Investigate using symengine

[terrorfisch]

https://github.com/symengine/symengine.py

Looks easily adaptable. Some features are missing, but this probably is not a roadblocker. A lot of sympy's features is not used anyways. I propose defining a set of operations that is supported on any system so one can be sure that a pulse works independent of the used backend while still using sophisticated features if porability is no concern.

A problem could be the implementation of vector valued expressions. This is already hacky in sympy. If I see this correctly symengine only allows matricies there is symarray.

Will using symengine actually be faster?

TODO:

• [x] Define supported operations
  • [ ] Collect list of example strings that must work in all backends. Starting point can be sympy_tests.py
• [ ] Define interface for backend
• [ ] Investigate difference to sympy in lambdification
• [ ] (Optional) Investigate interplay with numba

[terrorfisch]

Supported Expressions:

• Operators:
  • +, -, *, /, // i.e. addition, subtraction, multiplication, division, floored division
  • Also via alias Add etc?
  • <, >, ==, !=, <=, >= and Eq, Le etc
  • Do we include @ matrix multiplication operator
  • Numpy provided unary functions:
  • Elementary functions: sin, cos, tan, cot, csc, sec, asin, acos, atan, acot, acsc, asec, sinh, cosh, tanh, coth, sech, csch, asinh, acosh, atanh, acoth, asech, acsch, gamma, log, sqrt, exp
    • sign, floor, ceiling, conjugate
    • Non unary numeric: atan2
  • Piecewise
  • Abs, Max, Min
  • a[i] i.e. indexing of symbols

Custom functions:

• Sum (not in symengine?)
• len, Len: Already customized for sympy
• Broadcast: Already costomized for sympy