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Taddeüs Kroes
trs
Commits
a0a12318
Commit
a0a12318
authored
Apr 19, 2012
by
Taddeus Kroes
Browse files
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Plain Diff
Tweaked some logarithmic rules.
parent
6b44c68e
Changes
3
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Inline
Side-by-side
Showing
3 changed files
with
142 additions
and
25 deletions
+142
-25
src/rules/__init__.py
src/rules/__init__.py
+3
-2
src/rules/logarithmic.py
src/rules/logarithmic.py
+79
-18
tests/test_rules_logarithmic.py
tests/test_rules_logarithmic.py
+60
-5
No files found.
src/rules/__init__.py
View file @
a0a12318
...
@@ -22,7 +22,7 @@ from .derivatives import match_zero_derivative, \
...
@@ -22,7 +22,7 @@ from .derivatives import match_zero_derivative, \
match_goniometric
,
match_sum_product_rule
,
match_quotient_rule
match_goniometric
,
match_sum_product_rule
,
match_quotient_rule
from
.logarithmic
import
match_constant_logarithm
,
\
from
.logarithmic
import
match_constant_logarithm
,
\
match_add_logarithms
,
match_raised_base
,
match_factor_out_exponent
,
\
match_add_logarithms
,
match_raised_base
,
match_factor_out_exponent
,
\
match_factor_in_multiplicant
match_factor_in_multiplicant
,
match_expand_terms
from
.integrals
import
match_solve_indef
,
match_constant_integral
,
\
from
.integrals
import
match_solve_indef
,
match_constant_integral
,
\
match_integrate_variable_power
,
match_factor_out_constant
,
\
match_integrate_variable_power
,
match_factor_out_constant
,
\
match_division_integral
,
match_function_integral
match_division_integral
,
match_function_integral
...
@@ -56,7 +56,8 @@ RULES = {
...
@@ -56,7 +56,8 @@ RULES = {
match_variable_power
,
match_const_deriv_multiplication
,
match_variable_power
,
match_const_deriv_multiplication
,
match_logarithmic
,
match_goniometric
,
match_sum_product_rule
,
match_logarithmic
,
match_goniometric
,
match_sum_product_rule
,
match_quotient_rule
],
match_quotient_rule
],
OP_LOG
:
[
match_constant_logarithm
,
match_factor_out_exponent
],
OP_LOG
:
[
match_constant_logarithm
,
match_factor_out_exponent
,
match_expand_terms
],
OP_INT
:
[
match_integrate_variable_power
,
match_constant_integral
,
OP_INT
:
[
match_integrate_variable_power
,
match_constant_integral
,
match_factor_out_constant
,
match_division_integral
,
match_factor_out_constant
,
match_division_integral
,
match_function_integral
],
match_function_integral
],
...
...
src/rules/logarithmic.py
View file @
a0a12318
from
itertools
import
combinations
,
product
from
itertools
import
combinations
,
product
,
ifilterfalse
from
.utils
import
find_variables
,
partition
from
.utils
import
find_variables
,
partition
,
divides
,
is_numeric_node
from
..node
import
ExpressionLeaf
as
L
,
OP_LOG
,
OP_ADD
,
OP_MUL
,
OP_POW
,
\
from
..node
import
ExpressionLeaf
as
L
,
OP_LOG
,
OP_ADD
,
OP_MUL
,
OP_POW
,
\
Scope
,
log
Scope
,
log
,
DEFAULT_LOGARITHM_BASE
,
E
,
OP_DIV
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..translate
import
_
from
..translate
import
_
...
@@ -11,8 +11,8 @@ def match_constant_logarithm(node):
...
@@ -11,8 +11,8 @@ def match_constant_logarithm(node):
"""
"""
log_1(a) -> # raise ValueError for base 1
log_1(a) -> # raise ValueError for base 1
log(1) -> 0
log(1) -> 0
log(a, a) -> 1
# Explicit possibility to prevent cycles
log(a, a) -> 1
log(a,
a) -> log(a) / log(a) # -> 1
log(a,
b) and b not in (10, e) -> log(a) / log(b)
"""
"""
assert
node
.
is_op
(
OP_LOG
)
assert
node
.
is_op
(
OP_LOG
)
...
@@ -30,8 +30,9 @@ def match_constant_logarithm(node):
...
@@ -30,8 +30,9 @@ def match_constant_logarithm(node):
if
raised
==
base
:
if
raised
==
base
:
# log(a, a) -> 1
# log(a, a) -> 1
p
.
append
(
P
(
node
,
base_equals_raised
))
p
.
append
(
P
(
node
,
base_equals_raised
))
# log(a, a) -> log(a) / log(a) # -> 1
p
.
append
(
P
(
node
,
divide_same_base
))
# TODO: When to do this except for this case?
elif
base
not
in
(
DEFAULT_LOGARITHM_BASE
,
E
):
# log(a, b) -> log(a) / log(b)
p
.
append
(
P
(
node
,
divide_same_base
))
p
.
append
(
P
(
node
,
divide_same_base
))
return
p
return
p
...
@@ -56,12 +57,12 @@ def base_equals_raised(root, args):
...
@@ -56,12 +57,12 @@ def base_equals_raised(root, args):
return
L
(
1
).
negate
(
root
.
negated
)
return
L
(
1
).
negate
(
root
.
negated
)
MESSAGES
[
base_equals_raised
]
=
_
(
'Logarithm {0} re
c
uces to 1.'
)
MESSAGES
[
base_equals_raised
]
=
_
(
'Logarithm {0} re
d
uces to 1.'
)
def
divide_same_base
(
root
,
args
):
def
divide_same_base
(
root
,
args
):
"""
"""
log(a, b) -> log(a) / log(b)
log(a, b)
and b != 10
-> log(a) / log(b)
"""
"""
raised
,
base
=
root
raised
,
base
=
root
...
@@ -73,10 +74,10 @@ MESSAGES[divide_same_base] = _('Apply log_b(a) = log(a) / log(b) on {0}.')
...
@@ -73,10 +74,10 @@ MESSAGES[divide_same_base] = _('Apply log_b(a) = log(a) / log(b) on {0}.')
def
match_add_logarithms
(
node
):
def
match_add_logarithms
(
node
):
"""
"""
log(a) + log(b) -> log(ab)
log(a) + log(b)
and a,b in Z
-> log(ab)
-log(a) - log(b) -> -(log(a) + log(b)) # -> -log(ab)
-log(a) - log(b)
and a,b in Z
-> -(log(a) + log(b)) # -> -log(ab)
log(a) - log(b) -> log(a / b)
log(a) - log(b)
and a/b in Z
-> log(a / b)
-log(a) + log(b) -> log(b / a)
-log(a) + log(b)
and a/b in Z
-> log(b / a)
"""
"""
assert
node
.
is_op
(
OP_ADD
)
assert
node
.
is_op
(
OP_ADD
)
...
@@ -86,7 +87,10 @@ def match_add_logarithms(node):
...
@@ -86,7 +87,10 @@ def match_add_logarithms(node):
for
log_a
,
log_b
in
combinations
(
logarithms
,
2
):
for
log_a
,
log_b
in
combinations
(
logarithms
,
2
):
# Compare base
# Compare base
if
log_a
[
1
]
!=
log_b
[
1
]:
(
a
,
base_a
),
(
b
,
base_b
)
=
log_a
,
log_b
if
base_a
!=
base_b
or
not
a
.
is_numeric
()
\
or
not
b
.
is_numeric
():
# pragma: nocover
continue
continue
a_negated
=
log_a
.
negated
==
1
a_negated
=
log_a
.
negated
==
1
...
@@ -98,10 +102,10 @@ def match_add_logarithms(node):
...
@@ -98,10 +102,10 @@ def match_add_logarithms(node):
elif
a_negated
and
b_negated
:
elif
a_negated
and
b_negated
:
# -log(a) - log(b) -> -(log(a) + log(b))
# -log(a) - log(b) -> -(log(a) + log(b))
p
.
append
(
P
(
node
,
expand_negations
,
(
scope
,
log_a
,
log_b
)))
p
.
append
(
P
(
node
,
expand_negations
,
(
scope
,
log_a
,
log_b
)))
elif
not
log_a
.
negated
and
b_negated
:
elif
not
log_a
.
negated
and
b_negated
and
divides
(
b
.
value
,
a
.
value
)
:
# log(a) - log(b) -> log(a / b)
# log(a) - log(b) -> log(a / b)
p
.
append
(
P
(
node
,
subtract_logarithms
,
(
scope
,
log_a
,
log_b
)))
p
.
append
(
P
(
node
,
subtract_logarithms
,
(
scope
,
log_a
,
log_b
)))
elif
a_negated
and
not
log_b
.
negated
:
elif
a_negated
and
not
log_b
.
negated
and
divides
(
a
.
value
,
b
.
value
)
:
# -log(a) + log(b) -> log(b / a)
# -log(a) + log(b) -> log(b / a)
p
.
append
(
P
(
node
,
subtract_logarithms
,
(
scope
,
log_b
,
log_a
)))
p
.
append
(
P
(
node
,
subtract_logarithms
,
(
scope
,
log_b
,
log_a
)))
...
@@ -161,8 +165,8 @@ MESSAGES[subtract_logarithms] = _('Apply log(a) - log(b) = log(a / b).')
...
@@ -161,8 +165,8 @@ MESSAGES[subtract_logarithms] = _('Apply log(a) - log(b) = log(a / b).')
def
match_raised_base
(
node
):
def
match_raised_base
(
node
):
"""
"""
g ^ log_g(a) -> a
g ^ log_g(a)
-> a
g ^ (blog_g(a)) -> g ^ log_g(a ^ b)
g ^ (b
*
log_g(a)) -> g ^ log_g(a ^ b)
"""
"""
assert
node
.
is_op
(
OP_POW
)
assert
node
.
is_op
(
OP_POW
)
...
@@ -188,11 +192,18 @@ def match_raised_base(node):
...
@@ -188,11 +192,18 @@ def match_raised_base(node):
def
factor_in_exponent_multiplicant
(
root
,
args
):
def
factor_in_exponent_multiplicant
(
root
,
args
):
"""
g ^ (b * log_g(a)) -> g ^ log_g(a ^ b)
"""
r
,
e
=
root
r
,
e
=
root
return
r
**
factor_in_multiplicant
(
e
,
args
)
return
r
**
factor_in_multiplicant
(
e
,
args
)
MESSAGES
[
factor_in_exponent_multiplicant
]
=
\
_
(
'Bring {2} into {3} as exponent so that the power can be removed.'
)
def
raised_base
(
root
,
args
):
def
raised_base
(
root
,
args
):
"""
"""
g ^ log_g(a) -> a
g ^ log_g(a) -> a
...
@@ -285,3 +296,53 @@ def factor_in_multiplicant(root, args):
...
@@ -285,3 +296,53 @@ def factor_in_multiplicant(root, args):
MESSAGES
[
factor_in_multiplicant
]
=
\
MESSAGES
[
factor_in_multiplicant
]
=
\
_
(
'Bring multiplicant {2} into {3} as the exponent of {3[0]}.'
)
_
(
'Bring multiplicant {2} into {3} as the exponent of {3[0]}.'
)
def
match_expand_terms
(
node
):
"""
log(ab) and a not in Z -> log(a) + log(b)
log(a / b) -> log(a) - log(b)
"""
assert
node
.
is_op
(
OP_LOG
)
exp
=
node
[
0
]
if
exp
.
is_op
(
OP_MUL
):
scope
=
Scope
(
exp
)
return
[
P
(
node
,
expand_multiplication_terms
,
(
scope
,
n
))
\
for
n
in
ifilterfalse
(
is_numeric_node
,
scope
)]
if
exp
.
is_op
(
OP_DIV
):
return
[
P
(
node
,
expand_division_terms
)]
return
[]
def
expand_multiplication_terms
(
root
,
args
):
"""
log(ab) and a not in Z -> log(a) + log(b)
"""
scope
,
n
=
args
scope
.
remove
(
n
)
base
=
root
[
1
]
addition
=
log
(
n
,
base
=
base
)
+
log
(
scope
.
as_nary_node
(),
base
=
base
)
return
addition
.
negate
(
root
.
negated
)
MESSAGES
[
expand_multiplication_terms
]
=
_
(
'Extract {2} from {0}.'
)
def
expand_division_terms
(
root
,
args
):
"""
log(a / b) -> log(a) - log(b)
"""
division
,
base
=
root
n
,
d
=
division
addition
=
log
(
n
.
negate
(
division
.
negated
),
base
=
base
)
-
log
(
d
,
base
=
base
)
return
addition
.
negate
(
root
.
negated
)
MESSAGES
[
expand_division_terms
]
=
_
(
'Expand {0} to a subtraction.'
)
tests/test_rules_logarithmic.py
View file @
a0a12318
...
@@ -4,7 +4,9 @@ from src.rules.logarithmic import log, match_constant_logarithm, \
...
@@ -4,7 +4,9 @@ from src.rules.logarithmic import log, match_constant_logarithm, \
subtract_logarithms
,
match_raised_base
,
raised_base
,
\
subtract_logarithms
,
match_raised_base
,
raised_base
,
\
match_factor_out_exponent
,
split_negative_exponent
,
\
match_factor_out_exponent
,
split_negative_exponent
,
\
factor_out_exponent
,
match_factor_in_multiplicant
,
\
factor_out_exponent
,
match_factor_in_multiplicant
,
\
factor_in_multiplicant
factor_in_multiplicant
,
match_expand_terms
,
\
expand_multiplication_terms
,
expand_division_terms
,
\
factor_in_exponent_multiplicant
from
src.node
import
Scope
from
src.node
import
Scope
from
src.possibilities
import
Possibility
as
P
from
src.possibilities
import
Possibility
as
P
from
tests.rulestestcase
import
RulesTestCase
,
tree
from
tests.rulestestcase
import
RulesTestCase
,
tree
...
@@ -30,10 +32,21 @@ class TestRulesLogarithmic(RulesTestCase):
...
@@ -30,10 +32,21 @@ class TestRulesLogarithmic(RulesTestCase):
[
P
(
root
,
base_equals_raised
),
[
P
(
root
,
base_equals_raised
),
P
(
root
,
divide_same_base
)])
P
(
root
,
divide_same_base
)])
root
=
tree
(
'log(a, b)'
)
self
.
assertEqualPos
(
match_constant_logarithm
(
root
),
[
P
(
root
,
divide_same_base
)])
def
test_logarithm_of_one
(
self
):
def
test_logarithm_of_one
(
self
):
root
=
tree
(
'log 1'
)
root
=
tree
(
'log 1'
)
self
.
assertEqual
(
logarithm_of_one
(
root
,
()),
0
)
self
.
assertEqual
(
logarithm_of_one
(
root
,
()),
0
)
def
test_base_equals_raised
(
self
):
root
,
expect
=
tree
(
'log(a, a), 1'
)
self
.
assertEqual
(
base_equals_raised
(
root
,
()),
expect
)
root
,
expect
=
tree
(
'-log(a, a), -1'
)
self
.
assertEqual
(
base_equals_raised
(
root
,
()),
expect
)
def
test_divide_same_base
(
self
):
def
test_divide_same_base
(
self
):
root
,
l5
,
l6
=
tree
(
'log(5, 6), 5, 6'
)
root
,
l5
,
l6
=
tree
(
'log(5, 6), 5, 6'
)
self
.
assertEqual
(
divide_same_base
(
root
,
()),
log
(
l5
)
/
log
(
l6
))
self
.
assertEqual
(
divide_same_base
(
root
,
()),
log
(
l5
)
/
log
(
l6
))
...
@@ -42,19 +55,27 @@ class TestRulesLogarithmic(RulesTestCase):
...
@@ -42,19 +55,27 @@ class TestRulesLogarithmic(RulesTestCase):
root
=
tree
(
'log a + ln b'
)
root
=
tree
(
'log a + ln b'
)
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
[])
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
[])
log_a
,
log_b
=
root
=
tree
(
'log a + log b'
)
# log(ab) is not desired if ab is not reduceable
root
=
tree
(
'log a + log b'
)
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
[])
log_a
,
log_b
=
root
=
tree
(
'log 2 + log 3'
)
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
[
P
(
root
,
add_logarithms
,
(
Scope
(
root
),
log_a
,
log_b
))])
[
P
(
root
,
add_logarithms
,
(
Scope
(
root
),
log_a
,
log_b
))])
log_a
,
log_b
=
root
=
tree
(
'-log
a - log b
'
)
log_a
,
log_b
=
root
=
tree
(
'-log
2 - log 3
'
)
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
[
P
(
root
,
expand_negations
,
(
Scope
(
root
),
log_a
,
log_b
))])
[
P
(
root
,
expand_negations
,
(
Scope
(
root
),
log_a
,
log_b
))])
log_a
,
log_b
=
root
=
tree
(
'log a - log b'
)
# log(2 / 3) is not desired because 2 / 3 cannot be reduced
log_a
,
log_b
=
root
=
tree
(
'log 2 - log 3'
)
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
[])
log_a
,
log_b
=
root
=
tree
(
'log 4 - log 2'
)
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
[
P
(
root
,
subtract_logarithms
,
(
Scope
(
root
),
log_a
,
log_b
))])
[
P
(
root
,
subtract_logarithms
,
(
Scope
(
root
),
log_a
,
log_b
))])
log_a
,
log_b
=
root
=
tree
(
'-log
a + log b
'
)
log_a
,
log_b
=
root
=
tree
(
'-log
2 + log 4
'
)
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
self
.
assertEqualPos
(
match_add_logarithms
(
root
),
[
P
(
root
,
subtract_logarithms
,
(
Scope
(
root
),
log_b
,
log_a
))])
[
P
(
root
,
subtract_logarithms
,
(
Scope
(
root
),
log_b
,
log_a
))])
...
@@ -93,6 +114,18 @@ class TestRulesLogarithmic(RulesTestCase):
...
@@ -93,6 +114,18 @@ class TestRulesLogarithmic(RulesTestCase):
root
=
tree
(
'2 ^ log_3(a)'
)
root
=
tree
(
'2 ^ log_3(a)'
)
self
.
assertEqualPos
(
match_raised_base
(
root
),
[])
self
.
assertEqualPos
(
match_raised_base
(
root
),
[])
root
=
tree
(
'e ^ (2ln x)'
)
l2
,
lnx
=
mul
=
root
[
1
]
self
.
assertEqualPos
(
match_raised_base
(
root
),
[
P
(
root
,
factor_in_exponent_multiplicant
,
(
Scope
(
mul
),
l2
,
lnx
))])
def
test_factor_in_exponent_multiplicant
(
self
):
root
,
expect
=
tree
(
'e ^ (2ln x), e ^ ln x ^ 2'
)
l2
,
lnx
=
mul
=
root
[
1
]
self
.
assertEqual
(
factor_in_exponent_multiplicant
(
root
,
(
Scope
(
mul
),
l2
,
lnx
)),
expect
)
def
test_raised_base
(
self
):
def
test_raised_base
(
self
):
root
,
a
=
tree
(
'2 ^ log_2(a), a'
)
root
,
a
=
tree
(
'2 ^ log_2(a), a'
)
self
.
assertEqual
(
raised_base
(
root
,
(
root
[
1
][
0
],)),
a
)
self
.
assertEqual
(
raised_base
(
root
,
(
root
[
1
][
0
],)),
a
)
...
@@ -136,3 +169,25 @@ class TestRulesLogarithmic(RulesTestCase):
...
@@ -136,3 +169,25 @@ class TestRulesLogarithmic(RulesTestCase):
l2
,
log3
=
root
l2
,
log3
=
root
self
.
assertEqual
(
factor_in_multiplicant
(
root
,
(
Scope
(
root
),
l2
,
log3
)),
self
.
assertEqual
(
factor_in_multiplicant
(
root
,
(
Scope
(
root
),
l2
,
log3
)),
expect
)
expect
)
def
test_match_expand_terms
(
self
):
ab
,
base
=
root
=
tree
(
'log(2x)'
)
a
,
b
=
ab
self
.
assertEqualPos
(
match_expand_terms
(
root
),
[
P
(
root
,
expand_multiplication_terms
,
(
Scope
(
ab
),
b
))])
root
=
tree
(
'log(2 * 3)'
)
self
.
assertEqualPos
(
match_expand_terms
(
root
),
[])
root
=
tree
(
'log(2 / a)'
)
self
.
assertEqualPos
(
match_expand_terms
(
root
),
[
P
(
root
,
expand_division_terms
)])
def
test_expand_multiplication_terms
(
self
):
root
,
expect
=
tree
(
'log(2x), log x + log 2'
)
self
.
assertEqual
(
expand_multiplication_terms
(
root
,
(
Scope
(
root
[
0
]),
root
[
0
][
1
])),
expect
)
def
test_expand_division_terms
(
self
):
root
,
expect
=
tree
(
'log(2 / x), log 2 - log x'
)
self
.
assertEqual
(
expand_division_terms
(
root
,
()),
expect
)
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