstr[0] in ['real', 'complex']:
+ if charstr[0]=='complex' or charstr[0].startswith('Float'):
for i in range(coeff_start, 2 * coeff_start):
singular_poly_list[i] = singular_poly_list[i].replace('(','').replace(')','')
@@ -1992,7 +1992,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
sage: S = singular.ring('real', '(a,b)', 'lp')
sage: singular.current_ring()
polynomial ring, over a field, global ordering
- // coefficients: float
+ // coefficients: Float()
// number of vars : 2
// block 1 : ordering lp
// : names a b
@@ -2072,7 +2072,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
sage: R._tab_completion()
['exteriorPower',
...
- 'flintZ']
+ 'crossprod']
"""
return self.parent()._tab_completion()
@@ -2358,7 +2358,7 @@ def singular_version():
EXAMPLES::
sage: singular.version()
- "Singular ... version 4.1.0 ...
+ "Singular ... version 4...
"""
return singular.eval('system("--version");')
diff --git a/src/sage/libs/singular/decl.pxd b/src/sage/libs/singular/decl.pxd
index 4b658c4..d863740 100644
--- a/src/sage/libs/singular/decl.pxd
+++ b/src/sage/libs/singular/decl.pxd
@@ -170,7 +170,7 @@ cdef extern from "singular/Singular/libsingular.h":
int n_NumberOfParameters(const n_Procs_s* r)
- ctypedef struct poly "polyrec":
+ ctypedef struct poly "spolyrec":
poly *next
number *coef
unsigned long exp[1]
@@ -630,9 +630,13 @@ cdef extern from "singular/Singular/libsingular.h":
# return p*q, destroys p and q
poly *p_Mult_q(poly *p, poly *q, ring *r)
+ # polynomial division, ignoring the rest
+ # via singclap_pdivide resp. idLift, destroys p,q
+ poly *p_Divide(poly *p, poly *q, ring *r)
+
# divide monomial p by monomial q, p,q const
- poly *pDivide(poly *p,poly *q)
+ poly *pMDivide(poly *p,poly *q)
# return the i-th power of p; p destroyed, requires global ring
diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
index 2a8d9ae..aeff53a 100644
--- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
@@ -190,8 +190,8 @@ from sage.libs.singular.decl cimport (
n_IsUnit, n_Invers,
p_ISet, rChangeCurrRing, p_Copy, p_Init, p_SetCoeff, p_Setm, p_SetExp, p_Add_q,
p_NSet, p_GetCoeff, p_Delete, p_GetExp, pNext, rRingVar, omAlloc0, omStrDup,
- omFree, pDivide, p_SetCoeff0, n_Init, p_DivisibleBy, pLcm, p_LmDivisibleBy,
- pDivide, p_IsConstant, p_ExpVectorEqual, p_String, p_LmInit, n_Copy,
+ omFree, pMDivide, p_Divide, p_SetCoeff0, n_Init, p_DivisibleBy, pLcm, p_LmDivisibleBy,
+ pMDivide, p_IsConstant, p_ExpVectorEqual, p_String, p_LmInit, n_Copy,
p_IsUnit, p_Series, p_Head, idInit, fast_map_common_subexp, id_Delete,
p_IsHomogeneous, p_Homogen, p_Totaldegree,pLDeg1_Totaldegree, singclap_pdivide, singclap_factorize,
idLift, IDELEMS, On, Off, SW_USE_CHINREM_GCD, SW_USE_EZGCD,
@@ -1693,8 +1693,8 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
if not g._poly:
raise ZeroDivisionError
- if r!=currRing: rChangeCurrRing(r) # pDivide
- res = pDivide(f._poly, g._poly)
+ if r!=currRing: rChangeCurrRing(r) # pMDivide
+ res = pMDivide(f._poly, g._poly)
if coeff:
if r.cf.type == n_unknown or r.cf.cfDivBy(p_GetCoeff(f._poly, r), p_GetCoeff(g._poly, r), r.cf):
n = r.cf.cfDiv( p_GetCoeff(f._poly, r) , p_GetCoeff(g._poly, r), r.cf)
@@ -1853,8 +1853,8 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
and (<MPolynomial_libsingular>g) \
and g.parent() is self \
and p_LmDivisibleBy((<MPolynomial_libsingular>g)._poly, m, r):
- if r!=currRing: rChangeCurrRing(r) # pDivide
- flt = pDivide(f._poly, (<MPolynomial_libsingular>g)._poly)
+ if r!=currRing: rChangeCurrRing(r) # pMDivide
+ flt = pMDivide(f._poly, (<MPolynomial_libsingular>g)._poly)
#p_SetCoeff(flt, n_Div( p_GetCoeff(f._poly, r) , p_GetCoeff((<MPolynomial_libsingular>g)._poly, r), r), r)
p_SetCoeff(flt, n_Init(1, r), r)
return new_MP(self,flt), g
@@ -4023,16 +4023,6 @@ cdef class MPolynomial_libsingular(MPolynomial):
Traceback (most recent call last):
...
NotImplementedError: Division of multivariate polynomials over non fields by non-monomials not implemented.
-
- TESTS::
-
- sage: P.<x,y> = ZZ[]
- sage: p = 3*(-x^8*y^2 - x*y^9 + 6*x^8*y + 17*x^2*y^6 - x^3*y^2)
- sage: q = 7*(x^2 + x*y + y^2 + 1)
- sage: p*q//q == p
- True
- sage: p*q//p == q
- True
"""
cdef MPolynomialRing_libsingular parent = self._parent
cdef ring *r = self._parent_ring
@@ -4052,13 +4042,18 @@ cdef class MPolynomial_libsingular(MPolynomial):
_right = <MPolynomial_libsingular>right
if r.cf.type != n_unknown:
+ if r.cf.type == n_Z:
+ P = parent.change_ring(RationalField())
+ f = P(self)//P(right)
+ CM = list(f)
+ return parent(sum([c.floor()*m for c,m in CM]))
if _right.is_monomial():
p = _self._poly
quo = p_ISet(0,r)
- if r != currRing: rChangeCurrRing(r) # pDivide
+ if r != currRing: rChangeCurrRing(r) # pMDivide
while p:
if p_DivisibleBy(_right._poly, p, r):
- temp = pDivide(p, _right._poly)
+ temp = pMDivide(p, _right._poly)
p_SetCoeff0(temp, n_Copy(p_GetCoeff(p, r), r), r)
quo = p_Add_q(quo, temp, r)
p = pNext(p)
@@ -4794,6 +4789,8 @@ cdef class MPolynomial_libsingular(MPolynomial):
sage: p = -x*y + x*z + 54*x - 2
sage: (5*p^2).lcm(3*p) == 15*p^2
True
+ sage: lcm(2*x,2*x*y)
+ 2*x*y
"""
cdef ring *_ring = self._parent_ring
cdef poly *ret
@@ -4821,9 +4818,7 @@ cdef class MPolynomial_libsingular(MPolynomial):
if _ring!=currRing: rChangeCurrRing(_ring) # singclap_gcd
gcd = singclap_gcd(p_Copy(self._poly, _ring), p_Copy(_g._poly, _ring), _ring )
prod = pp_Mult_qq(self._poly, _g._poly, _ring)
- ret = singclap_pdivide(prod , gcd , _ring)
- p_Delete(&prod, _ring)
- p_Delete(&gcd, _ring)
+ ret = p_Divide(prod, gcd, _ring)
if count >= 20:
sig_off()
return new_MP(self._parent, ret)
@@ -4866,7 +4861,7 @@ cdef class MPolynomial_libsingular(MPolynomial):
sage: f.quo_rem(y)
(2*x^2, x + 1)
sage: f.quo_rem(3*x)
- (2*x*y + 1, -4*x^2*y - 2*x + 1)
+ (0, 2*x^2*y + x + 1)
TESTS::
@@ -4888,7 +4883,7 @@ cdef class MPolynomial_libsingular(MPolynomial):
if right.is_zero():
raise ZeroDivisionError
- if not self._parent._base.is_field() and not is_IntegerRing(self._parent._base):
+ if not self._parent._base.is_field():
py_quo = self//right
py_rem = self - right*py_quo
return py_quo, py_rem
diff --git a/src/sage/rings/polynomial/plural.pyx b/src/sage/rings/polynomial/plural.pyx
index d5439f7f..ad20ebc 100644
--- a/src/sage/rings/polynomial/plural.pyx
+++ b/src/sage/rings/polynomial/plural.pyx
@@ -998,7 +998,7 @@ cdef class NCPolynomialRing_plural(Ring):
if not g._poly:
raise ZeroDivisionError
- res = pDivide(f._poly,g._poly)
+ res = pMDivide(f._poly,g._poly)
if coeff:
if (r.cf.type == n_unknown) or r.cf.cfDivBy(p_GetCoeff(f._poly, r), p_GetCoeff(g._poly, r), r.cf):
n = r.cf.cfDiv( p_GetCoeff(f._poly, r) , p_GetCoeff(g._poly, r), r.cf)
@@ -1193,7 +1193,7 @@ cdef class NCPolynomialRing_plural(Ring):
if isinstance(g, NCPolynomial_plural) \
and (<NCPolynomial_plural>g) \
and p_LmDivisibleBy((<NCPolynomial_plural>g)._poly, m, r):
- flt = pDivide(f._poly, (<NCPolynomial_plural>g)._poly)
+ flt = pMDivide(f._poly, (<NCPolynomial_plural>g)._poly)
#p_SetCoeff(flt, n_Div( p_GetCoeff(f._poly, r) , p_GetCoeff((<NCPolynomial_plural>g)._poly, r), r), r)
p_SetCoeff(flt, n_Init(1, r), r)
return new_NCP(self,flt), g
diff --git a/src/sage/rings/polynomial/polynomial_singular_interface.py b/src/sage/rings/polynomial/polynomial_singular_interface.py
index 9331169..f753610 100644
--- a/src/sage/rings/polynomial/polynomial_singular_interface.py
+++ b/src/sage/rings/polynomial/polynomial_singular_interface.py
@@ -81,8 +81,8 @@ class PolynomialRing_singular_repr:
sage: R.<x,y> = PolynomialRing(CC)
sage: singular(R)
polynomial ring, over a field, global ordering
- // coefficients: float[I](complex:15 digits, additional 0 digits)/(I^2+1)
- // number of vars : 2
+ // coefficients: real[I](complex:15 digits, additional 0 digits)/(I^2+1)
+ // number of vars : 2
// block 1 : ordering dp
// : names x y
// block 2 : ordering C
@@ -90,8 +90,8 @@ class PolynomialRing_singular_repr:
sage: R.<x,y> = PolynomialRing(RealField(100))
sage: singular(R)
polynomial ring, over a field, global ordering
- // coefficients: float
- // number of vars : 2
+ // coefficients: Float()
+ // number of vars : 2
// block 1 : ordering dp
// : names x y
// block 2 : ordering C
|