Mathy core is a python package (with type annotations) for working with math problems. It has a tokenizer for converting plain text into tokens, a parser for converting tokens into expression trees, a rule-based system for manipulating the trees, a layout system for visualizing trees, and a set of problem generation functions that can be used to generate datasets for ML training.
You can install mathy_core from pip:
pip install mathy_core
Check out https://core.mathy.ai for API documentation, examples, and more!
Consider a few examples to get a feel for what Mathy core does.
Arithmetic is a snap.
from mathy_core import ExpressionParser
expression = ExpressionParser().parse("4 + 2")
assert expression.evaluate() == 6
Variable values can be specified when evaluating an expression.
from mathy_core import ExpressionParser, MathExpression
expression: MathExpression = ExpressionParser().parse("4x + 2y")
assert expression.evaluate({"x": 2, "y": 5}) == 18
Expressions can be changed using rules based on the properties of numbers.
from mathy_core import ExpressionParser
from mathy_core.rules import DistributiveFactorOutRule
input = "4x + 2x"
output = "(4 + 2) * x"
parser = ExpressionParser()
input_exp = parser.parse(input)
output_exp = parser.parse(output)
# Verify that the rule transforms the tree as expected
change = DistributiveFactorOutRule().apply_to(input_exp)
assert str(change.result) == output
# Verify that both trees evaluate to the same value
ctx = {"x": 3}
assert input_exp.evaluate(ctx) == output_exp.evaluate(ctx)
Install the prerequisites in a virtual environment (python3 required)
sh tools/setup.sh
Run the test suite and view code-coverage statistics
sh tools/test.sh
The tests cover ~90% of the code so they're a good reference for how to use the various APIs.
Before Mathy Core reaches v1.0 the project is not guaranteed to have a consistent API, which means that types and classes may move around or be removed. That said, we try to be predictable when it comes to breaking changes, so the project uses semantic versioning to help users avoid breakage.
Specifically, new releases increase the patch semver component for new features and fixes, and the minor component when there are breaking changes. If you don't know much about semver strings, they're usually formatted {major}.{minor}.{patch} so increasing the patch component means incrementing the last number.
Consider a few examples:
| From Version | To Version | Changes are Breaking |
|---|---|---|
| 0.2.0 | 0.2.1 | No |
| 0.3.2 | 0.3.6 | No |
| 0.3.1 | 0.3.17 | No |
| 0.2.2 | 0.3.0 | Yes |
If you are concerned about breaking changes, you can pin the version in your requirements so that it does not go beyond the current semver minor component, for example if the current version was 0.1.37:
mathy_core>=0.1.37,<0.2.0
Mathy Core wouldn't be possible without the wonderful contributions of the following people:
 Justin DuJardin |  JT Stukes |
This project follows the all-contributors specification. Contributions of any kind welcome!
Tokenizer(self, exclude_padding: bool = True)
The Tokenizer produces a list of tokens from an input string.
Tokenizer.eat_token(
self,
context: mathy_core.tokenizer.TokenContext,
typeFn: Callable[[str], bool],
) -> str
Eat all of the tokens of a given type from the front of the stream until a different type is hit, and return the text.
Tokenizer.identify_alphas(
self,
context: mathy_core.tokenizer.TokenContext,
) -> int
Identify and tokenize functions and variables.
Tokenizer.identify_constants(
self,
context: mathy_core.tokenizer.TokenContext,
) -> int
Identify and tokenize a constant number.
Tokenizer.identify_operators(
self,
context: mathy_core.tokenizer.TokenContext,
) -> bool
Identify and tokenize operators.
Tokenizer.is_alpha(self, c: str) -> bool
Is this character a letter
Tokenizer.is_number(self, c: str) -> bool
Is this character a number
Tokenizer.tokenize(self, buffer: str) -> List[mathy_core.tokenizer.Token]
Return an array of Tokens from a given string input.
This throws an exception if an unknown token type is found in the input.
ExpressionParser(self) -> None
Parser for converting text into binary trees. Trees encode the order of operations for an input, and allow evaluating it to detemrine the expression value.
Symbols:
( ) == Non-terminal
{ }* == 0 or more occurrences
{ }+ == 1 or more occurrences
{ }? == 0 or 1 occurrences
[ ] == Mandatory (1 must occur)
| == logical OR
" " == Terminal symbol (literal)
Non-terminals defined/parsed by Tokenizer:
(Constant) = anything that can be parsed by `float(in)`
(Variable) = any string containing only letters (a-z and A-Z)
Rules:
(Function) = [ functionName ] "(" (AddExp) ")"
(Factor) = { (Variable) | (Function) | "(" (AddExp) ")" }+ { { "^" }? (UnaryExp) }?
(FactorPrefix) = [ (Constant) { (Factor) }? | (Factor) ]
(UnaryExp) = { "-" }? (FactorPrefix)
(ExpExp) = (UnaryExp) { { "^" }? (UnaryExp) }?
(MultExp) = (ExpExp) { { "*" | "/" }? (ExpExp) }*
(AddExp) = (MultExp) { { "+" | "-" }? (MultExp) }*
(EqualExp) = (AddExp) { { "=" }? (AddExp) }*
(start) = (EqualExp)
ExpressionParser.check(
self,
tokens: mathy_core.parser.TokenSet,
do_assert: bool = False,
) -> bool
Check if the self.current_token is a member of a set Token types
Args: - tokens The set of Token types to check against
Returns True if the current_token's type is in the set else False
ExpressionParser.eat(self, type: int) -> bool
Assign the next token in the queue to current_token if its type matches that of the specified parameter. If the type does not match, raise a syntax exception.
Args: - type The type that your syntax expects @current_token to be
ExpressionParser.next(self) -> bool
Assign the next token in the queue to self.current_token.
Return True if there are still more tokens in the queue, or False if there are no more tokens to look at.
ExpressionParser.parse(
self,
input_text: str,
) -> mathy_core.expressions.MathExpression
Parse a string representation of an expression into a tree that can be later evaluated.
Returns : The evaluatable expression tree.
TokenSet(self, source: int)
TokenSet objects are bitmask combinations for checking to see if a token is part of a valid set.
TokenSet.add(self, addTokens: int) -> 'TokenSet'
Add tokens to self set and return a TokenSet representing
their combination of flags. Value can be an integer or an instance
of TokenSet
TokenSet.contains(self, type: int) -> bool
Returns true if the given type is part of this set
BinaryTreeNode(
self: ~NodeType,
left: Optional[~NodeType] = None,
right: Optional[~NodeType] = None,
parent: Optional[~NodeType] = None,
id: Optional[str] = None,
)
The binary tree node is the base node for all of our trees, and provides a rich set of methods for constructing, inspecting, and modifying them. The node itself defines the structure of the binary tree, having left and right children, and a parent.
BinaryTreeNode.clone(self: ~NodeType) -> ~NodeType
Create a clone of this tree
BinaryTreeNode.get_children(self: ~NodeType) -> List[~NodeType]
Get children as an array. If there are two children, the first object will always represent the left child, and the second will represent the right.
BinaryTreeNode.get_root(self: ~NodeType) -> ~NodeType
Return the root element of this tree
BinaryTreeNode.get_root_side(self: ~NodeType) -> Literal['left', 'right']
Return the side of the tree that this node lives on
BinaryTreeNode.get_sibling(self: ~NodeType) -> Optional[~NodeType]
Get the sibling node of this node. If there is no parent, or the node has no sibling, the return value will be None.
BinaryTreeNode.get_side(
self,
child: Optional[~NodeType],
) -> Literal['left', 'right']
Determine whether the given child is the left or right child of this
node
BinaryTreeNode.is_leaf(self) -> bool
Is this node a leaf? A node is a leaf if it has no children.
BinaryTreeNode.rotate(self: ~NodeType) -> ~NodeType
Rotate a node, changing the structure of the tree, without modifying the order of the nodes in the tree.
BinaryTreeNode.set_left(
self: ~NodeType,
child: Optional[~NodeType] = None,
clear_old_child_parent: bool = False,
) -> ~NodeType
Set the left node to the passed child
BinaryTreeNode.set_right(
self: ~NodeType,
child: Optional[~NodeType] = None,
clear_old_child_parent: bool = False,
) -> ~NodeType
Set the right node to the passed child
BinaryTreeNode.set_side(
self,
child: ~NodeType,
side: Literal['left', 'right'],
) -> ~NodeType
Set a new child on the given side
BinaryTreeNode.visit_inorder(
self,
visit_fn: Callable[[Any, int, Optional[Any]], Optional[Literal['stop']]],
depth: int = 0,
data: Optional[Any] = None,
) -> Optional[Literal['stop']]
Visit the tree inorder, which visits the left child, then the current node, and then its right child.
Left -> Visit -> Right
This method accepts a function that will be invoked for each node in the tree. The callback function is passed three arguments: the node being visited, the current depth in the tree, and a user specified data parameter.
!!! info
Traversals may be canceled by returning `STOP` from any visit function.
BinaryTreeNode.visit_postorder(
self,
visit_fn: Callable[[Any, int, Optional[Any]], Optional[Literal['stop']]],
depth: int = 0,
data: Optional[Any] = None,
) -> Optional[Literal['stop']]
Visit the tree postorder, which visits its left child, then its right child, and finally the current node.
Left -> Right -> Visit
This method accepts a function that will be invoked for each node in the tree. The callback function is passed three arguments: the node being visited, the current depth in the tree, and a user specified data parameter.
!!! info
Traversals may be canceled by returning `STOP` from any visit function.
BinaryTreeNode.visit_preorder(
self,
visit_fn: Callable[[Any, int, Optional[Any]], Optional[Literal['stop']]],
depth: int = 0,
data: Optional[Any] = None,
) -> Optional[Literal['stop']]
Visit the tree preorder, which visits the current node, then its left child, and then its right child.
Visit -> Left -> Right
This method accepts a function that will be invoked for each node in the tree. The callback function is passed three arguments: the node being visited, the current depth in the tree, and a user specified data parameter.
!!! info
Traversals may be canceled by returning `STOP` from any visit function.
Template type of user data passed to visit functions.
AbsExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
Evaluates the absolute value of an expression.
AddExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Add one and two
BinaryExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
An expression that operates on two sub-expressions
BinaryExpression.get_priority(self) -> int
Return a number representing the order of operations priority
of this node. This can be used to check if a node is locked
with respect to another node, i.e. the other node must be resolved
first during evaluation because of it's priority.
BinaryExpression.to_math_ml_fragment(self) -> str
Render this node as a MathML element fragment
ConstantExpression(self, value: Optional[float, int] = None)
A Constant value node, where the value is accessible as node.value
DivideExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Divide one by two
EqualExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Evaluate equality of two expressions
EqualExpression.operate(
self,
one: Union[float, int],
two: Union[float, int],
) -> Union[float, int]
Return the value of the equation if one == two.
Raise ValueError if both sides of the equation don't agree.
FactorialExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
Factorial of a constant, e.g. 5 evaluates to 120
FunctionExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
A Specialized UnaryExpression that is used for functions. The function name in text (used by the parser and tokenizer) is derived from the name() method on the class.
MathExpression(
self,
id: Optional[str] = None,
left: Optional[MathExpression] = None,
right: Optional[MathExpression] = None,
parent: Optional[MathExpression] = None,
)
Math tree node with helpers for manipulating expressions.
mathy:x+y=z
MathExpression.add_class(
self,
classes: Union[List[str], str],
) -> 'MathExpression'
Associate a class name with an expression. This class name will be attached to nodes when the expression is converted to a capable output format.
See MathExpression.to_math_ml_fragment
MathExpression.all_changed(self) -> None
Mark this node and all of its children as changed
MathExpression.clear_classes(self) -> None
Clear all the classes currently set on the nodes in this expression.
MathExpression.clone(self) -> 'MathExpression'
A specialization of the clone method that can track and report a cloned subtree node.
See MathExpression.clone_from_root for more details.
MathExpression.clone_from_root(
self,
node: Optional[MathExpression] = None,
) -> 'MathExpression'
Clone this node including the entire parent hierarchy that it has. This is useful when you want to clone a subtree and still maintain the overall hierarchy.
Arguments
Returns
(MathExpression): The cloned node.
Color to use for this node when rendering it as changed with
.terminal_text
MathExpression.evaluate(
self,
context: Optional[Dict[str, Union[float, int]]] = None,
) -> Union[float, int]
Evaluate the expression, resolving all variables to constant values
MathExpression.find_id(self, id: str) -> Optional[MathExpression]
Find an expression by its unique ID.
Returns: The found MathExpression or None
MathExpression.find_type(self, instanceType: Type[~NodeType]) -> List[~NodeType]
Find an expression in this tree by type.
Returns the found MathExpression objects of the given type.
MathExpression.make_ml_tag(
self,
tag: str,
content: str,
classes: List[str] = [],
) -> str
Make a MathML tag for the given content while respecting the node's given classes.
Arguments
Returns
(str): A MathML element with the given tag, content, and classes
MathExpression.path_to_root(self) -> str
Generate a namespaced path key to from the current node to the root. This key can be used to identify a node inside of a tree.
raw text representation of the expression.
MathExpression.set_changed(self) -> None
Mark this node as having been changed by the application of a Rule
Text output of this node that includes terminal color codes that highlight which nodes have been changed in this tree as a result of a transformation.
MathExpression.to_list(
self,
visit: str = 'preorder',
) -> List[MathExpression]
Convert this node hierarchy into a list.
MathExpression.to_math_ml(self) -> str
Convert this expression into a MathML container.
MathExpression.to_math_ml_fragment(self) -> str
Convert this single node into MathML.
MathExpression.with_color(self, text: str, style: str = 'bright') -> str
Render a string that is colored if something has changed
MultiplyExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Multiply one and two
NegateExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
Negate an expression, e.g. 4 becomes -4
NegateExpression.to_math_ml_fragment(self) -> str
Convert this single node into MathML.
PowerExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Raise one to the power of two
SgnExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
SgnExpression.operate(self, value: Union[float, int]) -> Union[float, int]
Determine the sign of an value.
Returns
(int): -1 if negative, 1 if positive, 0 if 0
SubtractExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Subtract one from two
UnaryExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
An expression that operates on one sub-expression
AssociativeSwapRule(self, args, kwargs)
Associative Property
Addition: (a + b) + c = a + (b + c)
(y) + + (x)
/ \ / \
/ \ / \
(x) + c -> a + (y)
/ \ / \
/ \ / \
a b b c
Multiplication: (ab)c = a(bc)
(x) * * (y)
/ \ / \
/ \ / \
(y) * c <- a * (x)
/ \ / \
/ \ / \
a b b c
BalancedMoveRule(self, args, kwargs)
Balanced rewrite rule moves nodes from one side of an equation to the other by performing the same operation on both sides.
Addition: a + 2 = 3 -> a + 2 - 2 = 3 - 2
Multiplication: 3a = 3 -> 3a / 3 = 3 / 3
BalancedMoveRule.get_type(
self,
node: mathy_core.expressions.MathExpression,
) -> Optional[str]
Determine the configuration of the tree for this transformation.
Supports the following configurations:
CommutativeSwapRule(self, preferred: bool = True)
Commutative Property
For Addition: a + b = b + a
+ +
/ \ / \
/ \ -> / \
/ \ / \
a b b a
For Multiplication: a * b = b * a
* *
/ \ / \
/ \ -> / \
/ \ / \
a b b a
ConstantsSimplifyRule(self, args, kwargs)
Given a binary operation on two constants, simplify to the resulting constant expression
ConstantsSimplifyRule.get_type(
self,
node: mathy_core.expressions.MathExpression,
) -> Optional[Tuple[str, mathy_core.expressions.ConstantExpression, mathy_core.expressions.ConstantExpression]]
Determine the configuration of the tree for this transformation.
Support the three types of tree configurations:
Structure:
DistributiveFactorOutRule(self, constants: bool = False)
Distributive Property
ab + ac = a(b + c)
The distributive property can be used to expand out expressions to allow for simplification, as well as to factor out common properties of terms.
Factor out a common term
This handles the ab + ac conversion of the distributive property, which
factors out a common term from the given two addition operands.
+ *
/ \ / \
/ \ / \
/ \ -> / \
* * a +
/ \ / \ / \
a b a c b c
DistributiveFactorOutRule.get_type(
self,
node: mathy_core.expressions.MathExpression,
) -> Optional[Tuple[str, mathy_core.util.TermEx, mathy_core.util.TermEx]]
Determine the configuration of the tree for this transformation.
Support the three types of tree configurations:
Structure:
DistributiveMultiplyRule(self, args, kwargs)
Distributive Property
a(b + c) = ab + ac
The distributive property can be used to expand out expressions to allow for simplification, as well as to factor out common properties of terms.
Distribute across a group
This handles the a(b + c) conversion of the distributive property, which
distributes a across both b and c.
note: this is useful because it takes a complex Multiply expression and replaces it with two simpler ones. This can expose terms that can be combined for further expression simplification.
+
* / \
/ \ / \
/ \ / \
a + -> * *
/ \ / \ / \
/ \ / \ / \
b c a b a c
VariableMultiplyRule(self, args, kwargs)
This restates x^b * x^d as x^(b + d) which has the effect of isolating
the exponents attached to the variables, so they can be combined.
1. When there are two terms with the same base being multiplied together, their
exponents are added together. "x * x^3" = "x^4" because "x = x^1" so
"x^1 * x^3 = x^(1 + 3) = x^4"
TODO: 2. When there is a power raised to another power, they can be combined by
multiplying the exponents together. "x^(2^2) = x^4"
The rule identifies terms with explicit and implicit powers, so the following transformations are all valid:
Explicit powers: x^b * x^d = x^(b+d)
*
/ \
/ \ ^
/ \ = / \
^ ^ x +
/ \ / \ / \
x b x d b d
Implicit powers: x * x^d = x^(1 + d)
*
/ \
/ \ ^
/ \ = / \
x ^ x +
/ \ / \
x d 1 d
VariableMultiplyRule.get_type(
self,
node: mathy_core.expressions.MathExpression,
) -> Optional[Tuple[str, mathy_core.util.TermEx, mathy_core.util.TermEx]]
Determine the configuration of the tree for this transformation.
Support two types of tree configurations:
Structure:
TreeLayout(self, args, kwargs)
Calculate a visual layout for input trees.
TreeLayout.layout(
self,
node: mathy_core.tree.BinaryTreeNode,
unit_x_multiplier: float = 1.0,
unit_y_multiplier: float = 1.0,
) -> 'TreeMeasurement'
Assign x/y values to all nodes in the tree, and return an object containing the measurements of the tree.
Returns a TreeMeasurement object that describes the bounds of the tree
TreeLayout.transform(
self,
node: Optional[mathy_core.tree.BinaryTreeNode] = None,
x: float = 0,
unit_x_multiplier: float = 1,
unit_y_multiplier: float = 1,
measure: Optional[TreeMeasurement] = None,
) -> 'TreeMeasurement'
Transform relative to absolute coordinates, and measure the bounds of the tree.
Return a measurement of the tree in output units.
TreeMeasurement(self) -> None
Summary of the rendered tree
Utility functions for helping generate input problems.
Template type for a default return value
gen_binomial_times_binomial(
op: str = '+',
min_vars: int = 1,
max_vars: int = 2,
simple_variables: bool = True,
powers_probability: float = 0.33,
like_variables_probability: float = 1.0,
) -> Tuple[str, int]
Generate a binomial multiplied by another binomial.
Example
(2e + 12p)(16 + 7e)
mathy:(2e + 12p)(16 + 7e)
gen_binomial_times_monomial(
op: str = '+',
min_vars: int = 1,
max_vars: int = 2,
simple_variables: bool = True,
powers_probability: float = 0.33,
like_variables_probability: float = 1.0,
) -> Tuple[str, int]
Generate a binomial multiplied by a monomial.
Example
(4x^3 + y) * 2x
mathy:(4x^3 + y) * 2x
gen_combine_terms_in_place(
min_terms: int = 16,
max_terms: int = 26,
easy: bool = True,
powers: bool = False,
) -> Tuple[str, int]
Generate a problem that puts one pair of like terms next to each other somewhere inside a large tree of unlike terms.
The problem is intended to be solved in a very small number of moves, making training across many episodes relatively quick, and reducing the combinatorial explosion of branches that need to be searched to solve the task.
The hope is that by focusing the agent on selecting the right moves inside of a ridiculously large expression it will learn to select actions to combine like terms invariant of the sequence length.
Example
4y + 12j + 73q + 19k + 13z + 56l + (24x + 12x) + 43n + 17j
mathy:4y + 12j + 73q + 19k + 13z + 56l + (24x + 12x) + 43n + 17j
gen_commute_haystack(
min_terms: int = 5,
max_terms: int = 8,
commute_blockers: int = 1,
easy: bool = True,
powers: bool = False,
) -> Tuple[str, int]
A problem with a bunch of terms that have no matches, and a single set of two terms that do match, but are separated by one other term. The challenge is to commute the terms to each other in one move.
Example
4y + 12j + 73q + 19k + 13z + 24x + 56l + 12x + 43n + 17j"
^-----------^
mathy:4y + 12j + 73q + 19k + 13z + 24x + 56l + 12x + 43n + 17j
gen_move_around_blockers_one(
number_blockers: int,
powers_probability: float = 0.5,
) -> Tuple[str, int]
Two like terms separated by (n) blocker terms.
Example
4x + (y + f) + x
mathy:4x + (y + f) + x
gen_move_around_blockers_two(
number_blockers: int,
powers_probability: float = 0.5,
) -> Tuple[str, int]
Two like terms with three blockers.
Example
7a + 4x + (2f + j) + x + 3d
mathy:7a + 4x + (2f + j) + x + 3d
gen_simplify_multiple_terms(
num_terms: int,
optional_var: bool = False,
op: Optional[List[str], str] = None,
common_variables: bool = True,
inner_terms_scaling: float = 0.3,
powers_probability: float = 0.33,
optional_var_probability: float = 0.8,
noise_probability: float = 0.8,
shuffle_probability: float = 0.66,
share_var_probability: float = 0.5,
grouping_noise_probability: float = 0.66,
noise_terms: Optional[int] = None,
) -> Tuple[str, int]
Generate a polynomial problem with like terms that need to be combined and simplified.
Example
2a + 3j - 7b + 17.2a + j
mathy:2a + 3j - 7b + 17.2a + j
get_blocker(
num_blockers: int = 1,
exclude_vars: Optional[List[str]] = None,
) -> str
Get a string of terms to place between target simplification terms in order to challenge the agent's ability to use commutative/associative rules to move terms around.
get_rand_vars(
num_vars: int,
exclude_vars: Optional[List[str]] = None,
common_variables: bool = False,
) -> List[str]
Get a list of random variables, excluding the given list of hold-out variables
MathyTermTemplate(
self,
variable: Optional[str] = None,
exponent: Optional[float, int] = None,
) -> None
MathyTermTemplate(variable: Optional[str] = None, exponent: Union[float, int, NoneType] = None)
split_in_two_random(value: int) -> Tuple[int, int]
Split a given number into two smaller numbers that sum to it. Returns: a tuple of (lower, higher) numbers that sum to the input
use_pretty_numbers(enabled: bool = True) -> None
Determine if problems should include only pretty numbers or
a whole range of integers and floats. Using pretty numbers will
restrict the numbers that are generated to integers between 1 and 12. When not using pretty numbers, floats and large integers will
be included in the output from rand_number
Tokenizer(self, exclude_padding: bool = True)
The Tokenizer produces a list of tokens from an input string.
Tokenizer.eat_token(
self,
context: mathy_core.tokenizer.TokenContext,
typeFn: Callable[[str], bool],
) -> str
Eat all of the tokens of a given type from the front of the stream until a different type is hit, and return the text.
Tokenizer.identify_alphas(
self,
context: mathy_core.tokenizer.TokenContext,
) -> int
Identify and tokenize functions and variables.
Tokenizer.identify_constants(
self,
context: mathy_core.tokenizer.TokenContext,
) -> int
Identify and tokenize a constant number.
Tokenizer.identify_operators(
self,
context: mathy_core.tokenizer.TokenContext,
) -> bool
Identify and tokenize operators.
Tokenizer.is_alpha(self, c: str) -> bool
Is this character a letter
Tokenizer.is_number(self, c: str) -> bool
Is this character a number
Tokenizer.tokenize(self, buffer: str) -> List[mathy_core.tokenizer.Token]
Return an array of Tokens from a given string input.
This throws an exception if an unknown token type is found in the input.
ExpressionParser(self) -> None
Parser for converting text into binary trees. Trees encode the order of operations for an input, and allow evaluating it to detemrine the expression value.
Symbols:
( ) == Non-terminal
{ }* == 0 or more occurrences
{ }+ == 1 or more occurrences
{ }? == 0 or 1 occurrences
[ ] == Mandatory (1 must occur)
| == logical OR
" " == Terminal symbol (literal)
Non-terminals defined/parsed by Tokenizer:
(Constant) = anything that can be parsed by `float(in)`
(Variable) = any string containing only letters (a-z and A-Z)
Rules:
(Function) = [ functionName ] "(" (AddExp) ")"
(Factor) = { (Variable) | (Function) | "(" (AddExp) ")" }+ { { "^" }? (UnaryExp) }?
(FactorPrefix) = [ (Constant) { (Factor) }? | (Factor) ]
(UnaryExp) = { "-" }? (FactorPrefix)
(ExpExp) = (UnaryExp) { { "^" }? (UnaryExp) }?
(MultExp) = (ExpExp) { { "*" | "/" }? (ExpExp) }*
(AddExp) = (MultExp) { { "+" | "-" }? (MultExp) }*
(EqualExp) = (AddExp) { { "=" }? (AddExp) }*
(start) = (EqualExp)
ExpressionParser.check(
self,
tokens: mathy_core.parser.TokenSet,
do_assert: bool = False,
) -> bool
Check if the self.current_token is a member of a set Token types
Args: - tokens The set of Token types to check against
Returns True if the current_token's type is in the set else False
ExpressionParser.eat(self, type: int) -> bool
Assign the next token in the queue to current_token if its type matches that of the specified parameter. If the type does not match, raise a syntax exception.
Args: - type The type that your syntax expects @current_token to be
ExpressionParser.next(self) -> bool
Assign the next token in the queue to self.current_token.
Return True if there are still more tokens in the queue, or False if there are no more tokens to look at.
ExpressionParser.parse(
self,
input_text: str,
) -> mathy_core.expressions.MathExpression
Parse a string representation of an expression into a tree that can be later evaluated.
Returns : The evaluatable expression tree.
TokenSet(self, source: int)
TokenSet objects are bitmask combinations for checking to see if a token is part of a valid set.
TokenSet.add(self, addTokens: int) -> 'TokenSet'
Add tokens to self set and return a TokenSet representing
their combination of flags. Value can be an integer or an instance
of TokenSet
TokenSet.contains(self, type: int) -> bool
Returns true if the given type is part of this set
BinaryTreeNode(
self: ~NodeType,
left: Optional[~NodeType] = None,
right: Optional[~NodeType] = None,
parent: Optional[~NodeType] = None,
id: Optional[str] = None,
)
The binary tree node is the base node for all of our trees, and provides a rich set of methods for constructing, inspecting, and modifying them. The node itself defines the structure of the binary tree, having left and right children, and a parent.
BinaryTreeNode.clone(self: ~NodeType) -> ~NodeType
Create a clone of this tree
BinaryTreeNode.get_children(self: ~NodeType) -> List[~NodeType]
Get children as an array. If there are two children, the first object will always represent the left child, and the second will represent the right.
BinaryTreeNode.get_root(self: ~NodeType) -> ~NodeType
Return the root element of this tree
BinaryTreeNode.get_root_side(self: ~NodeType) -> Literal['left', 'right']
Return the side of the tree that this node lives on
BinaryTreeNode.get_sibling(self: ~NodeType) -> Optional[~NodeType]
Get the sibling node of this node. If there is no parent, or the node has no sibling, the return value will be None.
BinaryTreeNode.get_side(
self,
child: Optional[~NodeType],
) -> Literal['left', 'right']
Determine whether the given child is the left or right child of this
node
BinaryTreeNode.is_leaf(self) -> bool
Is this node a leaf? A node is a leaf if it has no children.
BinaryTreeNode.rotate(self: ~NodeType) -> ~NodeType
Rotate a node, changing the structure of the tree, without modifying the order of the nodes in the tree.
BinaryTreeNode.set_left(
self: ~NodeType,
child: Optional[~NodeType] = None,
clear_old_child_parent: bool = False,
) -> ~NodeType
Set the left node to the passed child
BinaryTreeNode.set_right(
self: ~NodeType,
child: Optional[~NodeType] = None,
clear_old_child_parent: bool = False,
) -> ~NodeType
Set the right node to the passed child
BinaryTreeNode.set_side(
self,
child: ~NodeType,
side: Literal['left', 'right'],
) -> ~NodeType
Set a new child on the given side
BinaryTreeNode.visit_inorder(
self,
visit_fn: Callable[[Any, int, Optional[Any]], Optional[Literal['stop']]],
depth: int = 0,
data: Optional[Any] = None,
) -> Optional[Literal['stop']]
Visit the tree inorder, which visits the left child, then the current node, and then its right child.
Left -> Visit -> Right
This method accepts a function that will be invoked for each node in the tree. The callback function is passed three arguments: the node being visited, the current depth in the tree, and a user specified data parameter.
!!! info
Traversals may be canceled by returning `STOP` from any visit function.
BinaryTreeNode.visit_postorder(
self,
visit_fn: Callable[[Any, int, Optional[Any]], Optional[Literal['stop']]],
depth: int = 0,
data: Optional[Any] = None,
) -> Optional[Literal['stop']]
Visit the tree postorder, which visits its left child, then its right child, and finally the current node.
Left -> Right -> Visit
This method accepts a function that will be invoked for each node in the tree. The callback function is passed three arguments: the node being visited, the current depth in the tree, and a user specified data parameter.
!!! info
Traversals may be canceled by returning `STOP` from any visit function.
BinaryTreeNode.visit_preorder(
self,
visit_fn: Callable[[Any, int, Optional[Any]], Optional[Literal['stop']]],
depth: int = 0,
data: Optional[Any] = None,
) -> Optional[Literal['stop']]
Visit the tree preorder, which visits the current node, then its left child, and then its right child.
Visit -> Left -> Right
This method accepts a function that will be invoked for each node in the tree. The callback function is passed three arguments: the node being visited, the current depth in the tree, and a user specified data parameter.
!!! info
Traversals may be canceled by returning `STOP` from any visit function.
Template type of user data passed to visit functions.
AbsExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
Evaluates the absolute value of an expression.
AddExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Add one and two
BinaryExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
An expression that operates on two sub-expressions
BinaryExpression.get_priority(self) -> int
Return a number representing the order of operations priority
of this node. This can be used to check if a node is locked
with respect to another node, i.e. the other node must be resolved
first during evaluation because of it's priority.
BinaryExpression.to_math_ml_fragment(self) -> str
Render this node as a MathML element fragment
ConstantExpression(self, value: Optional[float, int] = None)
A Constant value node, where the value is accessible as node.value
DivideExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Divide one by two
EqualExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Evaluate equality of two expressions
EqualExpression.operate(
self,
one: Union[float, int],
two: Union[float, int],
) -> Union[float, int]
Return the value of the equation if one == two.
Raise ValueError if both sides of the equation don't agree.
FactorialExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
Factorial of a constant, e.g. 5 evaluates to 120
FunctionExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
A Specialized UnaryExpression that is used for functions. The function name in text (used by the parser and tokenizer) is derived from the name() method on the class.
MathExpression(
self,
id: Optional[str] = None,
left: Optional[MathExpression] = None,
right: Optional[MathExpression] = None,
parent: Optional[MathExpression] = None,
)
Math tree node with helpers for manipulating expressions.
mathy:x+y=z
MathExpression.add_class(
self,
classes: Union[List[str], str],
) -> 'MathExpression'
Associate a class name with an expression. This class name will be attached to nodes when the expression is converted to a capable output format.
See MathExpression.to_math_ml_fragment
MathExpression.all_changed(self) -> None
Mark this node and all of its children as changed
MathExpression.clear_classes(self) -> None
Clear all the classes currently set on the nodes in this expression.
MathExpression.clone(self) -> 'MathExpression'
A specialization of the clone method that can track and report a cloned subtree node.
See MathExpression.clone_from_root for more details.
MathExpression.clone_from_root(
self,
node: Optional[MathExpression] = None,
) -> 'MathExpression'
Clone this node including the entire parent hierarchy that it has. This is useful when you want to clone a subtree and still maintain the overall hierarchy.
Arguments
Returns
(MathExpression): The cloned node.
Color to use for this node when rendering it as changed with
.terminal_text
MathExpression.evaluate(
self,
context: Optional[Dict[str, Union[float, int]]] = None,
) -> Union[float, int]
Evaluate the expression, resolving all variables to constant values
MathExpression.find_id(self, id: str) -> Optional[MathExpression]
Find an expression by its unique ID.
Returns: The found MathExpression or None
MathExpression.find_type(self, instanceType: Type[~NodeType]) -> List[~NodeType]
Find an expression in this tree by type.
Returns the found MathExpression objects of the given type.
MathExpression.make_ml_tag(
self,
tag: str,
content: str,
classes: List[str] = [],
) -> str
Make a MathML tag for the given content while respecting the node's given classes.
Arguments
Returns
(str): A MathML element with the given tag, content, and classes
MathExpression.path_to_root(self) -> str
Generate a namespaced path key to from the current node to the root. This key can be used to identify a node inside of a tree.
raw text representation of the expression.
MathExpression.set_changed(self) -> None
Mark this node as having been changed by the application of a Rule
Text output of this node that includes terminal color codes that highlight which nodes have been changed in this tree as a result of a transformation.
MathExpression.to_list(
self,
visit: str = 'preorder',
) -> List[MathExpression]
Convert this node hierarchy into a list.
MathExpression.to_math_ml(self) -> str
Convert this expression into a MathML container.
MathExpression.to_math_ml_fragment(self) -> str
Convert this single node into MathML.
MathExpression.with_color(self, text: str, style: str = 'bright') -> str
Render a string that is colored if something has changed
MultiplyExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Multiply one and two
NegateExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
Negate an expression, e.g. 4 becomes -4
NegateExpression.to_math_ml_fragment(self) -> str
Convert this single node into MathML.
PowerExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Raise one to the power of two
SgnExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
SgnExpression.operate(self, value: Union[float, int]) -> Union[float, int]
Determine the sign of an value.
Returns
(int): -1 if negative, 1 if positive, 0 if 0
SubtractExpression(
self,
left: Optional[mathy_core.expressions.MathExpression] = None,
right: Optional[mathy_core.expressions.MathExpression] = None,
)
Subtract one from two
UnaryExpression(
self,
child: Optional[mathy_core.expressions.MathExpression] = None,
child_on_left: bool = False,
)
An expression that operates on one sub-expression
AssociativeSwapRule(self, args, kwargs)
Associative Property
Addition: (a + b) + c = a + (b + c)
(y) + + (x)
/ \ / \
/ \ / \
(x) + c -> a + (y)
/ \ / \
/ \ / \
a b b c
Multiplication: (ab)c = a(bc)
(x) * * (y)
/ \ / \
/ \ / \
(y) * c <- a * (x)
/ \ / \
/ \ / \
a b b c
BalancedMoveRule(self, args, kwargs)
Balanced rewrite rule moves nodes from one side of an equation to the other by performing the same operation on both sides.
Addition: a + 2 = 3 -> a + 2 - 2 = 3 - 2
Multiplication: 3a = 3 -> 3a / 3 = 3 / 3
BalancedMoveRule.get_type(
self,
node: mathy_core.expressions.MathExpression,
) -> Optional[str]
Determine the configuration of the tree for this transformation.
Supports the following configurations:
CommutativeSwapRule(self, preferred: bool = True)
Commutative Property
For Addition: a + b = b + a
+ +
/ \ / \
/ \ -> / \
/ \ / \
a b b a
For Multiplication: a * b = b * a
* *
/ \ / \
/ \ -> / \
/ \ / \
a b b a
ConstantsSimplifyRule(self, args, kwargs)
Given a binary operation on two constants, simplify to the resulting constant expression
ConstantsSimplifyRule.get_type(
self,
node: mathy_core.expressions.MathExpression,
) -> Optional[Tuple[str, mathy_core.expressions.ConstantExpression, mathy_core.expressions.ConstantExpression]]
Determine the configuration of the tree for this transformation.
Support the three types of tree configurations:
Structure:
DistributiveFactorOutRule(self, constants: bool = False)
Distributive Property
ab + ac = a(b + c)
The distributive property can be used to expand out expressions to allow for simplification, as well as to factor out common properties of terms.
Factor out a common term
This handles the ab + ac conversion of the distributive property, which
factors out a common term from the given two addition operands.
+ *
/ \ / \
/ \ / \
/ \ -> / \
* * a +
/ \ / \ / \
a b a c b c
DistributiveFactorOutRule.get_type(
self,
node: mathy_core.expressions.MathExpression,
) -> Optional[Tuple[str, mathy_core.util.TermEx, mathy_core.util.TermEx]]
Determine the configuration of the tree for this transformation.
Support the three types of tree configurations:
Structure:
DistributiveMultiplyRule(self, args, kwargs)
Distributive Property
a(b + c) = ab + ac
The distributive property can be used to expand out expressions to allow for simplification, as well as to factor out common properties of terms.
Distribute across a group
This handles the a(b + c) conversion of the distributive property, which
distributes a across both b and c.
note: this is useful because it takes a complex Multiply expression and replaces it with two simpler ones. This can expose terms that can be combined for further expression simplification.
+
* / \
/ \ / \
/ \ / \
a + -> * *
/ \ / \ / \
/ \ / \ / \
b c a b a c
VariableMultiplyRule(self, args, kwargs)
This restates x^b * x^d as x^(b + d) which has the effect of isolating
the exponents attached to the variables, so they can be combined.
1. When there are two terms with the same base being multiplied together, their
exponents are added together. "x * x^3" = "x^4" because "x = x^1" so
"x^1 * x^3 = x^(1 + 3) = x^4"
TODO: 2. When there is a power raised to another power, they can be combined by
multiplying the exponents together. "x^(2^2) = x^4"
The rule identifies terms with explicit and implicit powers, so the following transformations are all valid:
Explicit powers: x^b * x^d = x^(b+d)
*
/ \
/ \ ^
/ \ = / \
^ ^ x +
/ \ / \ / \
x b x d b d
Implicit powers: x * x^d = x^(1 + d)
*
/ \
/ \ ^
/ \ = / \
x ^ x +
/ \ / \
x d 1 d
VariableMultiplyRule.get_type(
self,
node: mathy_core.expressions.MathExpression,
) -> Optional[Tuple[str, mathy_core.util.TermEx, mathy_core.util.TermEx]]
Determine the configuration of the tree for this transformation.
Support two types of tree configurations:
Structure:
TreeLayout(self, args, kwargs)
Calculate a visual layout for input trees.
TreeLayout.layout(
self,
node: mathy_core.tree.BinaryTreeNode,
unit_x_multiplier: float = 1.0,
unit_y_multiplier: float = 1.0,
) -> 'TreeMeasurement'
Assign x/y values to all nodes in the tree, and return an object containing the measurements of the tree.
Returns a TreeMeasurement object that describes the bounds of the tree
TreeLayout.transform(
self,
node: Optional[mathy_core.tree.BinaryTreeNode] = None,
x: float = 0,
unit_x_multiplier: float = 1,
unit_y_multiplier: float = 1,
measure: Optional[TreeMeasurement] = None,
) -> 'TreeMeasurement'
Transform relative to absolute coordinates, and measure the bounds of the tree.
Return a measurement of the tree in output units.
TreeMeasurement(self) -> None
Summary of the rendered tree
Utility functions for helping generate input problems.
Template type for a default return value
gen_binomial_times_binomial(
op: str = '+',
min_vars: int = 1,
max_vars: int = 2,
simple_variables: bool = True,
powers_probability: float = 0.33,
like_variables_probability: float = 1.0,
) -> Tuple[str, int]
Generate a binomial multiplied by another binomial.
Example
(2e + 12p)(16 + 7e)
mathy:(2e + 12p)(16 + 7e)
gen_binomial_times_monomial(
op: str = '+',
min_vars: int = 1,
max_vars: int = 2,
simple_variables: bool = True,
powers_probability: float = 0.33,
like_variables_probability: float = 1.0,
) -> Tuple[str, int]
Generate a binomial multiplied by a monomial.
Example
(4x^3 + y) * 2x
mathy:(4x^3 + y) * 2x
gen_combine_terms_in_place(
min_terms: int = 16,
max_terms: int = 26,
easy: bool = True,
powers: bool = False,
) -> Tuple[str, int]
Generate a problem that puts one pair of like terms next to each other somewhere inside a large tree of unlike terms.
The problem is intended to be solved in a very small number of moves, making training across many episodes relatively quick, and reducing the combinatorial explosion of branches that need to be searched to solve the task.
The hope is that by focusing the agent on selecting the right moves inside of a ridiculously large expression it will learn to select actions to combine like terms invariant of the sequence length.
Example
4y + 12j + 73q + 19k + 13z + 56l + (24x + 12x) + 43n + 17j
mathy:4y + 12j + 73q + 19k + 13z + 56l + (24x + 12x) + 43n + 17j
gen_commute_haystack(
min_terms: int = 5,
max_terms: int = 8,
commute_blockers: int = 1,
easy: bool = True,
powers: bool = False,
) -> Tuple[str, int]
A problem with a bunch of terms that have no matches, and a single set of two terms that do match, but are separated by one other term. The challenge is to commute the terms to each other in one move.
Example
4y + 12j + 73q + 19k + 13z + 24x + 56l + 12x + 43n + 17j"
^-----------^
mathy:4y + 12j + 73q + 19k + 13z + 24x + 56l + 12x + 43n + 17j
gen_move_around_blockers_one(
number_blockers: int,
powers_probability: float = 0.5,
) -> Tuple[str, int]
Two like terms separated by (n) blocker terms.
Example
4x + (y + f) + x
mathy:4x + (y + f) + x
gen_move_around_blockers_two(
number_blockers: int,
powers_probability: float = 0.5,
) -> Tuple[str, int]
Two like terms with three blockers.
Example
7a + 4x + (2f + j) + x + 3d
mathy:7a + 4x + (2f + j) + x + 3d
gen_simplify_multiple_terms(
num_terms: int,
optional_var: bool = False,
op: Optional[List[str], str] = None,
common_variables: bool = True,
inner_terms_scaling: float = 0.3,
powers_probability: float = 0.33,
optional_var_probability: float = 0.8,
noise_probability: float = 0.8,
shuffle_probability: float = 0.66,
share_var_probability: float = 0.5,
grouping_noise_probability: float = 0.66,
noise_terms: Optional[int] = None,
) -> Tuple[str, int]
Generate a polynomial problem with like terms that need to be combined and simplified.
Example
2a + 3j - 7b + 17.2a + j
mathy:2a + 3j - 7b + 17.2a + j
get_blocker(
num_blockers: int = 1,
exclude_vars: Optional[List[str]] = None,
) -> str
Get a string of terms to place between target simplification terms in order to challenge the agent's ability to use commutative/associative rules to move terms around.
get_rand_vars(
num_vars: int,
exclude_vars: Optional[List[str]] = None,
common_variables: bool = False,
) -> List[str]
Get a list of random variables, excluding the given list of hold-out variables
MathyTermTemplate(
self,
variable: Optional[str] = None,
exponent: Optional[float, int] = None,
) -> None
MathyTermTemplate(variable: Optional[str] = None, exponent: Union[float, int, NoneType] = None)
split_in_two_random(value: int) -> Tuple[int, int]
Split a given number into two smaller numbers that sum to it. Returns: a tuple of (lower, higher) numbers that sum to the input
use_pretty_numbers(enabled: bool = True) -> None
Determine if problems should include only pretty numbers or
a whole range of integers and floats. Using pretty numbers will
restrict the numbers that are generated to integers between 1 and 12. When not using pretty numbers, floats and large integers will
be included in the output from rand_number
FAQs
Computer Algebra System for working with math expressions
We found that mathy-core demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 1 open source maintainer collaborating on the project.
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