rpn

8b9ea747-437c-488d-b4c7-73ae55d59c02 206 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

rpn

rpn\0024\ A.11 CHS EXP LN RE IM 1/X ¬! SIGN ABS SQRT PI CHS exp ln Re Im RINV R¬ R! sign abs sqrt PI 212 mat : A.12 SIN COS TAN ASIN ACOS ATAN sin cos tan asin acos atan 26 mat : A.13 SINH COSH TANH ASINH ACOSH ATANH sinh cosh tanh asinh acosh atanh 26 mat : A.14 FRAC INT FRAC trunc 22 mat : A.1 A.11 A.12 A.13 A.14 augment : A.2 + - * / Y^X & | < ≤ ≡ NTHROOT MOD R\002B\ R\002D\ R\002A\ R\002F\ R\005E\ AND OR LT LE EQ nthroot mod 212 mat : A.3 R2P P2R xy2pol pol2xy 22 mat : A A.1 transpose 1 augment A.2 transpose 2 augment A.3 transpose 3 augment stack : M S T 02 matrix : A M k 1 A rows range s A k 2 el S1 el(S,1) strrep : s s S2 el(S,2) strrep : 12 mat s s Mt el(M,t) strrep : s s K1 el(K,1) strrep : 12 mat s s Ft el(F,t) strrep : A k 2 el s SMF mat(S,M,F,1,3) strrep : 12 mat 31 line for T T A stack : 21 line for T 31 line : T.1 X=0? if(S1≡0,0,K1:1) X≠0? if(S1≠0,0,K1:1) X<0? if(S1<0,0,K1:1) X>0? if(S1>0,0,K1:1) X≤0? if(S1≤0,0,K1:1) X≥0? if(S1≥0,0,K1:1) 62 mat : T.4 X=Y? if(S1≡S2,0,K1:1) X≠0? if(S1≠S2,0,K1:1) X<Y? if(S1<S2,0,K1:1) X>Y? if(S1>S2,0,K1:1) X≤Y? if(S1≤S2,0,K1:1) X≥Y? if(S1≥S2,0,K1:1) 62 mat : 12 mat T.5 X<>Y line(tmp:S2,S2:S1,S1:tmp,3,1) RUP S:stack(el(S,N),submatrix(S,1,N-1,1,1)) RDN S:stack(submatrix(S,2,N,1,1),S1) END break 42 mat : T.2 ↑ S:stack(S1,S) CLS S:matrix(1,1) RET j:PUSH(k)+1 32 mat : T.3 MODE MODE(a) CLX S:submatrix(S,2,N,1,1) LST X S:stack(el(K,4),S) 32 mat : 12 mat U.1 STO Mt:S1 STO+ Mt:Mt+S1 STO- Mt:Mt-S1 STO* Mt:Mt*S1 STO/ Mt:Mt/S1 52 mat : U.2 RCL S:stack(Mt,S) RCL+ S:stack(Mt+S1,S) RCL- S:stack(Mt-S1,S) RCL* S:stack(Mt*S1,S) RCL/ S:stack(Mt/S1,S) 52 mat : 12 mat U.4 PRG line(el(P,t):transpose(A),break,2,1) XEQ SMF:XEQ(el(P,t),1) 22 mat : U.5 SF Ft:1 CF Ft:0 22 mat : U.6 FS? if(Ft≡1,0,K1:1) FC? if(Ft≡0,0,K1:1) 22 mat : 12 mat U.7 FS?C line(if(Ft≡1,0,K1:1),Ft:0,2,1) FC?S line(if(Ft≡0,0,K1:1),Ft:1,2,1) 22 mat : U.8 GTO j:t-1 GTO+ j:j+t-1 GTO- j:j-t+1 32 mat : U.9 GSB line(SMF:XEQ(B,t),k:POP(j,k),2,1) GSB+ line(SMF:XEQ(B,t+j),k:POP(j,k),2,1) GSB- line(SMF:XEQ(B,t-j),k:POP(j,k),2,1) 32 mat : 12 mat A T.1 T.2 T.3 T.4 T.5 15 mat S U.1 U.2 U.4 U.5 U.6 U.7 U.8 U.9 18 mat S 13 mat eval 181 line :

rpn\0024\ rpn\0024\ :

A Π rpn x CHS x - : x R\00AC\ x ¬ : x R\0021\ x! : x RINV 1 x / : x PI π : x FRAC x x trunc - : 16 mat x y R\002B\ x y + : x y R\002D\ x y - : x y R\002A\ x y * : x y R\002F\ x y / : 14 mat x y R\005E\ x y^: x y AND x y & (: x y OR x y | (: 13 mat x y LT x y < (: x y LE x y ≤ (: x y EQ x y ≡ (: 13 mat s L s IsString s strlen 0 if 11 line : X V W 0 : k 0 : 12 mat x X W k k 1 + : el x : for W 31 line : x N2S x num2str : x S2N x str2num : m n σ a m n substr : 31 mat 13 mat n a FR rpn\0024\ n el a 1 findrows : M m n SV M m n 11 submatrix : 12 mat j k POP k j k stack : 11 line : k PUSH push k 1 el : k k 2 k length SV : push 31 line : 12 mat x MODE ToDo : B j XEQ S M F K P 15 mat A B V : j 1 + A length SV DO : S M F 13 mat 21 line : A DO j 0 : j A length < j j 1 + : a A j el : N S length : 13 mat S trace a RST ≡ Π S 11 matrix : M RPN 1 matrix : F M : K M : P M : 15 mat : n a L : (5 ≡ (α 13 σ : (SF ≡ (α CF ≡ (| (& a α 42 σ concat : 0 if K 1 el 0 ≡ f 1 a FR : (0 ≠ K 4 el S 1 el : f 3 el 1 ≡ S 1 el f 2 el (S 1 el N2S) concat S2N : R f 2 el (S 2 el N2S, S 1 el N2S) concat S2N : f 3 el 2 ≡ S R S 3 N SV stack : S R 1 el R 2 el S 3 N SV stack : if 21 line if 21 line f 2 a FR : (0 ≠ val f 2 el S2N : n a L : (4 > (f 314 σ FR : (0 ≠ (& t n 1 - 2 σ S2N : val f 2 el S2N : 12 mat S a S stack : if if if K 1 el 0 : if 21 line if 31 line while S M F K P 15 mat 31 line : S Π 1 el : M Π 2 el : F Π 3 el : K Π 4 el : P Π 5 el : 15 mat Π A V DO : (1 el transpose 121 line :

ToDo

MODE: PRG, DEG, FIX, SCI, ENG, STAT R/S, ISG, ... etc.

RPN Examples

Individual call

RPN 4 :

Mem, Prg & Flags length

RST RPN rpn 011 mat

RPN Stk Mem Flg Prg K 15 mat ≡

5 RPN rpn 5012 mat

3 RPN rpn 35013 mat

- RPN rpn 2012 mat

LN RPN rpn 0.6931 012 mat

STO 03 RPN rpn 0.6931 012 mat

RPN 2 el 3 el 0.6931

5 RPN rpn 5 0.6931 013 mat

1/X RPN rpn 0.2 0.6931 013 mat

Y^X RPN rpn 0.9293 012 mat

2 ln 5 nthroot 0.9293

NTHROOT RPN rpn 1.019 012 mat

6 RPN rpn 6 0.9293 013 mat

! RPN rpn 720 0.9293 013 mat

1/X RPN rpn 0.0014 0.9293 013 mat

CHS RPN rpn 0.0014 - 0.9293 013 mat

+ RPN rpn 0.9279 012 mat

RCL+03 RPN rpn 1.6211 0.9279 013 mat

3 RPN rpn 3 1.6211 0.9279 014 mat

2 RPN rpn 23 1.6211 0.9279 015 mat

SF 02 RPN rpn 23 1.6211 0.9279 015 mat

RPN 3 el 2 el 1

RDN RPN rpn 3 1.6211 0.9279 0215 mat

Grouped call

RST RPN rpn 011 mat

2 LN STO 03 5 NTHROOT 15 mat RPN rpn 0.9293 012 mat

6! 1/X CHS + RCL+03 32 SF 02 RDN 110 mat RPN rpn 3 1.6211 0.9279 0215 mat

Functions check

CLS RPN rpn 011 mat

9 RPN rpn 9012 mat

↑ RPN rpn 99013 mat

2 RPN rpn 299014 mat

MOD RPN rpn 19013 mat

LST X RPN rpn 219014 mat

CLX RPN rpn 19013 mat

43 R2P 13 mat RPN rpn 5 0.6435 19015 mat

X<>Y 11 mat RPN rpn 0.6435 519015 mat

43 xy2pol 5 0.6435 21 sys

P2R RPN rpn 4319015 mat

RUP RPN rpn 0431915 mat

XEQ

Programming

RPN 4 :

Simple program

RST RPN rpn 011 mat

PRG 01 X<Y? 500 STO 01 600 END 16 mat RPN rpn 011 mat

Programs must to be inside of an only one rpn call, because there are not PRG Mode.

CLS 1120 XEQ 01 14 mat RPN rpn 6002011014 mat

CLS 2010 XEQ 01 14 mat RPN rpn 6005001020015 mat

Calling another program

PRG 02 20 XEQ 01 STO 02 55 END 16 mat RPN rpn 6005001020015 mat

CLS 10 XEQ 02 13 mat RPN rpn 556002010015 mat

CLS 30 XEQ 02 13 mat RPN rpn 556005002030016 mat

GTO

+01 +02 +03

PRG 03 1 FC? 01 GTO 06 4 GTO 07 67 END 19 mat RPN rpn 556005002030016 mat

PRG.03 PRG 03 1 FC? 01 GTO 06 4 GTO 07 67 END 19 mat :

CLS CF 01 XEQ 03 13 mat RPN rpn 761014 mat

0 1 2 3 4 5 6 7 8

CLS SF 01 XEQ 03 13 mat RPN rpn 741014 mat

PRG 03 1 FC? 01 GTO+03 4 GTO+02 67 END 19 mat RPN rpn 741014 mat

CLS CF 01 XEQ 03 13 mat RPN rpn 761014 mat

CLS SF 01 XEQ 03 13 mat RPN rpn 741014 mat

GSB

PRG 04 20 X>Y? GSB 06 + END 55 RET 18 mat RPN rpn 741014 mat

CLS 10 XEQ 04 13 mat RPN rpn 7510013 mat

CLS 30 XEQ 04 13 mat RPN rpn 50012 mat

PRG 04 20 X>Y? GSB+03 + END 55 RET 18 mat RPN rpn 50012 mat

CLS 10 XEQ 04 13 mat RPN rpn 7510013 mat

CLS 30 XEQ 04 13 mat RPN rpn 50012 mat

RPN 50021 mat 5006000041 mat 100041 mat 000041 mat PRG 01 X<Y? 500 STO 01 600 END 16 mat PRG 02 20 XEQ 01 STO 02 55 END 16 mat PRG 03 1 FC? 01 GTO+03 4 GTO+02 67 END 19 mat PRG 04 20 X>Y? GSB+03 + END 55 RET 18 mat 41 mat 15 mat

rpn Calculus 1V Example

Calculus Example

x f x 3^5 x 2^* + 3 - x 2^1 + / :

x f

RPN 4 :

Function

RST RPN rpn 011 mat

PRG PRG 01 RCL 01 3 Y^X RCL 01 2 Y^X 5 * + 3 - 112 mat :

PRG PRG RCL 01 2 Y^X 1 + / END 17 mat augment :

α 4 - :

PRG RPN rpn 011 mat

CLS α STO 01 XEQ 01 14 mat RPN rpn 0.7647 4 - 013 mat

α f 0.7647

Derivative

PRG PRG 02 XEQ 01 107 -^STO+01 X<>Y XEQ 01 - X<>Y STO-01 / CHS END 112 mat :

PRG RPN rpn 0.7647 4 - 013 mat

CLS α STO 01 XEQ 02 14 mat RPN rpn 0.8304 4 - 013 mat

α f α diff 0.8304

Newton - Raphson

PRG PRG 03 RCL 01 XEQ 01 XEQ 02 / RCL 01 - CHS STO 01 - ABS 109 -^112 mat :

PRG PRG X<Y? GTO+05 CLX CLX RCL 01 END CLX CLX GTO 01 19 mat augment :

PRG RPN rpn 0.8304 4 - 013 mat

CLS α STO 01 XEQ 03 14 mat RPN rpn 4.8737 - 4 - 013 mat

RPN 1 el 1 el f 2.067 1014 -^*

109 -^α β α α f α f α diff / - : (- abs < α β : while α 21 line 4.8737 -

Alvaro