Mathematical Functions, Constants, Evaluations (with Sympy)
phcreery opened this issue · 4 comments
This is an attempt to document and create a running list all the desired mathematical Functions, Constants, and Evaluations.
This issue is aimed at Sympy but the list should be compatible with or easily inclusive to competitive CASs.
https://en.wikipedia.org/wiki/Template:Areas_of_mathematics
https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols
Operations
https://cortexjs.io/compute-engine/guides/dictionaries/
| MathJSON | MathJSON -> Sympy | Sympy -> MathJSON |
|---|---|---|
| MathJSON name | Sympy function name | Sympy printer function/name |
| (checked if fully tested) | (checked if implemented) | (checked if implemented) |
| Arithmatic | ||
| ☒ Parentheses | ☒ | ☒ |
| ☒ Add | ☒ Sympy.Add | ☒ _print_Add |
| ☒ Subtract | ☒ Sympy.Add(x,sympy.mul(y,-1)) | ☒ |
| ☐ Negate (*-1) | ☒ | ☐ |
| ☒ Multiply | ☒ Sympy.Mul | ☒ |
| ☒ (Divide) | ☒ | ☒ |
| ☒ Power | ☒ Sympy.Pow | ☒ |
| ☐ Root | ☒ sympy.root | ☐ |
| ☐ Sqrt * | ☒ Sympy.sqrt | ☒ Sqrt (capital s?) |
| ☐ Square | ☐ | ☐ |
| ☐ Exp * | ☐ | ☐ exp |
| ☐ | ☐ | ☐ |
| Algebra | ||
| ☐ Log * | ☐ | ☒ ln |
| ☐ Log2 * | ☐ | ☒ log2 |
| ☐ Log10 * | ☐ | ☒ log10 |
| ☐ LogOnePlus | ☐ | ☒ log1p |
| ☐ Abs * | ☒ Sympy.Abs | ☐ |
| ☐ Ceil * | ☐ | ☒ ceiling |
| ☐ Chop | ☐ | ☐ |
| ☐ Floor * | ☐ | ☒ floor |
| ☐ Round | ☐ | ☐ |
| ☐ Factorial | ☒ sympy.factorial | ☒ factorial |
| ☐ | ☐ | ☐ |
| Trigonometry | ||
| ☒ Sin | ☒ sympy.sin | ☒ sin |
| ☒ Cos | ☒ sympy.cos | ☒ cos |
| ☒ Tan (defaults to tg?) | ☒ sympy.tan | ☒ tan |
| ☐ Sec | ☒ sympy.sec | ☒ sec |
| ☐ Csc | ☒ sympy.csc | ☒ csc |
| ☐ Cot | ☒ sympy.cot | ☒ cot |
| ☒ Arcsin** | ☒ Sympy.asin | ☒ asin |
| ☒ Arccos** | ☒ Sympy.acos | ☒ acos |
| ☒ Arctan** | ☒ Sympy.atan | ☒ atan |
| ☒ Arctan2** | ☒ sympy.atan2 | ☒ atan2 |
| ☐ Asec** | ☒ Sympy.asec | ☒ asec |
| ☐ Acsc** | ☒ Sympy.acsc | ☒ acsc |
| ☐ Acot** | ☒ Sympy.acot | ☒ acot |
| ☒ Sinh | ☒ Sympy.sinh | ☒ sinh |
| ☒ Cosh | ☒ Sympy.cosh | ☒ cosh |
| ☒ Tanh | ☒ Sympy.tanh | ☒ tanh |
| ☐ Sech** | ☒ Sympy.sech | ☒ sech |
| ☐ Csch** | ☒ Sympy.csch | ☒ csch |
| ☐ Coth** | ☒ Sympy.coth | ☒ coth |
| ☒ Arsinh** | ☒ Sympy.asinh | ☒ asinh |
| ☒ Arcosh** | ☒ Sympy.acosh | ☒ acosh |
| ☒ Artanh** | ☒ Sympy.atanh | ☒ atanh |
| ☐ Asech** | ☒ Sympy.asech | ☒ asech |
| ☐ Acsch** | ☒ Sympy.acsch | ☒ acsch |
| ☐ Arcoth** | ☒ Sympy.acoth | ☒ acoth |
| ☐ Degrees | ☐ | ☐ |
| ☐ FromPolarCoordinates | ☐ | ☐ |
| ☐ ToPolarCoordinates | ☐ | ☐ |
| ☐ Hypot ** | ☐ | ☐ |
| ☐ Haversine | ☐ | ☐ |
| ☐ InverseHaversine | ☐ | ☐ |
| ☐ | ☐ | ☐ |
| Calculus | ||
| ☐ Integrate * | ☐ | ☐ _print_Integral |
| ☐ Derivative/Prime (D, ') * | ☐ | ☐ _print_Derivative |
| ☐ (Partial Derivative) | ☐ | ☐ |
| ☐ (Limit - lim(f,x,a)?) | ☐ | ☐ _print_Limit |
| ☐ (SumSeries) | ☐ | ☐ _print_Sum |
| ☐ (Product of Sequence- CapitalPi) | ☐ | ☐ |
| ☐ | ☐ | ☐ |
| Linear Algebra | ||
| ☐ (System of Equations) | ☐ | ☐ |
| ☐ (EigenValues) | ☐ | ☐ |
| ☐ (EigenVectors) | ☐ | ☐ |
| ☐ (Matricies) | ☐ | ☐ |
| ☐ (Vectors) | ☐ | ☐ |
| Matrix Operations | ||
| ☐ (Matrix Define) | ☐ | ☐ |
| ☐ (Addition) | ☐ | ☐ |
| ☐ (Multiplication) | ☐ | ☐ _print_MatMul ? |
| ☐ (Transpose) | ☐ | ☐ _print_Transpose |
| ☐ (Multiplication) | ☐ | ☐ |
| ☐ (Power) | ☐ | ☐ _print_MatPow ? |
| ☐ (Normal) | ☐ | ☐ |
| Logic/Relational | ||
| ☐ True** | ☐ | ☐ _print_BooleanTrue |
| ☐ False** | ☐ | ☐ _print_BooleanFalse |
| ☐ Maybe** | ☐ | ☐ |
| ☐ And | ☐ | ☐ _print_And |
| ☐ Or | ☐ | ☐ _print_Or |
| ☐ (Xor) | ☐ | ☐ _print_Xor |
| ☐ Not | ☐ | ☐ _print_Not |
| ☐ Equivalent (\equiv) | ☐ | ☐ |
| ☐ Implies | ☐ | ☐ |
| ☐ Equal (taken) | ☐ | ☐ |
| ☐ NotEqual | ☐ | ☐ |
| ☐ GreaterEqual | ☐ sympy.GreaterThan | ☐ |
| ☐ LessEqual | ☐ sympy.LessThan | ☐ |
| ☐ Greater | ☐ sympy.GreaterThanStrict | ☐ |
| ☐ Less | ☐ sympy.LessThanStrict | ☐ |
| ☐ | ☐ | ☐ |
| Special | ||
| ☐ Gamma | ☒ sympy.gamma | ☒ gamma |
| ☐ LogGamma | ☒ sympy.loggamma | ☒ loggamma |
| ☐ Erf | ☒ sympy.erf | ☒ erf |
| ☐ Erfc | ☒ sympy.erfc | ☒ erfc |
| ☐ EulerGamma | ☒ Sympy.EulerGamma | ☒ _print_EulerGamma |
| ☐ | ☐ | ☐ |
| Misc | ||
| ☐ List | ☐ | ☐ _print_list |
| ☐ Set | ☐ | ☐ _print_set |
| ☐ Lambda | ☐ sympy.Lambda | ☐ _print_Lambda |
| ☐ InverseFunction | ☐ | ☐ _print_Inverse ? |
| ☐ Parse (Latex) | ☐ | ☐ |
| ☐ String | ☐ | ☐ |
| ☐ | ☐ | ☐ |
| ☐ | ☐ | ☐ |
* MathLive broken at the moment? Usually happens when the expression is converted to latex then parsed back.
** MathLive Unsupported
Constants
http://www.ebyte.it/library/educards/constants/ConstantsOfPhysicsAndMath.html
https://cortexjs.io/mathlive/reference/commands/
| MathJSON | MathJSON -> Sympy | Sympy -> MathJSON |
|---|---|---|
| Mathematical | ||
| ☒ Pi | ☒ Sympy.pi | ☒ _print_Pi |
| ☒ ImaginaryUnit (\imaginaryI) | ☒ Sympy.I | ☒ _print_ImaginaryUnit |
| ☒ ExponentialE (\exponentialE) | ☒ Sympy.E | ☒ _print_Exp1 |
| ☐ GoldenRatio | ☒ Sympy.GoldenRatio | ☒ _print_GoldenRatio |
| ☐ (Infinity) | ☐ | ☐ _print_Infinity |
| ☐ (-Infinity) | ☐ | ☐ _print_NegativeInfinity |
| ☐ | ☐ | ☐ _print_TribonacciConstant |
| ☐ (NaN) | ☐ | ☐ _print_NaN |
| ☐ | ☐ | ☐ |
Evaluations
Some examples: https://docs.sympy.org/latest/tutorial/simplification.html#simplification
- Solve (for variable)
- Expand
- Factor
This list is nowhere near complete.
Please comment with more expressions you wish to see supported
One place which has quite a few interesting functions are the default compute-engine dictionaries. I suppose we can take some from there as well.
e.g. https://cortexjs.io/compute-engine/reference/trigonometry/
rewrite ?
Lets leave rewriting for a future issue/pull request. I got some ideas that go well above and beyond the scope of this.
Regarding Root, Sympy has a root function. I updated the code on the math-expansion branch
Infinity would be another constant that we'll have to support at some point