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Taddeüs Kroes
trs
Commits
3cfe9c2e
Commit
3cfe9c2e
authored
Mar 27, 2012
by
Taddeus Kroes
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Added integral rules for functions and fractions.
parent
fa682fe0
Changes
3
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Showing
3 changed files
with
91 additions
and
7 deletions
+91
-7
src/rules/__init__.py
src/rules/__init__.py
+3
-2
src/rules/integrals.py
src/rules/integrals.py
+63
-3
tests/test_rules_integrals.py
tests/test_rules_integrals.py
+25
-2
No files found.
src/rules/__init__.py
View file @
3cfe9c2e
...
@@ -26,7 +26,7 @@ from src.rules.logarithmic import match_constant_logarithm, \
...
@@ -26,7 +26,7 @@ from src.rules.logarithmic import match_constant_logarithm, \
match_factor_in_multiplicant
match_factor_in_multiplicant
from
src.rules.integrals
import
match_solve_indef
,
match_constant_integral
,
\
from
src.rules.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_division_integral
,
match_function_integral
RULES
=
{
RULES
=
{
OP_ADD
:
[
match_add_numerics
,
match_add_constant_fractions
,
OP_ADD
:
[
match_add_numerics
,
match_add_constant_fractions
,
...
@@ -57,6 +57,7 @@ RULES = {
...
@@ -57,6 +57,7 @@ RULES = {
match_quotient_rule
],
match_quotient_rule
],
OP_LOG
:
[
match_constant_logarithm
,
match_factor_out_exponent
],
OP_LOG
:
[
match_constant_logarithm
,
match_factor_out_exponent
],
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
],
OP_INT_INDEF
:
[
match_solve_indef
],
OP_INT_INDEF
:
[
match_solve_indef
],
}
}
src/rules/integrals.py
View file @
3cfe9c2e
from
.utils
import
find_variables
,
infinity
,
replace_variable
,
find_variable
,
\
from
.utils
import
find_variables
,
infinity
,
replace_variable
,
find_variable
,
\
absolute
absolute
from
.logarithmic
import
ln
from
.logarithmic
import
ln
#
from .goniometry import sin, cos
from
.goniometry
import
sin
,
cos
from
..node
import
ExpressionNode
as
N
,
ExpressionLeaf
as
L
,
OP_INT
,
\
from
..node
import
ExpressionNode
as
N
,
ExpressionLeaf
as
L
,
OP_INT
,
\
OP_INT_INDEF
,
OP_MUL
,
OP_DIV
,
Scope
OP_INT_INDEF
,
OP_MUL
,
OP_DIV
,
OP_LOG
,
OP_SIN
,
OP_COS
,
Scope
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..translate
import
_
from
..translate
import
_
...
@@ -215,7 +215,7 @@ def division_integral(root, args):
...
@@ -215,7 +215,7 @@ def division_integral(root, args):
MESSAGES
[
division_integral
]
=
\
MESSAGES
[
division_integral
]
=
\
_
(
'1 / {0[1]} has the standard ant
-derivative ln|{0[1]}|
.'
)
_
(
'1 / {0[1]} has the standard ant
i-derivative ln|{0[1]}| + c
.'
)
def
extend_division_integral
(
root
,
args
):
def
extend_division_integral
(
root
,
args
):
...
@@ -229,3 +229,63 @@ def extend_division_integral(root, args):
...
@@ -229,3 +229,63 @@ def extend_division_integral(root, args):
MESSAGES
[
extend_division_integral
]
=
_
(
'Bring nominator {0[0][0]} out of the'
\
MESSAGES
[
extend_division_integral
]
=
_
(
'Bring nominator {0[0][0]} out of the'
\
' fraction to obtain a standard 1 / {0[0][1]} integral.'
)
' fraction to obtain a standard 1 / {0[0][1]} integral.'
)
def
match_function_integral
(
node
):
"""
int log_g(x) dx -> (xln(x) - x) / log_g(x)
int sin(x) dx -> -cos(x)
int cos(x) dx -> sin(x)
"""
assert
node
.
is_op
(
OP_INT
)
fx
,
x
=
node
[:
2
]
if
fx
.
is_leaf
or
fx
[
0
]
!=
x
:
return
[]
if
fx
.
op
==
OP_LOG
:
return
[
P
(
node
,
logarithm_integral
)]
if
fx
.
op
==
OP_SIN
:
return
[
P
(
node
,
sinus_integral
)]
if
fx
.
op
==
OP_COS
:
return
[
P
(
node
,
cosinus_integral
)]
return
[]
def
logarithm_integral
(
root
,
args
):
"""
int log_g(x) dx -> (xln(x) - x) / log_g(x)
"""
x
,
g
=
root
[
0
]
return
solve_integral
(
root
,
(
x
*
ln
(
x
)
-
x
)
/
ln
(
g
))
MESSAGES
[
logarithm_integral
]
=
_
(
'log_g(x) has the standard anti-derivative '
\
'(xln(x) - x) / log_g(x) + c.'
)
def
sinus_integral
(
root
,
args
):
"""
int sin(x) dx -> -cos(x)
"""
return
solve_integral
(
root
,
-
cos
(
root
[
0
][
0
]))
MESSAGES
[
sinus_integral
]
=
\
_
(
'{0[0]} has the standard anti-derivative -cos({0[0][0]}) + c.'
)
def
cosinus_integral
(
root
,
args
):
"""
int cos(x) dx -> sin(x)
"""
return
solve_integral
(
root
,
sin
(
root
[
0
][
0
]))
MESSAGES
[
cosinus_integral
]
=
\
_
(
'{0[0]} has the standard anti-derivative sin({0[0][0]}) + c.'
)
tests/test_rules_integrals.py
View file @
3cfe9c2e
...
@@ -3,9 +3,11 @@ from src.rules.integrals import indef, choose_constant, solve_integral, \
...
@@ -3,9 +3,11 @@ from src.rules.integrals import indef, choose_constant, solve_integral, \
integrate_variable_root
,
integrate_variable_exponent
,
\
integrate_variable_root
,
integrate_variable_exponent
,
\
match_constant_integral
,
constant_integral
,
\
match_constant_integral
,
constant_integral
,
\
match_factor_out_constant
,
factor_out_constant
,
\
match_factor_out_constant
,
factor_out_constant
,
\
match_division_integral
,
division_integral
,
extend_division_integral
match_division_integral
,
division_integral
,
extend_division_integral
,
\
match_function_integral
,
logarithm_integral
,
sinus_integral
,
\
cosinus_integral
from
src.rules.logarithmic
import
ln
from
src.rules.logarithmic
import
ln
#from
.goniometry import sin, cos
from
src.rules
.goniometry
import
sin
,
cos
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
...
@@ -103,3 +105,24 @@ class TestRulesIntegrals(RulesTestCase):
...
@@ -103,3 +105,24 @@ class TestRulesIntegrals(RulesTestCase):
# FIXME: 'a int 1 / x dx', # fix with strategy
# FIXME: 'a int 1 / x dx', # fix with strategy
# FIXME: 'aln|x| + c',
# FIXME: 'aln|x| + c',
])
])
def
test_match_function_integral
(
self
):
root0
,
root1
,
root2
=
tree
(
'int ln x, int sin x, int cos x'
)
self
.
assertEqualPos
(
match_function_integral
(
root0
),
[
P
(
root0
,
logarithm_integral
)])
self
.
assertEqualPos
(
match_function_integral
(
root1
),
[
P
(
root1
,
sinus_integral
)])
self
.
assertEqualPos
(
match_function_integral
(
root2
),
[
P
(
root2
,
cosinus_integral
)])
def
test_logarithm_integral
(
self
):
root
,
expect
=
tree
(
'int ln x, (xlnx - x) / ln e + c'
)
self
.
assertEqual
(
logarithm_integral
(
root
,
()),
expect
)
def
test_sinus_integral
(
self
):
root
,
expect
=
tree
(
'int sin x, -cos x + c'
)
self
.
assertEqual
(
sinus_integral
(
root
,
()),
expect
)
def
test_cosinus_integral
(
self
):
root
,
expect
=
tree
(
'int cos x, sin x + c'
)
self
.
assertEqual
(
cosinus_integral
(
root
,
()),
expect
)
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