FazBrowse GitHub Viewer
|
Trending
|
URL:
|
Home
Tools:
[Download Repo ZIP]
[View Raw Code]
[Original HTTPS Page]
algorithms-python/algorithms/maths/polynomial.py at master · ivan1911/algorithms-python · GitHub
ivan1911
/
algorithms-python
Public
forked from
keon/algorithms
Notifications
You must be signed in to change notification settings
Fork
0
Star
0
Code
Pull requests
0
Actions
Projects
Wiki
Security and quality
0
Insights
Additional navigation options
Code
Pull requests
Actions
Projects
Wiki
Security and quality
Insights
Expand file tree
Breadcrumbs
algorithms-python
/
algorithms
/
maths
/
polynomial.py
Copy path
More file actions
More file actions
Latest commit
History
History
History
532 lines (453 loc) · 19.8 KB
Breadcrumbs
algorithms-python
/
algorithms
/
maths
/
polynomial.py
Copy path
File metadata and controls
532 lines (453 loc) · 19.8 KB
Raw
Copy raw file
Download raw file
Open symbols panel
Edit and raw actions
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
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
# from __future__ import annotations
from
fractions
import
Fraction
from
typing
import
Dict
,
Union
,
Set
,
Iterable
from
numbers
import
Rational
from
functools
import
reduce
class
Monomial
:
"""
A simple Monomial class to
record the details of all variables
that a typical monomial is composed of.
"""
def
__init__
(
self
,
variables
:
Dict
[
int
,
int
],
coeff
:
Union
[
int
,
float
,
Fraction
,
None
]
=
None
)
->
None
:
'''
Create a monomial in the given variables:
Examples:
Monomial({1:1}) = (a_1)^1
Monomial({
1:3,
2:2,
4:1,
5:0
}, 12) = 12(a_1)^3(a_2)^2(a_4)
Monomial({}) = 0
Monomial({2:3, 3:-1}, 1.5) = (3/2)(a_2)^3(a_3)^(-1)
'''
self
.
variables
=
dict
()
if
coeff
is
None
:
if
len
(
variables
)
==
0
:
coeff
=
Fraction
(
0
,
1
)
else
:
coeff
=
Fraction
(
1
,
1
)
elif
coeff
==
0
:
self
.
coeff
=
Fraction
(
0
,
1
)
return
if
len
(
variables
)
==
0
:
self
.
coeff
=
Monomial
.
_rationalize_if_possible
(
coeff
)
return
for
i
in
variables
:
if
variables
[
i
]
!=
0
:
self
.
variables
[
i
]
=
variables
[
i
]
self
.
coeff
=
Monomial
.
_rationalize_if_possible
(
coeff
)
@
staticmethod
def
_rationalize_if_possible
(
num
):
'''
A helper for converting numbers
to Fraction only when possible.
'''
if
isinstance
(
num
,
Rational
):
res
=
Fraction
(
num
,
1
)
return
Fraction
(
res
.
numerator
,
res
.
denominator
)
else
:
return
num
# def equal_upto_scalar(self, other: Monomial) -> bool:
def
equal_upto_scalar
(
self
,
other
)
->
bool
:
"""
Return True if other is a monomial
and is equivalent to self up to a scalar
multiple.
"""
if
not
isinstance
(
other
,
Monomial
):
raise
ValueError
(
'Can only compare monomials.'
)
return
other
.
variables
==
self
.
variables
# def __add__(self, other: Union[int, float, Fraction, Monomial]):
def
__add__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
]):
"""
Define the addition of two
monomials or the addition of
a monomial with an int, float, or a Fraction.
"""
if
isinstance
(
other
,
int
)
or
isinstance
(
other
,
float
)
or
isinstance
(
other
,
Fraction
):
return
self
.
__add__
(
Monomial
({},
Monomial
.
_rationalize_if_possible
(
other
)))
if
not
isinstance
(
other
,
Monomial
):
raise
ValueError
(
'Can only add monomials, ints, floats, or Fractions.'
)
if
self
.
variables
==
other
.
variables
:
mono
=
{
i
:
self
.
variables
[
i
]
for
i
in
self
.
variables
}
return
Monomial
(
mono
,
Monomial
.
_rationalize_if_possible
(
self
.
coeff
+
other
.
coeff
)).
clean
()
# If they don't share same variables then by the definition,
# if they are added, the result becomes a polynomial and not a monomial.
# Thus, raise ValueError in that case.
raise
ValueError
(
f'Cannot add
{
str
(
other
)
}
to
{
self
.
__str__
()
}
because they don
\'
t have same variables.'
)
# def __eq__(self, other: Monomial) -> bool:
def
__eq__
(
self
,
other
)
->
bool
:
"""
Return True if two monomials
are equal upto a scalar multiple.
"""
return
self
.
equal_upto_scalar
(
other
)
and
self
.
coeff
==
other
.
coeff
# def __mul__(self, other: Union[int, float, Fraction, Monomial]) -> Monomial:
def
__mul__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
]):
"""
Multiply two monomials and merge the variables
in both of them.
Examples:
Monomial({1:1}) * Monomial({1: -3, 2: 1}) = (a_1)^(-2)(a_2)
Monomial({3:2}) * 2.5 = (5/2)(a_3)^2
"""
if
isinstance
(
other
,
float
)
or
isinstance
(
other
,
int
)
or
isinstance
(
other
,
Fraction
):
mono
=
{
i
:
self
.
variables
[
i
]
for
i
in
self
.
variables
}
return
Monomial
(
mono
,
Monomial
.
_rationalize_if_possible
(
self
.
coeff
*
other
)).
clean
()
if
not
isinstance
(
other
,
Monomial
):
raise
ValueError
(
'Can only multiply monomials, ints, floats, or Fractions.'
)
else
:
mono
=
{
i
:
self
.
variables
[
i
]
for
i
in
self
.
variables
}
for
i
in
other
.
variables
:
if
i
in
mono
:
mono
[
i
]
+=
other
.
variables
[
i
]
else
:
mono
[
i
]
=
other
.
variables
[
i
]
temp
=
dict
()
for
k
in
mono
:
if
mono
[
k
]
!=
0
:
temp
[
k
]
=
mono
[
k
]
return
Monomial
(
temp
,
Monomial
.
_rationalize_if_possible
(
self
.
coeff
*
other
.
coeff
)).
clean
()
# def inverse(self) -> Monomial:
def
inverse
(
self
):
"""
Compute the inverse of a monomial.
Examples:
Monomial({1:1, 2:-1, 3:2}, 2.5).inverse() = Monomial({1:-1, 2:1, 3:-2} ,2/5)
"""
mono
=
{
i
:
self
.
variables
[
i
]
for
i
in
self
.
variables
if
self
.
variables
[
i
]
!=
0
}
for
i
in
mono
:
mono
[
i
]
*=
-
1
if
self
.
coeff
==
0
:
raise
ValueError
(
"Coefficient must not be 0."
)
return
Monomial
(
mono
,
Monomial
.
_rationalize_if_possible
(
1
/
self
.
coeff
)).
clean
()
# def __truediv__(self, other: Union[int, float, Fraction, Monomial]) -> Monomial:
def
__truediv__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
]):
"""
Compute the division between two monomials
or a monomial and some other datatype
like int/float/Fraction.
"""
if
isinstance
(
other
,
int
)
or
isinstance
(
other
,
float
)
or
isinstance
(
other
,
Fraction
):
mono
=
{
i
:
self
.
variables
[
i
]
for
i
in
self
.
variables
}
if
other
==
0
:
raise
ValueError
(
'Cannot divide by 0.'
)
return
Monomial
(
mono
,
Monomial
.
_rationalize_if_possible
(
self
.
coeff
/
other
)).
clean
()
o
=
other
.
inverse
()
return
self
.
__mul__
(
o
)
# def __floordiv__(self, other: Union[int, float, Fraction, Monomial]) -> Monomial:
def
__floordiv__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
]):
"""
For monomials,
floor div is the same as true div.
"""
return
self
.
__truediv__
(
other
)
# def clone(self) -> Monomial:
def
clone
(
self
):
"""
Clone the monomial.
"""
temp_variables
=
{
i
:
self
.
variables
[
i
]
for
i
in
self
.
variables
}
return
Monomial
(
temp_variables
,
Monomial
.
_rationalize_if_possible
(
self
.
coeff
)).
clean
()
# def clean(self) -> Monomial:
def
clean
(
self
):
"""
Clean the monomial by dropping any variables that have power 0.
"""
temp_variables
=
{
i
:
self
.
variables
[
i
]
for
i
in
self
.
variables
if
self
.
variables
[
i
]
!=
0
}
return
Monomial
(
temp_variables
,
Monomial
.
_rationalize_if_possible
(
self
.
coeff
))
# def __sub__(self, other: Union[int, float, Fraction, Monomial]) -> Monomial:
def
__sub__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
]):
"""
Compute the subtraction
of a monomial and a datatype
such as int, float, Fraction, or Monomial.
"""
if
isinstance
(
other
,
int
)
or
isinstance
(
other
,
float
)
or
isinstance
(
other
,
Fraction
):
mono
=
{
i
:
self
.
variables
[
i
]
for
i
in
self
.
variables
if
self
.
variables
[
i
]
!=
0
}
if
len
(
mono
)
!=
0
:
raise
ValueError
(
'Can only subtract like monomials.'
)
other_term
=
Monomial
(
mono
,
Monomial
.
_rationalize_if_possible
(
other
))
return
self
.
__sub__
(
other_term
)
if
not
isinstance
(
other
,
Monomial
):
raise
ValueError
(
'Can only subtract monomials'
)
return
self
.
__add__
(
other
.
__mul__
(
Fraction
(
-
1
,
1
)))
def
__hash__
(
self
)
->
int
:
"""
Define the hash of a monomial
by the underlying variables.
If hashing is implemented in O(v*log(v))
where v represents the number of
variables in the monomial,
then search queries for the
purposes of simplification of a
polynomial can be performed in
O(v*log(v)) as well; much better than
the length of the polynomial.
"""
arr
=
[]
for
i
in
sorted
(
self
.
variables
):
if
self
.
variables
[
i
]
>
0
:
for
_
in
range
(
self
.
variables
[
i
]):
arr
.
append
(
i
)
return
hash
(
tuple
(
arr
))
def
all_variables
(
self
)
->
Set
:
"""
Get the set of all variables
present in the monomial.
"""
return
set
(
sorted
(
self
.
variables
.
keys
()))
def
substitute
(
self
,
substitutions
:
Union
[
int
,
float
,
Fraction
,
Dict
[
int
,
Union
[
int
,
float
,
Fraction
]]])
->
Fraction
:
"""
Substitute the variables in the
monomial for values defined by
the substitutions dictionary.
"""
if
isinstance
(
substitutions
,
int
)
or
isinstance
(
substitutions
,
float
)
or
isinstance
(
substitutions
,
Fraction
):
substitutions
=
{
v
:
Monomial
.
_rationalize_if_possible
(
substitutions
)
for
v
in
self
.
all_variables
()}
else
:
if
not
self
.
all_variables
().
issubset
(
set
(
substitutions
.
keys
())):
raise
ValueError
(
'Some variables didn
\'
t receive their values.'
)
if
self
.
coeff
==
0
:
return
Fraction
(
0
,
1
)
ans
=
Monomial
.
_rationalize_if_possible
(
self
.
coeff
)
for
k
in
self
.
variables
:
ans
*=
Monomial
.
_rationalize_if_possible
(
substitutions
[
k
]
**
self
.
variables
[
k
])
return
Monomial
.
_rationalize_if_possible
(
ans
)
def
__str__
(
self
)
->
str
:
"""
Get a string representation of
the monomial.
"""
if
len
(
self
.
variables
)
==
0
:
return
str
(
self
.
coeff
)
result
=
str
(
self
.
coeff
)
result
+=
'('
for
i
in
self
.
variables
:
temp
=
'a_{}'
.
format
(
str
(
i
))
if
self
.
variables
[
i
]
>
1
:
temp
=
'('
+
temp
+
')**{}'
.
format
(
self
.
variables
[
i
])
elif
self
.
variables
[
i
]
<
0
:
temp
=
'('
+
temp
+
')**(-{})'
.
format
(
-
self
.
variables
[
i
])
elif
self
.
variables
[
i
]
==
0
:
continue
else
:
temp
=
'('
+
temp
+
')'
result
+=
temp
return
result
+
')'
class
Polynomial
:
"""
A simple implementation
of a polynomial class that
records the details about two polynomials
that are potentially comprised of multiple
variables.
"""
def
__init__
(
self
,
monomials
:
Iterable
[
Union
[
int
,
float
,
Fraction
,
Monomial
]])
->
None
:
'''
Create a polynomial in the given variables:
Examples:
Polynomial([
Monomial({1:1}, 2),
Monomial({2:3, 1:-1}, -1),
math.pi,
Fraction(-1, 2)
]) = (a_1)^2 + (-1)(a_2)^3(a_1)^(-1) + 2.6415926536
Polynomial([]) = 0
'''
self
.
monomials
=
set
()
for
m
in
monomials
:
if
any
(
map
(
lambda
x
:
isinstance
(
m
,
x
), [
int
,
float
,
Fraction
])):
self
.
monomials
|=
{
Monomial
({},
m
)}
elif
isinstance
(
m
,
Monomial
):
self
.
monomials
|=
{
m
}
else
:
raise
ValueError
(
'Iterable should have monomials, int, float, or Fraction.'
)
self
.
monomials
-=
{
Monomial
({},
0
)}
@
staticmethod
def
_rationalize_if_possible
(
num
):
'''
A helper for converting numbers
to Fraction only when possible.
'''
if
isinstance
(
num
,
Rational
):
res
=
Fraction
(
num
,
1
)
return
Fraction
(
res
.
numerator
,
res
.
denominator
)
else
:
return
num
# def __add__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial:
def
__add__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
,
Monomial
]):
"""
Add a given poylnomial to a copy of self.
"""
if
isinstance
(
other
,
int
)
or
isinstance
(
other
,
float
)
or
isinstance
(
other
,
Fraction
):
return
self
.
__add__
(
Monomial
({},
Polynomial
.
_rationalize_if_possible
(
other
)))
elif
isinstance
(
other
,
Monomial
):
monos
=
{
m
.
clone
()
for
m
in
self
.
monomials
}
for
_own_monos
in
monos
:
if
_own_monos
.
equal_upto_scalar
(
other
):
scalar
=
_own_monos
.
coeff
monos
-=
{
_own_monos
}
temp_variables
=
{
i
:
other
.
variables
[
i
]
for
i
in
other
.
variables
}
monos
|=
{
Monomial
(
temp_variables
,
Polynomial
.
_rationalize_if_possible
(
scalar
+
other
.
coeff
))}
return
Polynomial
([
z
for
z
in
monos
])
monos
|=
{
other
.
clone
()}
return
Polynomial
([
z
for
z
in
monos
])
elif
isinstance
(
other
,
Polynomial
):
temp
=
list
(
z
for
z
in
{
m
.
clone
()
for
m
in
self
.
all_monomials
()})
p
=
Polynomial
(
temp
)
for
o
in
other
.
all_monomials
():
p
=
p
.
__add__
(
o
.
clone
())
return
p
else
:
raise
ValueError
(
'Can only add int, float, Fraction, Monomials, or Polynomials to Polynomials.'
)
# def __sub__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial:
def
__sub__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
,
Monomial
]):
"""
Subtract the given polynomial
from a copy of self.
"""
if
isinstance
(
other
,
int
)
or
isinstance
(
other
,
float
)
or
isinstance
(
other
,
Fraction
):
return
self
.
__sub__
(
Monomial
({},
Polynomial
.
_rationalize_if_possible
(
other
)))
elif
isinstance
(
other
,
Monomial
):
monos
=
{
m
.
clone
()
for
m
in
self
.
all_monomials
()}
for
_own_monos
in
monos
:
if
_own_monos
.
equal_upto_scalar
(
other
):
scalar
=
_own_monos
.
coeff
monos
-=
{
_own_monos
}
temp_variables
=
{
i
:
other
.
variables
[
i
]
for
i
in
other
.
variables
}
monos
|=
{
Monomial
(
temp_variables
,
Polynomial
.
_rationalize_if_possible
(
scalar
-
other
.
coeff
))}
return
Polynomial
([
z
for
z
in
monos
])
to_insert
=
other
.
clone
()
to_insert
.
coeff
*=
-
1
monos
|=
{
to_insert
}
return
Polynomial
([
z
for
z
in
monos
])
elif
isinstance
(
other
,
Polynomial
):
p
=
Polynomial
(
list
(
z
for
z
in
{
m
.
clone
()
for
m
in
self
.
all_monomials
()}))
for
o
in
other
.
all_monomials
():
p
=
p
.
__sub__
(
o
.
clone
())
return
p
else
:
raise
ValueError
(
'Can only subtract int, float, Fraction, Monomials, or Polynomials from Polynomials.'
)
return
# def __mul__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial:
def
__mul__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
,
Monomial
]):
"""
Multiply a given polynomial
to a copy of self.
"""
if
isinstance
(
other
,
int
)
or
isinstance
(
other
,
float
)
or
isinstance
(
other
,
Fraction
):
result
=
Polynomial
([])
monos
=
{
m
.
clone
()
for
m
in
self
.
all_monomials
()}
for
m
in
monos
:
result
=
result
.
__add__
(
m
.
clone
()
*
other
)
return
result
elif
isinstance
(
other
,
Monomial
):
result
=
Polynomial
([])
monos
=
{
m
.
clone
()
for
m
in
self
.
all_monomials
()}
for
m
in
monos
:
result
=
result
.
__add__
(
m
.
clone
()
*
other
)
return
result
elif
isinstance
(
other
,
Polynomial
):
temp_self
=
{
m
.
clone
()
for
m
in
self
.
all_monomials
()}
temp_other
=
{
m
.
clone
()
for
m
in
other
.
all_monomials
()}
result
=
Polynomial
([])
for
i
in
temp_self
:
for
j
in
temp_other
:
result
=
result
.
__add__
(
i
*
j
)
return
result
else
:
raise
ValueError
(
'Can only multiple int, float, Fraction, Monomials, or Polynomials with Polynomials.'
)
# def __floordiv__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial:
def
__floordiv__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
,
Monomial
]):
"""
For Polynomials, floordiv is the same
as truediv.
"""
return
self
.
__truediv__
(
other
)
# def __truediv__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial:
def
__truediv__
(
self
,
other
:
Union
[
int
,
float
,
Fraction
,
Monomial
]):
"""
For Polynomials, only division by a monomial
is defined.
TODO: Implement polynomial / polynomial.
"""
if
isinstance
(
other
,
int
)
or
isinstance
(
other
,
float
)
or
isinstance
(
other
,
Fraction
):
return
self
.
__truediv__
(
Monomial
({},
other
) )
elif
isinstance
(
other
,
Monomial
):
poly_temp
=
reduce
(
lambda
acc
,
val
:
acc
+
val
,
map
(
lambda
x
:
x
/
other
, [
z
for
z
in
self
.
all_monomials
()]),
Polynomial
([
Monomial
({},
0
)]))
return
poly_temp
elif
isinstance
(
other
,
Polynomial
):
if
Monomial
({},
0
)
in
other
.
all_monomials
():
if
len
(
other
.
all_monomials
())
==
2
:
temp_set
=
{
x
for
x
in
other
.
all_monomials
()
if
x
!=
Monomial
({},
0
)}
only
=
temp_set
.
pop
()
return
self
.
__truediv__
(
only
)
elif
len
(
other
.
all_monomials
())
==
1
:
temp_set
=
{
x
for
x
in
other
.
all_monomials
()}
only
=
temp_set
.
pop
()
return
self
.
__truediv__
(
only
)
raise
ValueError
(
'Can only divide a polynomial by an int, float, Fraction, or a Monomial.'
)
return
# def clone(self) -> Polynomial:
def
clone
(
self
):
"""
Clone the polynomial.
"""
return
Polynomial
(
list
({
m
.
clone
()
for
m
in
self
.
all_monomials
()}))
def
variables
(
self
)
->
Set
:
"""
Get all the variables present
in this polynomials.
"""
res
=
set
()
for
i
in
self
.
all_monomials
():
res
|=
{
j
for
j
in
i
.
variables
}
res
=
list
(
res
)
# res.sort()
return
set
(
res
)
def
all_monomials
(
self
)
->
Iterable
[
Monomial
]:
"""
Get the monomials of this polynomial.
"""
return
{
m
for
m
in
self
.
monomials
if
m
!=
Monomial
({},
0
)}
def
__eq__
(
self
,
other
)
->
bool
:
"""
Return True if the other polynomial is the same as
this.
"""
if
isinstance
(
other
,
int
)
or
isinstance
(
other
,
float
)
or
isinstance
(
other
,
Fraction
):
other_poly
=
Polynomial
([
Monomial
({},
other
)])
return
self
.
__eq__
(
other_poly
)
elif
isinstance
(
other
,
Monomial
):
return
self
.
__eq__
(
Polynomial
([
other
]))
elif
isinstance
(
other
,
Polynomial
):
return
self
.
all_monomials
()
==
other
.
all_monomials
()
else
:
raise
ValueError
(
'Can only compare a polynomial with an int, float, Fraction, Monomial, or another Polynomial.'
)
def
subs
(
self
,
substitutions
:
Union
[
int
,
float
,
Fraction
,
Dict
[
int
,
Union
[
int
,
float
,
Fraction
]]])
->
Union
[
int
,
float
,
Fraction
]:
"""
Get the value after substituting
certain values for the variables
defined in substitutions.
"""
if
isinstance
(
substitutions
,
int
)
or
isinstance
(
substitutions
,
float
)
or
isinstance
(
substitutions
,
Fraction
):
substitutions
=
{
i
:
Polynomial
.
_rationalize_if_possible
(
substitutions
)
for
i
in
set
(
self
.
variables
())}
return
self
.
subs
(
substitutions
)
elif
not
isinstance
(
substitutions
,
dict
):
raise
ValueError
(
'The substitutions should be a dictionary.'
)
if
not
self
.
variables
().
issubset
(
set
(
substitutions
.
keys
())):
raise
ValueError
(
'Some variables didn
\'
t receive their values.'
)
ans
=
0
for
m
in
self
.
all_monomials
():
ans
+=
Polynomial
.
_rationalize_if_possible
(
m
.
substitute
(
substitutions
))
return
Polynomial
.
_rationalize_if_possible
(
ans
)
def
__str__
(
self
)
->
str
:
"""
Get a string representation of
the polynomial.
"""
return
' + '
.
join
(
str
(
m
)
for
m
in
self
.
all_monomials
()
if
m
.
coeff
!=
Fraction
(
0
,
1
))
Back
|
FazBrowse Home
|
New Git URL