Adding vector functionality to TI Calculators

Although TI-83/84 calculators support multiple data types, such as real numbers, complex numbers, 1D and 2D lists, fuctions, etc., there is no data type for vectors. This program is my attempt to take the sequence three sequence functions (u v w), which are rarely used for their intended function, and transform them into two-dimensional vectors that can be expressed in terms of I and J.

In addition to adding vectors in terms of I and J, which can be operated on by most functions (including + - * / ^ and many more), functions have been added to determine (1) the angle between vectors, (2) the dot product of two vectors, and (3) the magnitude of a vector. The use of angle( has been altered to return the angle between to vectors, e.g. by angle(u,v. Also, * is now dot product (so uv is still implicit multiplication, but u*v is dot product). Finally, to get the magnitude of a vector, instead of absolute value notation ||u||, which only works with MathPrint, you should use brackets, for example, [u].

prgmVECTORS

ClrHome
1->I
While 1
 {e->K
 Input "",Str3
 "I"+Str3"I·Ans·K
 prgmQ
 Ans->Str3
 "?->Str4
 If 2<length(Str3
  sub(Str3,2,2->Str4
 Str3+"·J·i
 prgmQ
 If inString("u=v=w=",Str4
  "I"+sub(Ans,4,length(Ans)-3
 If Str4="u=
  Ans->u
 If Str4="v=
  Ans->v
 If Str4="w=
  Ans->w
 Ans+"·angle(·cos¹(cos(abs(ΔList(angle({
 prgmR
 If "I["=sub(Ans,1,2) and "]I"=sub(Ans,length(Ans)-1,2
 Then
  expr(sub(Ans,3,length(Ans)-4
  real(sqrt(Ansconj(Ans
  prgmS
 End
 If inString(Ans,"*
 Then
  Ans+"·*·,
  prgmR
  expr("{"+Ans
  prod(real(Ans))+prod(imag(Ans
  prgmS
 End
 expr(Ans->K
 If e≠LK(1
  Ans(1->K
 imag(Ans
 If Ans
 Then
  prgmS
  Ans->Str4
  real(K
  prgmS
  Ans+"I+"+Str4+"J
  If "0I"=sub(Ans,1,2
   sub(Ans,4,length(Ans)-3
  Ans+"·+~·-
  prgmR
  Disp sub("               ",1,16-length(Ans))+Ans
 Else
  Disp K
 End
End

-> represents the arrow (0x04), · represents 0x81, ~ represents negation (0xB0), and L represents the list token (0xEB).

Also, prgmVECTORS calls on three subprograms. prgmS converts a real number to a string, prgmR replaces the first instance of one string with another, and prgmQ replace all instances of one string with another. They are shown below:

prgmQ

Ans→Str9
inString(Ans,"~
sub(Str9,Ans,length(Str9)-Ans+1→Str8
Str9
prgmR
Repeat Str9=Ans+Str8
Ans+Str8→Str9
prgmR
End

prgmR

Ans→Str0
inString(Ans,"~→Z
inString(Str0,"~",Ans+1→Y
inString(sub(Str0,1,Z-1),sub(Str0,Z+1,Ans-Z-1→X
sub(Str0,1,-1+inString(Str0,"~
If X
sub(Str0,1,X-1)+sub(Str0,Y+1,length(Str0)-Y)+sub(Str0,X+length(sub(Str0,Z+1,Y-Z-1)),Z-X-length(sub(Str0,Z+1,Y-Z-1

prgmS

{0,Ans->L2
{0,1->L1
LinReg(ax+b) r6
Equ>String(r6,Str1
sub(Str1,1,length(Str1)-3