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Taddeüs Kroes
trs
Commits
d419cb36
Commit
d419cb36
authored
Feb 16, 2012
by
Taddeus Kroes
Browse files
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Plain Diff
Merge branch 'negated' of kompiler.org:trs
parents
8f398255
105cd269
Changes
10
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Inline
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Showing
10 changed files
with
171 additions
and
232 deletions
+171
-232
external/graph_drawing
external/graph_drawing
+1
-1
src/node.py
src/node.py
+33
-33
src/parser.py
src/parser.py
+19
-13
src/rules/factors.py
src/rules/factors.py
+2
-2
src/rules/fractions.py
src/rules/fractions.py
+9
-33
src/rules/groups.py
src/rules/groups.py
+2
-4
src/rules/negation.py
src/rules/negation.py
+27
-38
src/rules/numerics.py
src/rules/numerics.py
+9
-35
src/rules/poly.py
src/rules/poly.py
+2
-6
src/rules/powers.py
src/rules/powers.py
+67
-67
No files found.
graph_drawing
@
84ad376b
Subproject commit
11940973bdfef9432438b054c65b28af2eb97d0c
Subproject commit
84ad376b81ac72e163bacd7b538df16cac9be153
src/node.py
View file @
d419cb36
...
...
@@ -43,7 +43,7 @@ TYPE_MAP = {
OP_MAP
=
{
'+'
:
OP_ADD
,
# Either substraction or negation. Skip the operator sign in 'x' (= 2).
'-'
:
lambda
x
:
OP_SUB
if
len
(
x
)
>
2
else
OP_NEG
,
'-'
:
OP_SUB
,
'*'
:
OP_MUL
,
'/'
:
OP_DIV
,
'^'
:
OP_POW
,
...
...
@@ -60,6 +60,10 @@ def to_expression(obj):
class
ExpressionBase
(
object
):
def
__init__
(
self
,
*
args
,
**
kwargs
):
self
.
negated
=
0
def
clone
(
self
):
return
copy
.
deepcopy
(
self
)
...
...
@@ -86,16 +90,11 @@ class ExpressionBase(object):
if
self
.
is_leaf
:
if
other
.
is_leaf
:
# Both are leafs, string compare the value.
return
str
(
self
.
value
)
<
str
(
other
.
value
)
# Self is a leaf, thus has less value than an expression node.
return
True
self_value
=
'-'
*
(
self
.
negated
&
1
)
+
str
(
self
.
value
)
other_value
=
'-'
*
(
other
.
negated
&
1
)
+
str
(
other
.
value
)
return
self_value
<
other_value
if
self
.
is_op
(
OP_NEG
)
and
self
[
0
].
is_leaf
:
if
other
.
is_leaf
:
# Both are leafs, string compare the value.
return
(
'-'
+
str
(
self
.
value
))
<
str
(
other
.
value
)
if
other
.
is_op
(
OP_NEG
)
and
other
[
0
].
is_leaf
:
return
(
'-'
+
str
(
self
.
value
))
<
(
'-'
+
str
(
other
.
value
))
# Self is a leaf, thus has less value than an expression node.
return
True
...
...
@@ -113,24 +112,6 @@ class ExpressionBase(object):
def
is_op
(
self
,
op
):
return
not
self
.
is_leaf
and
self
.
op
==
op
def
is_op_or_negated
(
self
,
op
):
if
self
.
is_leaf
:
return
False
if
self
.
op
==
OP_NEG
:
return
self
[
0
].
is_op
(
op
)
return
self
.
op
==
op
def
is_leaf_or_negated
(
self
):
if
self
.
is_leaf
:
return
True
if
self
.
is_op
(
OP_NEG
):
return
self
[
0
].
is_leaf
return
False
def
is_power
(
self
):
return
not
self
.
is_leaf
and
self
.
op
==
OP_POW
...
...
@@ -164,8 +145,13 @@ class ExpressionBase(object):
def
__pow__
(
self
,
other
):
return
ExpressionNode
(
'^'
,
self
,
to_expression
(
other
))
def
__neg__
(
self
):
return
ExpressionNode
(
'-'
,
self
)
def
reduce_negation
(
self
,
n
=
1
):
"""Remove n negation flags from the node."""
return
self
.
negate
(
-
n
)
def
negate
(
self
,
n
=
1
):
"""Negate the node n times."""
return
negate
(
self
,
self
.
negated
+
n
)
class
ExpressionNode
(
Node
,
ExpressionBase
):
...
...
@@ -226,8 +212,10 @@ class ExpressionNode(Node, ExpressionBase):
return
(
ExpressionLeaf
(
1
),
self
[
0
],
self
[
1
])
# rule: -r -> (1, r, 1)
if
self
.
is_op
(
OP_NEG
):
return
(
ExpressionLeaf
(
1
),
-
self
[
0
],
ExpressionLeaf
(
1
))
# rule: --r -> (1, r, 1)
# rule: ---r -> (1, r, 1)
if
self
.
negated
:
return
(
ExpressionLeaf
(
1
),
self
,
ExpressionLeaf
(
1
))
if
self
.
op
!=
OP_MUL
:
return
...
...
@@ -309,7 +297,6 @@ class ExpressionNode(Node, ExpressionBase):
class
ExpressionLeaf
(
Leaf
,
ExpressionBase
):
def
__init__
(
self
,
*
args
,
**
kwargs
):
super
(
ExpressionLeaf
,
self
).
__init__
(
*
args
,
**
kwargs
)
self
.
type
=
TYPE_MAP
[
type
(
args
[
0
])]
def
__eq__
(
self
,
other
):
...
...
@@ -339,6 +326,11 @@ class ExpressionLeaf(Leaf, ExpressionBase):
# rule: 1 * r ^ 1 -> (1, r, 1)
return
(
ExpressionLeaf
(
1
),
self
,
ExpressionLeaf
(
1
))
def
actual_value
(
self
):
assert
self
.
is_numeric
()
return
(
1
-
2
*
(
self
.
negated
&
1
))
*
self
.
value
class
Scope
(
object
):
...
...
@@ -409,3 +401,11 @@ def get_scope(node):
scope
.
append
(
child
)
return
scope
def
negate
(
node
,
n
=
1
):
"""Negate the given node n times."""
node
=
node
.
clone
()
node
.
negated
=
n
return
node
src/parser.py
View file @
d419cb36
...
...
@@ -16,7 +16,7 @@ sys.path.insert(1, EXTERNAL_MODS)
from
pybison
import
BisonParser
,
BisonSyntaxError
from
graph_drawing.graph
import
generate_graph
from
node
import
TYPE_OPERATOR
,
OP_COMMA
from
node
import
TYPE_OPERATOR
,
OP_COMMA
,
OP_NEG
from
rules
import
RULES
from
possibilities
import
filter_duplicates
,
pick_suggestion
,
apply_suggestion
...
...
@@ -180,11 +180,13 @@ class Parser(BisonParser):
return
data
def
hook_handler
(
self
,
target
,
option
,
names
,
values
,
retval
):
if
target
in
[
'exp'
,
'line'
,
'input'
]
or
not
retval
\
or
retval
.
type
!=
TYPE_OPERATOR
:
if
target
in
[
'exp'
,
'line'
,
'input'
]
or
not
retval
:
return
retval
if
self
.
subtree_map
:
if
not
retval
.
negated
and
retval
.
type
!=
TYPE_OPERATOR
:
return
retval
if
self
.
subtree_map
and
retval
.
type
==
TYPE_OPERATOR
:
# Update the subtree map to let the subtree point to its parent
# node.
parent_nodes
=
self
.
subtree_map
.
keys
()
...
...
@@ -193,10 +195,15 @@ class Parser(BisonParser):
if
child
in
parent_nodes
:
self
.
subtree_map
[
child
]
=
retval
if
retval
.
op
not
in
RULES
:
return
retval
if
retval
.
type
==
TYPE_OPERATOR
and
retval
.
op
in
RULES
:
handlers
=
RULES
[
retval
.
op
]
else
:
handlers
=
[]
if
retval
.
negated
:
handlers
+=
RULES
[
OP_NEG
]
for
handler
in
RULES
[
retval
.
op
]
:
for
handler
in
handlers
:
possibilities
=
handler
(
retval
)
# Record the subtree root node in order to avoid tree traversal.
...
...
@@ -343,7 +350,9 @@ class Parser(BisonParser):
"""
if
option
==
0
:
# rule: NEG exp
return
Node
(
'-'
,
values
[
1
])
node
=
values
[
1
]
node
.
negated
+=
1
return
node
raise
BisonSyntaxError
(
'Unsupported option %d in target "%s".'
%
(
option
,
target
))
# pragma: nocover
...
...
@@ -361,11 +370,8 @@ class Parser(BisonParser):
return
Node
(
values
[
1
],
values
[
0
],
values
[
2
])
if
option
==
4
:
# rule: exp MINUS exp
# It is necessary to call the hook_handler here explicitly, since
# the minus operator is internally represented as two nodes (unary
# negation and binary plus).
node
=
Node
(
'-'
,
values
[
2
])
node
=
self
.
hook_handler
(
target
,
option
,
names
,
values
,
node
)
node
=
values
[
2
]
node
.
negated
+=
1
return
Node
(
'+'
,
values
[
0
],
node
)
raise
BisonSyntaxError
(
'Unsupported option %d in target "%s".'
...
...
src/rules/factors.py
View file @
d419cb36
from
itertools
import
product
,
combinations
from
..node
import
Scope
,
OP_ADD
,
OP_MUL
,
OP_NEG
from
..node
import
Scope
,
OP_ADD
,
OP_MUL
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..translate
import
_
...
...
@@ -18,7 +18,7 @@ def match_expand(node):
additions
=
[]
for
n
in
Scope
(
node
):
if
n
.
is_leaf
or
n
.
is_op
(
OP_NEG
)
and
n
[
0
].
is_leaf
:
if
n
.
is_leaf
:
leaves
.
append
(
n
)
elif
n
.
op
==
OP_ADD
:
additions
.
append
(
n
)
...
...
src/rules/fractions.py
View file @
d419cb36
from
itertools
import
combinations
from
.utils
import
least_common_multiple
from
..node
import
ExpressionLeaf
as
L
,
Scope
,
OP_DIV
,
OP_ADD
,
OP_MUL
,
OP_NEG
from
..node
import
ExpressionLeaf
as
L
,
Scope
,
OP_DIV
,
OP_ADD
,
OP_MUL
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..translate
import
_
...
...
@@ -80,22 +80,11 @@ def match_add_constant_fractions(node):
p
=
[]
def
is_division
(
node
):
return
node
.
is_op
(
OP_DIV
)
or
\
(
node
.
is_op
(
OP_NEG
)
and
node
[
0
].
is_op
(
OP_DIV
))
fractions
=
filter
(
is_division
,
Scope
(
node
))
fractions
=
filter
(
lambda
node
:
node
.
is_op
(
OP_DIV
),
Scope
(
node
))
for
a
,
b
in
combinations
(
fractions
,
2
):
if
a
.
is_op
(
OP_NEG
):
na
,
da
=
a
[
0
]
else
:
na
,
da
=
a
if
b
.
is_op
(
OP_NEG
):
nb
,
db
=
b
[
0
]
else
:
nb
,
db
=
b
na
,
da
=
a
nb
,
db
=
b
if
da
==
db
:
# Equal denominators, add nominators to create a single fraction
...
...
@@ -116,20 +105,17 @@ def equalize_denominators(root, args):
a / 2 + b / 4 -> 2a / 4 + b / 4
"""
denom
=
args
[
2
]
scope
=
Scope
(
root
)
for
fraction
in
args
[:
2
]:
n
,
d
=
fraction
[
0
]
if
fraction
.
is_op
(
OP_NEG
)
else
fraction
n
,
d
=
fraction
mult
=
denom
/
d
.
value
if
mult
!=
1
:
n
=
L
(
n
.
value
*
mult
)
if
n
.
is_numeric
()
else
L
(
mult
)
*
n
if
fraction
.
is_op
(
OP_NEG
):
scope
.
remove
(
fraction
,
-
(
n
/
L
(
d
.
value
*
mult
)))
else
:
scope
.
remove
(
fraction
,
n
/
L
(
d
.
value
*
mult
))
scope
.
remove
(
fraction
,
negate
(
n
/
L
(
d
.
value
*
mult
),
fraction
.
negated
))
return
scope
.
as_nary_node
()
...
...
@@ -147,21 +133,11 @@ def add_nominators(root, args):
"""
# TODO: is 'add' Appropriate when rewriting to "(a + (-c)) / b"?
ab
,
cb
=
args
if
ab
.
is_op
(
OP_NEG
):
a
,
b
=
ab
[
0
]
else
:
a
,
b
=
ab
if
cb
.
is_op
(
OP_NEG
):
c
=
-
cb
[
0
][
0
]
else
:
c
=
cb
[
0
]
a
,
b
=
ab
scope
=
Scope
(
root
)
# Replace the left node with the new expression
scope
.
remove
(
ab
,
(
a
+
c
)
/
b
)
scope
.
remove
(
ab
,
(
a
+
negate
(
cb
[
0
],
cb
.
negated
)
)
/
b
)
# Remove the right node
scope
.
remove
(
cb
)
...
...
src/rules/groups.py
View file @
d419cb36
from
itertools
import
combinations
from
..node
import
ExpressionNode
as
Node
,
ExpressionLeaf
as
Leaf
,
Scope
,
\
OP_ADD
,
OP_MUL
,
OP_NEG
OP_ADD
,
OP_MUL
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..translate
import
_
...
...
@@ -18,7 +18,6 @@ def match_combine_groups(node):
ab + 2ab -> 3ab
ab + ba -> 2ab
"""
# TODO: handle OP_NEG nodes
assert
node
.
is_op
(
OP_ADD
)
p
=
[]
...
...
@@ -34,8 +33,7 @@ def match_combine_groups(node):
l
=
len
(
scope
)
for
i
,
sub_node
in
enumerate
(
scope
):
if
sub_node
.
is_numeric
()
or
(
sub_node
.
is_op
(
OP_NEG
)
and
sub_node
[
0
].
is_numeric
()):
if
sub_node
.
is_numeric
():
others
=
[
scope
[
j
]
for
j
in
range
(
i
)
+
range
(
i
+
1
,
l
)]
if
len
(
others
)
==
1
:
...
...
src/rules/negation.py
View file @
d419cb36
from
..node
import
get_scope
,
nary_node
,
OP_
NEG
,
OP_
ADD
,
OP_MUL
,
OP_DIV
from
..node
import
get_scope
,
nary_node
,
OP_ADD
,
OP_MUL
,
OP_DIV
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..translate
import
_
...
...
@@ -6,58 +6,48 @@ from ..translate import _
def
match_negate_group
(
node
):
"""
--a -> a
--ab -> ab
-(-ab + c) -> --ab - c
-(a * ... * -b) -> ab
-(a + b + ... + z) -> -a + -b + ... + -z
"""
assert
node
.
is_op
(
OP_NEG
)
assert
node
.
negated
val
=
node
[
0
]
if
val
.
is_op
(
OP_NEG
):
if
node
.
negated
==
2
:
# --a
return
[
P
(
node
,
double_negation
,
(
node
,))]
if
not
val
.
is_leaf
:
scope
=
get_scope
(
val
)
if
not
any
(
map
(
lambda
n
:
n
.
is_op
(
OP_NEG
),
scope
)):
return
[]
if
not
node
.
is_leaf
:
scope
=
get_scope
(
node
)
if
val
.
is_op
(
OP_MUL
):
# -
-a
b
return
[
P
(
node
,
negate_
polynome
,
(
node
,
scope
))]
if
node
.
is_op
(
OP_MUL
)
and
any
(
map
(
lambda
n
:
n
.
negated
,
scope
)
):
# -
(-a)
b
return
[
P
(
node
,
negate_
group
,
(
node
,
scope
))]
elif
val
.
is_op
(
OP_ADD
):
if
node
.
is_op
(
OP_ADD
):
# -(ab + c) -> -ab - c
# -(-ab + c) -> ab - c
return
[
P
(
node
,
negate_
group
,
(
node
,
scope
))]
return
[
P
(
node
,
negate_
polynome
,
(
node
,
scope
))]
return
[]
def
negate_
polynome
(
root
,
args
):
def
negate_
group
(
root
,
args
):
"""
# -a * -3c -> a * 3c
--a * 3c -> a * 3c
--ab -> ab
--abc -> abc
-(a * -3c) -> a * 3c
-(a * ... * -b) -> ab
"""
node
,
scope
=
args
for
i
,
n
in
enumerate
(
scope
):
# XXX: validate this property!
if
n
.
is_op
(
OP_NEG
):
scope
[
i
]
=
n
[
0
]
return
nary_node
(
'*'
,
scope
)
if
n
.
negated
:
scope
[
i
]
=
n
.
reduce_negation
()
r
aise
RuntimeError
(
'No negation node found in scope.'
)
r
eturn
nary_node
(
'*'
,
scope
).
reduce_negation
(
)
MESSAGES
[
negate_
polynome
]
=
_
(
'Apply negation to the polynome {1[0]}.'
)
MESSAGES
[
negate_
group
]
=
_
(
'Apply negation to the polynome {1[0]}.'
)
def
negate_
group
(
root
,
args
):
def
negate_
polynome
(
root
,
args
):
"""
-(-ab + ... + c) -> --ab + ... + -c
"""
...
...
@@ -70,16 +60,14 @@ def negate_group(root, args):
return
nary_node
(
'+'
,
scope
)
MESSAGES
[
negate_
group
]
=
_
(
'Apply negation to the subexpression {1[0]}.'
)
MESSAGES
[
negate_
polynome
]
=
_
(
'Apply negation to the subexpression {1[0]}.'
)
def
double_negation
(
root
,
args
):
"""
--a -> a
"""
node
=
args
[
0
]
return
node
[
0
][
0
]
return
negate
(
args
[
0
],
args
[
0
].
negated
-
2
)
MESSAGES
[
double_negation
]
=
_
(
'Remove double negation in {1}.'
)
...
...
@@ -92,14 +80,12 @@ def match_negated_division(node):
assert
node
.
is_op
(
OP_DIV
)
a
,
b
=
node
a_neg
=
a
.
is_op
(
OP_NEG
)
b_neg
=
b
.
is_op
(
OP_NEG
)
if
a
_neg
and
b_neg
:
if
a
.
negated
and
b
.
negated
:
return
[
P
(
node
,
double_negated_division
,
(
node
,))]
elif
a
_neg
:
elif
a
.
negated
:
return
[
P
(
node
,
single_negated_division
,
(
a
[
0
],
b
))]
elif
b
_neg
:
elif
b
.
negated
:
return
[
P
(
node
,
single_negated_division
,
(
a
,
b
[
0
]))]
return
[]
...
...
@@ -132,3 +118,6 @@ def double_negated_division(root, args):
MESSAGES
[
double_negated_division
]
=
\
_
(
'Eliminate top and bottom negation in {1}.'
)
# TODO: negated multiplication: -a * -b = ab
src/rules/numerics.py
View file @
d419cb36
from
itertools
import
combinations
from
..node
import
ExpressionLeaf
as
Leaf
,
Scope
,
OP_DIV
,
OP_MUL
,
OP_NEG
from
..node
import
ExpressionLeaf
as
Leaf
,
Scope
,
negate
,
OP_DIV
,
OP_MUL
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..translate
import
_
...
...
@@ -16,21 +16,10 @@ def add_numerics(root, args):
-2 + -3 -> -5
"""
n0
,
n1
,
c0
,
c1
=
args
if
c0
.
is_op
(
OP_NEG
):
c0
=
-
c0
[
0
].
value
else
:
c0
=
c0
.
value
if
c1
.
is_op
(
OP_NEG
):
c1
=
(
-
c1
[
0
].
value
)
else
:
c1
=
c1
.
value
scope
=
Scope
(
root
)
# Replace the left node with the new expression
scope
.
remove
(
n0
,
Leaf
(
c0
+
c1
))
scope
.
remove
(
n0
,
Leaf
(
c0
.
actual_value
()
+
c1
.
actual_value
()
))
# Remove the right node
scope
.
remove
(
n1
)
...
...
@@ -119,20 +108,12 @@ def match_multiply_zero(node):
assert
node
.
is_op
(
OP_MUL
)
left
,
right
=
node
is_zero
=
lambda
n
:
n
.
is_leaf
and
n
.
value
==
0
if
is_zero
(
left
):
negated
=
right
.
is_op
(
OP_NEG
)
elif
is_zero
(
right
):
negated
=
left
.
is_op
(
OP_NEG
)
elif
left
.
is_op
(
OP_NEG
)
and
is_zero
(
left
[
0
]):
negated
=
not
right
.
is_op
(
OP_NEG
)
elif
right
.
is_op
(
OP_NEG
)
and
is_zero
(
right
[
0
]):
negated
=
not
left
.
is_op
(
OP_NEG
)
else
:
return
[]
return
[
P
(
node
,
multiply_zero
,
(
negated
,))]
if
(
left
.
is_leaf
and
left
.
value
==
0
)
\
or
(
right
.
is_leaf
and
right
.
value
==
0
):
return
[
P
(
node
,
multiply_zero
,
(
left
.
negated
+
right
.
negated
,))]
return
[]
def
multiply_zero
(
root
,
args
):
...
...
@@ -143,12 +124,7 @@ def multiply_zero(root, args):
0 * -a -> -0
-0 * -a -> 0
"""
negated
=
args
[
0
]
if
negated
:
return
-
Leaf
(
0
)
else
:
return
Leaf
(
0
)
return
negate
(
Leaf
(
0
),
args
[
0
])
MESSAGES
[
multiply_zero
]
=
_
(
'Multiplication with zero yields zero.'
)
...
...
@@ -168,9 +144,7 @@ def match_multiply_numerics(node):
for
n
in
Scope
(
node
):
if
n
.
is_numeric
():
numerics
.
append
((
n
,
n
.
value
))
elif
n
.
is_op
(
OP_NEG
)
and
n
[
0
].
is_numeric
():
numerics
.
append
((
n
,
-
n
[
0
].
value
))
numerics
.
append
((
n
,
n
.
actual_value
()))
for
(
n0
,
v0
),
(
n1
,
v1
)
in
combinations
(
numerics
,
2
):
p
.
append
(
P
(
node
,
multiply_numerics
,
(
n0
,
n1
,
v0
,
v1
)))
...
...
src/rules/poly.py
View file @
d419cb36
from
itertools
import
combinations
from
..node
import
Scope
,
OP_ADD
,
OP_NEG
from
..node
import
Scope
,
OP_ADD
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
.numerics
import
add_numerics
def
is_numeric_or_negated_numeric
(
n
):
return
n
.
is_numeric
()
or
(
n
.
is_op
(
OP_NEG
)
and
n
[
0
].
is_numeric
())
def
match_combine_polynomes
(
node
,
verbose
=
False
):
"""
n + exp + m -> exp + (n + m)
...
...
@@ -52,7 +48,7 @@ def match_combine_polynomes(node, verbose=False):
# roots, or: same root and exponent -> combine coefficients.
# TODO: Addition with zero, e.g. a + 0 -> a
if
c0
==
1
and
c1
==
1
and
e0
==
1
and
e1
==
1
\
and
all
(
map
(
is_numeric_or_negated_numeric
,
[
r0
,
r1
])):
and
all
(
map
(
lambda
n
:
n
.
is_numeric
()
,
[
r0
,
r1
])):
# 2 + 3 -> 5
# 2 + -3 -> -1
# -2 + 3 -> 1
...
...
src/rules/powers.py
View file @
d419cb36
from
itertools
import
combinations
from
..node
import
ExpressionNode
as
N
,
ExpressionLeaf
as
L
,
Scope
,
\
OP_
NEG
,
OP_
MUL
,
OP_DIV
,
OP_POW
,
OP_ADD
OP_MUL
,
OP_DIV
,
OP_POW
,
OP_ADD
from
..possibilities
import
Possibility
as
P
,
MESSAGES
from
..translate
import
_
...
...
@@ -91,6 +91,18 @@ def match_subtract_exponents(node):
return
[]
def
subtract_exponents
(
root
,
args
):
"""
a^p / a^q -> a^(p - q)
"""
a
,
p
,
q
=
args
return
a
**
(
p
-
q
)
MESSAGES
[
subtract_exponents
]
=
_
(
'Substract the exponents {2} and {3}.'
)
def
match_multiply_exponents
(
node
):
"""
(a^p)^q -> a^(pq)
...
...
@@ -105,6 +117,18 @@ def match_multiply_exponents(node):
return
[]
def
multiply_exponents
(
root
,
args
):
"""
(a^p)^q -> a^(pq)
"""
a
,
p
,
q
=
args
return
a
**
(
p
*
q
)
MESSAGES
[
multiply_exponents
]
=
_
(
'Multiply the exponents {2} and {3}.'
)
def
match_duplicate_exponent
(
node
):
"""
(ab)^p -> a^p * b^p
...
...
@@ -119,20 +143,49 @@ def match_duplicate_exponent(node):
return
[]
def
duplicate_exponent
(
root
,
args
):
"""
(ab)^p -> a^p * b^p
(abc)^p -> a^p * b^p * c^p
"""
ab
,
p
=
args
result
=
ab
[
0
]
**
p
for
b
in
ab
[
1
:]:
result
*=
b
**
p
return
result
MESSAGES
[
duplicate_exponent
]
=
_
(
'Duplicate the exponent {2}.'
)
def
match_remove_negative_exponent
(
node
):
"""
a^-p -> 1 / a^p
"""
assert
node
.
is_op
(
OP_POW
)
left
,
right
=
node
a
,
p
=
node
if
right
.
is_op
(
OP_NEG
)
:
return
[
P
(
node
,
remove_negative_exponent
,
(
left
,
right
[
0
]
))]
if
p
.
negated
:
return
[
P
(
node
,
remove_negative_exponent
,
(
a
,
p
))]
return
[]
def
remove_negative_exponent
(
root
,
args
):
"""
a^-p -> 1 / a^p
"""
a
,
p
=
args
return
L
(
1
)
/
a
**
p
.
reduce_negation
()
MESSAGES
[
remove_negative_exponent
]
=
_
(
'Remove negative exponent {2}.'
)
def
match_exponent_to_root
(
node
):
"""
a^(1 / m) -> sqrt(a, m)
...
...
@@ -148,6 +201,16 @@ def match_exponent_to_root(node):
return
[]
def
exponent_to_root
(
root
,
args
):
"""
a^(1 / m) -> sqrt(a, m)
a^(n / m) -> sqrt(a^n, m)
"""
a
,
n
,
m
=
args
return
N
(
'sqrt'
,
a
if
n
==
1
else
a
**
n
,
m
)
def
match_extend_exponent
(
node
):
"""
(a + ... + z)^n -> (a + ... + z)(a + ... + z)^(n - 1) # n > 1
...
...
@@ -174,66 +237,3 @@ def extend_exponent(root, args):
return
left
*
left
**
L
(
right
.
value
-
1
)
return
left
*
left
def
subtract_exponents
(
root
,
args
):
"""
a^p / a^q -> a^(p - q)
"""
a
,
p
,
q
=
args
return
a
**
(
p
-
q
)
MESSAGES
[
subtract_exponents
]
=
_
(
'Substract the exponents {2} and {3}.'
)
def
multiply_exponents
(
root
,
args
):
"""
(a^p)^q -> a^(pq)
"""
a
,
p
,
q
=
args
return
a
**
(
p
*
q
)
MESSAGES
[
multiply_exponents
]
=
_
(
'Multiply the exponents {2} and {3}.'
)
def
duplicate_exponent
(
root
,
args
):
"""
(ab)^p -> a^p * b^p
(abc)^p -> a^p * b^p * c^p
"""
ab
,
p
=
args
result
=
ab
[
0
]
**
p
for
b
in
ab
[
1
:]:
result
*=
b
**
p
return
result
MESSAGES
[
duplicate_exponent
]
=
_
(
'Duplicate the exponent {2}.'
)
def
remove_negative_exponent
(
root
,
args
):
"""
a^-p -> 1 / a^p
"""
a
,
p
=
args
return
L
(
1
)
/
a
**
p
MESSAGES
[
remove_negative_exponent
]
=
_
(
'Remove negative exponent {2}.'
)
def
exponent_to_root
(
root
,
args
):
"""
a^(1 / m) -> sqrt(a, m)
a^(n / m) -> sqrt(a^n, m)
"""
a
,
n
,
m
=
args
return
N
(
'sqrt'
,
a
if
n
==
1
else
a
**
n
,
m
)
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