Umbrella issue: Make complex numbers first-class citizens, similar to symbols

[Happypig375]

This aims to fix the underlying problem of #13. Currently, not all functions support complex numbers. Complex number specific functions are also not there. Making them supported everywhere will enhance consistency.

Sub-tasks:

Existing operators

• [ ] +
• [ ] -
• [ ] *
• [ ] /
• [ ] ^
  • [ ] i^0.5 form
  • [ ] x^i form (x^i = e^(i log(x)) = cos(log(x))+i sin(log(x)))
  • [ ] (i+1)^2 form
• [ ] !
• [ ] =
• [ ] :=
• [ ] ,

  133

• [ ] < (should keep current implementation returning false or throw?)
• [ ] <=
• [ ] ==
• [ ] !=
• [ ] > (should keep current implementation returning false or throw?)
• [ ] >=

  Existing functions

  trigonometric

• [ ] cos
• [ ] sin
• [ ] tan
• [ ] acos
• [ ] asin
• [ ] atan
• [ ] sec
• [ ] csc
• [ ] cot

  matrix and vector

• [ ] matrix
• [ ] imatrix (should throw?)
• [ ] matget
• [ ] matset
• [ ] invert
• [ ] transpose
• [ ] vector
• [ ] vecget
• [ ] vecset
• [ ] cross
• [ ] dot

  hyperbolic trig

• [ ] cosh
• [ ] sinh
• [ ] tanh
• [ ] acosh
• [ ] asinh
• [ ] atanh

  math functions

• [ ] log(i)
  • [ ] log(x, i)
  • [ ] log(i, x)
  • [ ] log(i, i)
• [ ] log10
• [ ] min
  • [ ] min(i, i)
• [ ] max
  • [ ] max(i, i)
• [ ] floor (floor(a+b i) => floor(a)+floor(b)i)
• [ ] ceil (ceil(a+b i) => ceil(a)+ceil(b)i)
• [ ] Si
• [ ] Ci
• [ ] Ei
• [ ] rect
• [ ] step
• [ ] sinc
• [ ] Shi
• [ ] Chi
• [ ] fact
• [ ] factorial
• [ ] dfactorial
• [ ] exp
• [ ] mod
• [ ] erf
• [ ] round (round(a+b i) => round(a)+round(b)i)
• [ ] pfactor
• [ ] sqrt
• [ ] expand
• [ ] fib
• [ ] tri

  Calculus

• [ ] sum
• [ ] product
• [ ] diff
• [ ] integrate
• [ ] defint

  Algebra

• [ ] divide
• [ ] factor
• [ ] gcd
• [ ] roots
• [ ] coeffs

  Solve

• [ ] solve
• [ ] solveFor
• [ ] solveEquations

  Extra

• [ ] laplace
• [ ] mean
• [ ] mode
• [ ] median
• [ ] smpvar
• [ ] variance
• [ ] smpstdev
• [ ] stdev

  Expression

• [ ] buildFunction
• [ ] evaluate
• [ ] sub
• [ ] variables
• [ ] toTeX
• [ ] text

  165

• [ ] IF
• [ ] div
• [ ] gamma_incomplete
• [ ] parens
• [ ] setEquation
• [ ] sign
• [ ] zscore

  New operators

• [ ] %

  New functions

• [x] arg (synonym to phase)
• [x] conjg
• [x] real
• [x] imaginary
• [ ] phase (synonym to arg)
• [ ] magnitude

  121

• [ ] sech
• [ ] csch
• [ ] coth
• [ ] asec
• [ ] acsc
• [ ] acot
• [ ] asech
• [ ] acsch
• [ ] acoth

  144

• [x] lcm

  145

• [x] trunc (trunc(a+b i) => trunc(a)+trunc(b)i)

  153

• [x] atan2

  160

• [x] determinant
• [x] size

[jiggzson]

Noted. Can you please lump them into one issue so it's easier to track. For instance nerdamer doesn't account for complex numbers and then update the functions you're requesting. This makes it easier for me to get an overall idea of what to work on.

[jiggzson]

Can you please lump them into one issue so it's easier to track. For instance nerdamer doesn't account for complex numbers and then update the functions you're requesting. This makes it easier for me to get an overall idea of what to work on.

Nevermind. This works too

[Happypig375]

Nevermind. This works too

Ok

[Happypig375]

I just figured out that GitHub markdown supports checkboxes. Will revamp the umbrella issue.

[jiggzson]

Wow. So much clearer. Thanks.

[Happypig375]

Unchecked all to avoid false assumptions.

[Happypig375]

Finalizing the list... Anything missing?

[jiggzson]

Nope that covers it all. There are some items on the list that are just in my playpen at the moment. Conditionals and branching is one such example. I doubt I'll be documenting those any time soon since I don't even know if I'll be adding them permanently. I'll be focusing on imaginaries for the time being since that seems the be the heaviest weighing issue.