| Copyright | Copyright 2024 Yoo Chung |
|---|---|
| License | Apache-2.0 |
| Maintainer | dev@chungyc.org |
| Safe Haskell | None |
| Language | GHC2021 |
Symtegration.Symbolic.Simplify
Description
Supports the simplification of the symbolic representation for a mathematical expression. This is aimed towards making it easier to find common factors for the purpose of integration. It requires the specification of which symbol represents the variable.
Synopsis
- simplify :: Expression -> Expression
- tidy :: Expression -> Expression
- simplifyForVariable :: Text -> Expression -> Expression
Documentation
simplify :: Expression -> Expression Source #
Simplifies symbolic representations of mathematical expressions.
All addition and multiplication will be associated to the left. The simplification is done with an eye towards making it easier to find common factors.
>>>toHaskell $ simplify $ 4 - "x" + "a" * "x" ** 3 + 2 * "x" - 3"1 + x + a * x ** 3"
tidy :: Expression -> Expression Source #
Tidies up expressions for nicer output.
Assumes that other simplifications have been applied first. In fact, it may undo changes that made other simplifications easier.
What is tidied up
This section shows examples of what this function tidies up.
>>>toHaskell $ tidy $ "x" + negate "y""x - y"
>>>toHaskell $ tidy $ "x" + Number (-2) * "y""x - 2 * y"
>>>toHaskell $ tidy $ Number (-1) / Number 2"negate (1 / 2)"
>>>toHaskell $ tidy $ Number (-1) * "x""negate x"
>>>toHaskell $ tidy $ (-"x") * "y""negate (x * y)"
>>>toHaskell $ tidy $ "x" * (-"y")"negate (x * y)"
>>>toHaskell $ tidy $ (-"x") * (-"y")"x * y"
>>>toHaskell $ tidy $ "x" + ((-"y") + "z")"x - y + z"
Arguments
| :: Text | Symbol for the variable. |
| -> Expression | Expression to be simplified. |
| -> Expression | Simplified expression. |
Simplifies symbolic representations of mathematical expressions with special consideration for a particular variable.
All addition and multiplication will be associated to the left. Terms with higher orders of the variable will appear later. The simplification is done with an eye towards making it easier to find common factors.
>>>toHaskell $ simplifyForVariable "x" $ 1 + "a" * "x" ** 3 + "x""1 + x + a * x ** 3">>>toHaskell $ simplifyForVariable "x" $ "a" ** 143 + "x" + "b" ** 2"a ** 143 + b ** 2 + x">>>toHaskell $ simplifyForVariable "x" $ "a" * "x" + "x" + "b ** 2" + "x" ** 2"b ** 2 + x + a * x + x ** 2"