Mathematical Functions, Constants, Evaluations (with Sympy)

[phcreery]

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

[stefnotch]

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/

[stefnotch]

rewrite ?

Lets leave rewriting for a future issue/pull request. I got some ideas that go well above and beyond the scope of this.

[stefnotch]

Regarding Root, Sympy has a root function. I updated the code on the math-expansion branch

[stefnotch]

Infinity would be another constant that we'll have to support at some point