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Gustavo Ramatornaria
Gustavo Rama
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tornaria
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Eliminates the use of matrix constructor in internal loop of the function sage.quadratic_forms.ternary._reduced_ternary_form_eisenstein_with_matrix.
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‎src/sage/quadratic_forms/ternary.pyx

Lines changed: 128 additions & 55 deletions
Original file line numberDiff line numberDiff line change
@@ -67,23 +67,31 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
6767
sage: Q(M) == Qr
6868
True
6969
"""
70-
M = identity_matrix(3)
70+
# M = identity_matrix(3)
71+
# M = matrix(ZZ, 3, [m11, m12, m13, m21, m22, m23, m31, m32, m33])
72+
m11, m12, m13, m21, m22, m23, m31, m32, m33 = 1, 0, 0, 0, 1, 0, 0, 0, 1
7173

7274
loop = True
7375

7476
while loop:
7577

7678
# adjust
77-
v = a1+a2+a23+a13+a12
78-
if v < 0:
79-
M *= matrix(ZZ, 3, [1, 0, 1, 0, 1, 1, 0, 0, 1])
79+
v = a1 + a2 + a23 + a13 + a12
80+
if (v < 0):
81+
# M *= matrix(ZZ, 3, [1, 0, 1, 0, 1, 1, 0, 0, 1])
82+
[m13] = [m11 + m12 + m13]
83+
[m23] = [m21 + m22 + m23]
84+
[m33] = [m31 + m32 + m33]
8085
a3 += v
81-
a23 += a12+2*a2
82-
a13 += a12+2*a1
86+
a23 += a12 + 2*a2
87+
a13 += a12 + 2*a1
8388

8489
# cuadred 12
8590
m = red_mfact(a1, a12)
86-
M *= matrix(ZZ, 3, [1, m, 0, 0, 1, 0, 0, 0, 1])
91+
# M *= matrix(ZZ, 3, [1, m, 0, 0, 1, 0, 0, 0, 1])
92+
[m12] = [m*m11 + m12]
93+
[m22] = [m*m21 + m22]
94+
[m32] = [m*m31 + m32]
8795
t = a1*m
8896
a12 += t
8997
a2 += a12*m
@@ -92,7 +100,10 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
92100

93101
# cuadred 23
94102
m = red_mfact(a2, a23)
95-
M *= matrix(ZZ, 3, [1, 0, 0, 0, 1, m, 0, 0, 1])
103+
# M *= matrix(ZZ, 3, [1, 0, 0, 0, 1, m, 0, 0, 1])
104+
[m13] = [m*m12 + m13]
105+
[m23] = [m*m22 + m23]
106+
[m33] = [m*m32 + m33]
96107
t = a2*m
97108
a23 += t
98109
a3 += a23*m
@@ -101,7 +112,10 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
101112

102113
# cuadred 13
103114
m = red_mfact(a1, a13)
104-
M *= matrix(ZZ, 3, [1, 0, m, 0, 1, 0, 0, 0, 1])
115+
# M *= matrix(ZZ, 3, [1, 0, m, 0, 1, 0, 0, 0, 1])
116+
[m13] = [m*m11 + m13]
117+
[m23] = [m*m21 + m23]
118+
[m33] = [m*m31 + m33]
105119
t = a1*m
106120
a13 += t
107121
a3 += a13*m
@@ -110,130 +124,189 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
110124

111125
# order 12
112126
if a1 > a2 or (a1 == a2 and abs(a23) > abs(a13)):
113-
M *= matrix(ZZ, 3, [0, -1, 0, -1, 0, 0, 0, 0, -1])
127+
# M *= matrix(ZZ, 3, [0, -1, 0, -1, 0, 0, 0, 0, -1])
128+
[m11, m12, m13] = [-m12, -m11, -m13]
129+
[m21, m22, m23] = [-m22, -m21, -m23]
130+
[m31, m32, m33] = [-m32, -m31, -m33]
114131
[a1, a2] = [a2, a1]
115132
[a13, a23] = [a23, a13]
116133

117134
# order 23
118135
if a2 > a3 or (a2 == a3 and abs(a13) > abs(a12)):
119-
M *= matrix(ZZ, 3, [-1, 0, 0, 0, 0, -1, 0, -1, 0])
136+
# M *= matrix(ZZ, 3, [-1, 0, 0, 0, 0, -1, 0, -1, 0])
137+
[m11, m12, m13] = [-m11, -m13, -m12]
138+
[m21, m22, m23] = [-m21, -m23, -m22]
139+
[m31, m32, m33] = [-m31, -m33, -m32]
120140
[a2, a3] = [a3, a2]
121141
[a13, a12] = [a12, a13]
122142

123143
# order 12
124144
if a1 > a2 or (a1 == a2 and abs(a23) > abs(a13)):
125-
M *= matrix(ZZ, 3, [0, -1, 0, -1, 0, 0, 0, 0, -1])
145+
# M *= matrix(ZZ, 3, [0, -1, 0, -1, 0, 0, 0, 0, -1])
146+
[m11, m12, m13] = [-m12, -m11, -m13]
147+
[m21, m22, m23] = [-m22, -m21, -m23]
148+
[m31, m32, m33] = [-m32, -m31, -m33]
126149
[a1, a2] = [a2, a1]
127150
[a13, a23] = [a23, a13]
128151

129152
# signs
130153
if a23*a13*a12 > 0:
131154
# a23, a13, a12 positive
132155

133-
if a23 < 0:
134-
M *= diagonal_matrix([-1, 1, 1])
156+
if (a23 < 0):
157+
# M *= diagonal_matrix([-1, 1, 1])
158+
m11 = -m11
159+
m21 = -m21
160+
m31 = -m31
135161
a23 = -a23
136-
if a13 < 0:
137-
M *= diagonal_matrix([1, -1, 1])
138-
a13 = -a13
139-
if a12 < 0:
140-
M *= diagonal_matrix([1, 1, -1])
162+
if (a13 < 0):
163+
# M *= diagonal_matrix([1, -1, 1])
164+
m12 = -m12
165+
m22 = -m22
166+
m32 = -m32
167+
a13=-a13
168+
if (a12 < 0):
169+
# M *= diagonal_matrix([1, 1, -1])
170+
m13 = -m13
171+
m23 = -m23
172+
m33 = -m33
141173
a12 = -a12
142174

143175
else:
144176
# a23, a13, a12 nonpositive
145177

146178
[s1, s2, s3] = [a23 > 0, a13 > 0, a12 > 0]
147-
if (s1+s2+s3) % 2:
179+
if (s1 + s2 + s3) % 2:
148180
if a23 == 0:
149181
s1 = 1
150182
else:
151183
if a13 == 0:
152184
s2 = 1
153185
else:
154-
if a12 == 0:
186+
if (a12 == 0):
155187
s3 = 1
156188
if s1:
157-
M *= diagonal_matrix([-1, 1, 1])
158-
a23 = -a23
189+
# M *= diagonal_matrix([-1, 1, 1])
190+
m11 = -m11
191+
m21 = -m21
192+
m31 = -m31
193+
a23 = -a23
159194
if s2:
160-
M *= diagonal_matrix([1, -1, 1])
161-
a13 = -a13
195+
# M *= diagonal_matrix([1, -1, 1])
196+
m12 = -m12
197+
m22 = -m22
198+
m32 = -m32
199+
a13 = -a13
162200
if s3:
163-
M *= diagonal_matrix([1, 1, -1])
164-
a12 = -a12
201+
# M *= diagonal_matrix([1, 1, -1])
202+
m13 = -m13
203+
m23 = -m23
204+
m33 = -m33
205+
a12 = -a12
165206

166-
loop = not (abs(a23) <= a2 and abs(a13) <= a1 and abs(a12) <= a1 and a1+a2+a23+a13+a12 >= 0)
207+
loop = not (abs(a23) <= a2 and abs(a13) <= a1 and abs(a12) <= a1 and a1 + a2 + a23 + a13 + a12 >= 0)
167208

168209
# adj 3
169-
if a1+a2+a23+a13+a12 == 0 and 2*a1+2*a13+a12 > 0:
170-
M *= matrix(ZZ, 3, [-1, 0, 1, 0, -1, 1, 0, 0, 1])
171-
# a3 += a1+a2+a23+a13+a12
172-
a23 = -2*a2-a23-a12
173-
a13 = -2*a1-a13-a12
210+
if a1 + a2 + a23 + a13 + a12 == 0 and 2*a1 + 2*a13 + a12 > 0:
211+
# M *= matrix(ZZ, 3, [-1, 0, 1, 0, -1, 1, 0, 0, 1])
212+
[m11, m12, m13] = [-m11, -m12, m11 + m12 + m13]
213+
[m21, m22, m23] = [-m21, -m22, m21 + m22 + m23]
214+
[m31, m32, m33] = [-m31, -m32, m31 + m32 + m33]
215+
# a3 += a1+a2+a23+a13+a12 = 0
216+
a23 = -2*a2 - a23 - a12
217+
a13 = -2*a1 - a13 - a12
174218

175219
# adj 5.12
176220
if a1 == -a12 and a13 != 0:
177-
M *= matrix(ZZ, 3, [-1, -1, 0, 0, -1, 0, 0, 0, 1])
178-
# a2 += a1+a12
179-
a23 = -a23-a13
221+
# M *= matrix(ZZ, 3, [-1, -1, 0, 0, -1, 0, 0, 0, 1])
222+
[m11, m12] = [-m11, -m11 - m12]
223+
[m21, m22] = [-m21, -m21 - m22]
224+
[m31, m32] = [-m31, -m31 - m32]
225+
# a2 += a1 + a12 = 0
226+
a23 = -a23 - a13
180227
a13 = -a13
181-
a12 = -a12 # = 2*a1+a12
228+
a12 = -a12 # = 2*a1 + a12
182229

183230
# adj 5.13
184231
if a1 == -a13 and a12 != 0:
185-
M *= matrix(ZZ, 3, [-1, 0, -1, 0, 1, 0, 0, 0, -1])
186-
# a3 += a1+a13
187-
a23 = -a23-a12
188-
a13 = -a13 # = 2*a1+a13
232+
# M *= matrix(ZZ, 3, [-1, 0, -1, 0, 1, 0, 0, 0, -1])
233+
[m11, m13] = [-m11, -m11 - m13]
234+
[m21, m23] = [-m21, -m21 - m23]
235+
[m31, m33] = [-m31, -m31 - m33]
236+
# a3 += a1 + a13 = 0
237+
a23 = -a23 - a12
238+
a13 = -a13 # = 2*a1 + a13
189239
a12 = -a12
190240

191241
# adj 5.23
192242
if a2 == -a23 and a12 != 0:
193-
M *= matrix(ZZ, 3, [1, 0, 0, 0, -1, -1, 0, 0, -1])
194-
# a3 += a2+a23
195-
a23 = -a23 # = 2*a2+a23
196-
a13 = -a13-a12
243+
# M *= matrix(ZZ, 3, [1, 0, 0, 0, -1, -1, 0, 0, -1])
244+
[m12, m13] = [-m12, -m12 - m13]
245+
[m22, m23] = [-m22, -m22 - m23]
246+
[m32, m33] = [-m32, -m32 - m33]
247+
# a3 += a2 + a23 = 0
248+
a23 = -a23 # = 2*a2 + a23
249+
a13 = -a13 - a12
197250
a12 = -a12
198251

199252
# adj 4.12
200253
if a1 == a12 and a13 > 2*a23:
201-
M *= matrix(ZZ, 3, [-1, -1, 0, 0, 1, 0, 0, 0, -1])
202-
# a 2 += a1-a12
254+
# M *= matrix(ZZ, 3, [-1, -1, 0, 0, 1, 0, 0, 0, -1])
255+
[m11, m12, m13] = [-m11, -m11 + m12, -m13]
256+
[m21, m22, m23] = [-m21, -m21 + m22, -m23]
257+
[m31, m32, m33] = [-m31, -m31 + m32, -m33]
258+
# a2 += a1 - a12 = 0
203259
a23 = -a23 + a13
204260
# a12 = 2*a1 - a12
205261

206262
# adj 4.13
207263
if a1 == a13 and a12 > 2*a23:
208-
M *= matrix(ZZ, 3, [-1, 0, -1, 0, -1, 0, 0, 0, 1])
209-
# a3 += a1-a13
264+
# M *= matrix(ZZ, 3, [-1, 0, -1, 0, -1, 0, 0, 0, 1])
265+
[m11, m12, m13] = [-m11, -m12, -m11 + m13]
266+
[m21, m22, m23] = [-m21, -m22, -m21 + m23]
267+
[m31, m32, m33] = [-m31, -m32, -m31 + m33]
268+
# a3 += a1 - a13 = 0
210269
a23 = -a23 + a12
211270
# a13 = 2*a1 - a13
212271

213272
# adj 4.23
214273
if a2 == a23 and a12 > 2*a13:
215-
M *= matrix(ZZ, 3, [-1, 0, 0, 0, -1, -1, 0, 0, 1])
216-
# a3 += a2-a23
274+
# M *= matrix(ZZ, 3, [-1, 0, 0, 0, -1, -1, 0, 0, 1])
275+
[m11, m12, m13] = [-m11, -m12, -m12 + m13]
276+
[m21, m22, m23] = [-m21, -m22, -m22 + m23]
277+
[m31, m32, m33] = [-m31, -m32, -m32 + m33]
278+
# a3 += a2 - a23 = 0
217279
# a23 = 2*a2 - a23
218280
a13 = -a13 + a12
219281

220282
# order 12
221283
if a1 == a2 and abs(a23) > abs(a13):
222-
M *= matrix(ZZ, 3, [0, -1, 0, -1, 0, 0, 0, 0, -1])
284+
# M *= matrix(ZZ, 3, [0, -1, 0, -1, 0, 0, 0, 0, -1])
285+
[m11, m12, m13] = [-m12, -m11, -m13]
286+
[m21, m22, m23] = [-m22, -m21, -m23]
287+
[m31, m32, m33] = [-m32, -m31, -m33]
223288
[a1, a2] = [a2, a1]
224289
[a13, a23] = [a23, a13]
225290

226291
# order 23
227292
if a2 == a3 and abs(a13) > abs(a12):
228-
M *= matrix(ZZ, 3, [-1, 0, 0, 0, 0, -1, 0, -1, 0])
293+
# M *= matrix(ZZ, 3, [-1, 0, 0, 0, 0, -1, 0, -1, 0])
294+
[m11, m12, m13] = [-m11, -m13, -m12]
295+
[m21, m22, m23] = [-m21, -m23, -m22]
296+
[m31, m32, m33] = [-m31, -m33, -m32]
229297
[a13, a12] = [a12, a13]
230298

231299
# order 12
232300
if a1 == a2 and abs(a23) > abs(a13):
233-
M *= matrix(ZZ, 3, [0, -1, 0, -1, 0, 0, 0, 0, -1])
301+
# M *= matrix(ZZ, 3, [0, -1, 0, -1, 0, 0, 0, 0, -1])
302+
[m11, m12, m13] = [-m12, -m11, -m13]
303+
[m21, m22, m23] = [-m22, -m21, -m23]
304+
[m31, m32, m33] = [-m32, -m31, -m33]
234305
[a13, a23] = [a23, a13]
235306

236-
return (a1, a2, a3, a23, a13, a12), M
307+
return (a1, a2, a3, a23, a13, a12), \
308+
matrix(ZZ, 3, (m11, m12, m13, m21, m22, m23, m31, m32, m33))
309+
237310

238311

239312
def _reduced_ternary_form_eisenstein_without_matrix(a1, a2, a3, a23, a13, a12):

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