• The ability to include token strings as data. I thought about a possible syntax for this, and I came up with ["String goes here"]. Perhaps there's a better syntax, but that's just what I came up with.
  

I was going to make the same exact request, with the same suggestion for syntax.
Ninja'd before I even made the post.

This axiom allows you to access the os variables and do floating point math with them!
Feel free to ask questions instead of trying to read and understand this entire post.

Did you ever want to store the value of the real/complex variable A into the real/complex variable B inside of an axe program? Now it is easier than ever!
:A→B
:#Axiom(CPLXMATH) .varA could be complex
:Select("varA")→Select("varB") .Select( is in the 2nd List Ops menu
:solve() .optional but suggested, frees used memory

But maybe you wanted to store A + B to C.  Well that is almost as simple.
:A+B→C
:#Axiom(CPLXMATH) .varA or varB could be complex
:solve(ᵀ+,Select("varA"),Select("varB"))→Select("varC") .solve( is on the Math Math menu
:solve() .optional, but suggested - frees used memory
In general, solve(ᵀ<op>,<args>) applies <op> to <args>. <op> can be be almost anything from ^, dim( to inString(!
Note: even though Axe changes inString( to inData(, it still does its original function when used in this command. Also, don't close the ( in <op>!

Well that's cool, but can I use Lists you ask? Of course!
:L₁∗A→L₂
:#Axiom(CPLXMATH) .L₁ or L₂ could be complex lists
:solve(ᵀ∗,Select("L₁"),Select("varA"))→Select("L₂")
:solve() .optional but suggested, frees used memory

But I only wanted to used the 42^nd number in L₁ you ask? Well, why not!
:L₁(42)‒A→L₂(42)
:#Axiom(CPLXMATH) ... see above
:solve(ᵀ‒,Select("L₁",42),Select("varA"))→Select("L₂",42)
:solve() ... see above
Notice how Select( loads or saves to a variable, and solve( applies an operation to loaded variables.

The above code doesn't work if L₁ is too small, you say? Well why don't we resize L₁.
:42→dim(L₁)
:#Axiom(CPLXMATH) ...you know
:dim("L₁",42) .notice the slight difference in syntax
Note that solve() is unnecessary because dim does not currently use any memory.

I'll bet you forgot about matricies, you say... Nope!
:{5,5}→dim([A])
:For(A,1,5)
:For(B,1,5)
:10A+B→[A](A,B)
:End
:End
:#Axiom(REALMATH) .only real numbers used AND no arbitrary variable access
:Buff(9)→GDB1 .a temp floating point - they are 9 bytes large
:dim("[A]",5,5)
:For(A,1,5) .remember, A and B are still Axe variables
:For(B,1,5)
:A∗10+B→float{GDB1} .load temp with A∗10+B converted to a floating point
:GDB1→Select("[A]",A,B) .see, I didn't forget matrix support
:solve() .especially important inside loops
:End
:End
Or, if you are familiar with the format of floating point numbers:
:#Axiom(REALMATH) .see above
:"[A]"→Str1
:[008100000000000000]→GDB1 .floating point zero, prepared for 2 digit numbers
:dim(Str1,5,5)
:For(A,1,5)
:For(B,1,5)
:A∗16+B→{GDB1+2} .A and B are between 0 and 10 exclusive, treat as bcd digits
:GDB1→Select(Str1,A,B)
:End
:solve() .delete temp memory at least moderately often (~100 bytes at this point!)
:End

Now for an example that actually does something useful.
:(-B+√(B²‒4AC))/(2A)→C
:(-B‒√(B²‒4AC))/(2A)→D
:#Axiom(CPLXMATH) .obviously
:Buff(9)→GDB2 .declare constants
:Buff(9)→GDB4
:2→float{GDB2} .initialize constants
:4→float{GDB4}
:solve(ᵀ/,solve(ᵀ+,solve(ᵀ-,Select("varB")),solve(ᵀ√(,solve(ᵀ‒,solve(ᵀ²,Select("varB")),solve(ᵀ∗,GDB4,solve(ᵀ∗,Select("varA"),Select("varB")))))),solve(ᵀ∗,GDB2,Select("varA")))→Select("varC")
:solve()
:solve(ᵀ/,solve(ᵀ‒,solve(ᵀ-,Select("varB")),solve(ᵀ√(,solve(ᵀ‒,solve(ᵀ²,Select("varB")),solve(ᵀ∗,GDB4,solve(ᵀ∗,Select("varA"),Select("varB")))))),solve(ᵀ∗,GDB2,Select("varA")))→Select("varC")
:solve()
JK, it doesn't have to be that unreadable. I just wanted to show what you could do if you really wanted to. (Yes, that means you can nest as much as you want, limited only by the amount of memory available.) A normal person might do something more like this:
:#Axiom(CPLXMATH) .obviously
:Buff(9)→GDB2 .declare constants
:Buff(9)→GDB4
:2→float{GDB2} .initialize constants
:4→float{GDB4}
:Select("varA")→A .yes you can do that
:Select("varB")→B
:Select("varC")→C
:solve(ᵀ√(,solve(ᵀ‒,solve(ᵀ²,B),solve(ᵀ∗,GDB4,solve(ᵀ∗,A,C))))→D
:solve(ᵀ-,B)→B .pre-calculate stuff
:solve(ᵀ∗,GDB2,A)→A
:solve(ᵀ/,solve(ᵀ+,B,D),A)→Select("varD")
:solve(ᵀ/,solve(ᵀ‒,B,D),A)→Select("varE")
:solve()

Let's return the result in Ans instead of D and E.
:(-B+{1,-1}√(B²+i²4AC))/(2A)
i²=-1, but it allows the result to be complex regardless of mode. Similarly, complex constants are used below, with no i component, in order to allow complex answers in any mode.
:#Axiom(CPLXMATH)
:[015D]"TEMP"→Str1LT .[015D] must be used instead of the ᴸ before a list in the current version of Axe
:[0C80200000000000000C8000000000000000]→GDB2 .still 2, but complex
:[0C80400000000000000C8000000000000000]→GDB4 .complex floating point 4
:Select("varA")→A
:Select("varB")→B
:Select("varC")→C
:solve(ᵀ√(,solve(ᵀ‒,solve(ᵀ²,B),solve(ᵀ∗,GDB4,solve(ᵀ∗,A,C))))→C .we don't need C anymore
:solve(ᵀ-,B)→B .pre-calculate stuff
:solve(ᵀ∗,GDB2,A)→A
:DelVar Str1LT .Delete ᴸTemp in case it already exists
:solve(ᵀ/,solve(ᵀ+,B,C),A)→Select(Str1LT,1)
:solve(ᵀ/,solve(ᵀ‒,B,C),A)→Select(Str1LT,2)
:Select(Str1LT)→Select("varAns") .yep, that's right
:DelVar Str1LT .no one needs ᴸTemp anymore
:solve() .we are done

Strange OP codes (used instead of ᵀ<token>)

ECE

ECF

ED0

ED1

ED2

ED3

ED4

ED5

ED6

ED7

ED8

ED9

EDA

EDB

npv(

irr(

bal(

∑Prn(

∑Int

➤Nom(

➤Eff(

dbd(

lcm(

gcd(

randInt(

randBin(

sub(

stdDev(

EDC

EDD

EDE

EDF

EE0

EE1

EE2

EE3

EE4

EE5

EE6

EE7

EE8

EE9

variance(

inString(

normalcdf(

invNorm(

tcdf(

Χ²cdf(

Ϝcdf(

binompdf(

binomcdf(

poissonpdf(

poissoncdf(

geometpdf(

geometcdf(

normalpdf(

EEA

EEB

EEC

EED

E89

E8A

E8B

E8C

E8D

E8E

E8F

E90

E91

E92

E93

tpdf(

Χ²pdf(

Ϝpdf(

randNorm(

conj(

real(

imag(

angle(

cumSum(

expr(

length(

ΔList(

ref(

rref(

Fill(

Update 0.1: Tutorial added.
Update 0.2: Major bugfix.
Update 0.3: Select( is replaced with get(. Key: seq(

*Warning: Please do not use RealMath unless you are absolutely sure that your code will never see anything that could posibly be complex. (unless you want corrupted mem, etc.) However, use it if you can, since it is smaller and faster.

Here is an easy one.
_L appearing inside of a string should expand to db ListObj,tVarLst, not itself.
In the mean time, "_LA" can be replaced with [015D]"A".

Just do this Copy(L₆,GetCalc("Pic1",756),756)

Here is a strange bug:

Code: (axm.z80) [Select] #include "Axe.inc" .dw AXM_HEADER .dw 3 .db AXM_ALL .dw tok_Load .db AXM_INLINE .db AXM_1ARG  call sub_Axiom2 .dw 1 .db AXM_ALL .dw 0 .db AXM_SUB .db AXM_0ARGS  ret .dw 0

Code: (A) [Select] :.AA :#Axiom(AXM) :Pic0 :Load() :Data(255)->Pic0

Code: (B) [Select] :.BB :#Axiom(AXM) :Data(255)->Pic0 :Pic0 :Load()

When A and B are compiled and disassembled:

Code: (AA) [Select] ld   hl,$9d9c  call $9d9c  ret  ret  .db $ff

Code: (BB) [Select] ld   hl,$9d9c  call $9d9d  ret  .db $ff  ret

In AA the data pointer is wrong, and in BB the second axiom comes after the data.

I actually was doing that at one point, so it is possible, but I kept forgetting the axiom format
Anyway, since I can't upload files yet, here is a link to a Mimas version of Axe.inc.

I changed axv_Theta to axv_θ since Mimas supports the theta character.
Also, since Mimas doesn't support macros:
;REP_NEXT becomes:
 DB   REP_NEXT
 RORG PC-1
;REP_NEXT(x) becomes:
 DB   REP_NEXT_OFF,x
 RORG PC-2


Yeah, I actually started calc programming 6 years ago.
I didn't even know there was a calc programming community until I found revsoft 2 years later.

If you really need line clipping, you can use this 449 byte routine (not including the subroutines used).
The routine uses the full signed 16-bits of each parameter, however it fails for large |x2-x1| and/or large |y2-y1| due to overflow
:Lbl LineC
:If r4<<r2
:r1->r5:r3->r1:r5->r3
:r2->r6:r4->r2:r6->r4
:End
:ReturnIf r4<<0
:ReturnIf r2>=>=64
:r1-r3->r5
:r4-r2->r6
:If r2<<0
:r4*r5//r6+r3->r1:0->r2
:End
:If r4>=>=64
:r2-63*r5//r6+r1->r3:63->r4
:End
:If r3<<r1
:r1->r5:r3->r1:r5->r3
:r2->r6:r4->r2:r6->r4
:End
:ReturnIf r3<<0
:ReturnIf r1>=>=96
:r2-r4->r5
:r3-r1->r6
:If r1<<0
:r3*r5//r6+r4->r2:0->r1
:End
:If r3>=>=96
:r1-95*r5//r6+r2->r4:95->r3
:End
:Line(r1,r2,r3,r4)
:Return