7b313f25-4e9d-41e0-ad6c-d166d52deb2c 487 4 5 false false 0 0 decimal
&[PAGENUM] / &[COUNT]

Code utility

 <content> <p>Code</p> </content>


RTN.D RTN.D :


RTN.D RTN.D description : RTN.M

1
2

Values for carriage return.

 <content> <p>Sintaxis</p> </content>

Sintaxis

Code take the script in the description or in a string and try to convert it into a SMath function

test(a,bₒ) // fn name

x:a+1 // use ₒ for local
y:bₒ-1 // varialbes

// use do for mask
// multiple lines
do u:1 , vₒ:2

while cond1
for k,rng
r:19
s:20
try a
b
if cond2 // if(#2)
t:21
if cond3 // if(#3)
if qq // nested if
t:22
else
u:22
if cond4 // if(#4)
t:23
elif cond4'
u:23
else
vₒ:23

f(u):u*cos(u) // one line fnc

let g(u): // multiple
if u>0 // lines fnc
u^2
else
3*u-1

m:mat( ... // continue
x,y, ... // in
r,s, ... // next line
2,2)

Code >> p // Another def
if cond
aₒ
else
b

test test : line(test(a,b.ₒtestₒ):line(x:a+1,y:b.ₒtestₒ-1,do.ₒtestₒ(u:1,v.ₒtestₒ:2),while(cond1,line(for(k,rng,line(r:19,s:20,try(a,line(b,1,1)),3,1)),if(cond2,line(t:21,1,1)),if(cond3,line(if(qq,line(t:22,1,1)),1,1),line(u:22,1,1)),if(cond4,line(t:23,1,1),cond4',line(u:23,1,1),line(v.ₒtestₒ:23,1,1)),4,1)),f(u):u*cos(u),(g(u):line(if(u>0,line(u^2,1,1),line(3*u-1,1,1)),1,1)),m:mat(x,y,r,s,2,2),7,1),p:line(if(cond,line(a.ₒpₒ,1,1),line(b,1,1)),1,1),2,3,1)

=>

Pasting the string without quotes

Use ₒ (unicode char 2092h) for get "local" variables as the variable name with a subscript with the function name.

 <content> <p>Further Examples</p> </content>

Code >> IsPrime(n) // basic
sq:trunc(sqrt(n)) // prime test
for k:2,k≤sq,k:k+1
if mod(n,k)≡0
break
k ≡ (1+sq)*(n≥2)

Code >> IsMersennePrime(p)
do m:2^p-1 , s:4
for k:2,k≤p-1,k:k+1 // Lehmer
s:s^2-2
s:s-m*trunc(s/m)
s ≡ 0

Code >> IsCircularPrime(p)
do n:trunc(log10(p)) , m:10^n , q:p
for k:0,k≤n,k:k+1
if q<p | ¬IsPrime(q)
break
else
q:10*mod(q,m)+trunc(q/m)
k ≡ n+1

Code >> Mobius(n) // Mobius number
p:0
for k,range(1,n+1)
if mod(n,k)≡0 & IsPrime(k)
if mod(n,k^2)≡0
break
else
p:p+1
(-1)^mod(p,2)*(k≡n+1)

Code >> Catalan(n) // Catalan number
C:mat(1,1,1) // from 1 to n
for k:1,k≤n,k:k+1
el(C,k+1):2*(2*k-1)/(k+1)*el(C,k)
C

Code >> Find(M) // index
k:range(1,length(M)) // where M=1
col(findrows(eval( ...
augment(el(M,k),k)),1,1),2)

NumTh NumTh : 6 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 15 1 mat 2 3 5 7 11 13 17 37 79 113 197 199 337 13 1 mat 3 5 7 13 17 19 6 1 mat 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 16 1 mat 1 1 - 1 - 0 1 - 1 1 - 0 0 1 1 - 0 1 - 1 1 0 1 - 0 1 - 0 1 1 1 - 0 0 1 0 0 1 - 1 - 1 - 0 1 1 1 0 1 - 1 1 0 1 - 1 - 1 - 0 0 1 1 - 0 0 0 1 0 1 - 0 1 0 1 1 1 - 0 1 - 1 0 0 1 1 - 1 - 0 1 1 - 1 - 0 1 - 1 0 0 1 1 - 1 - 0 0 1 1 - 0 1 1 1 0 1 - 0 1 0 1 1 1 0 1 - 0 0 0 5 20 mat

Code >> nIsZ(xₒ,Tₒ)
num2str(eval(normi(stack(xₒ))<Tₒ))≡"1"

Code >> nSort(Aₒ)
for rₒ,range(1,length(Aₒ))
qₒ:el(Aₒ,rₒ)
if num2str(IsDefined(qₒ))≡"1"
el(Vₒ,rₒ):normi(stack(el(Aₒ,rₒ)))
else
el(Vₒ,rₒ):10^300
col(eval(csort( ...
augment(Vₒ,range(1,length(Aₒ))),1)),2)

Code >> nRREF(Mₒ,Tₒ,Ρₒ) // Row reduced echelon form
do Aₒ:Mₒ , mₒ:rows(Aₒ) , nₒ:cols(Aₒ) , Bₒ:Aₒ
do krₒ:range(1,mₒ) , Ρₒ:eval(matrix(0,1))
do rₒ:1 , cₒ:1
while (rₒ≤mₒ)&(cₒ≤nₒ)
ρₒ:el(nSort(el(Aₒ,range(rₒ,mₒ),cₒ)),mₒ-rₒ+1)+rₒ-1
if nIsZ(el(Aₒ,ρₒ,cₒ),Tₒ)
kρₒ:range(ρₒ,mₒ) // fill with 0
el(Aₒ,kρₒ,cₒ):0 // above the ρ column
cₒ:cₒ+1
else
Ρₒ:eval(stack(Ρₒ,ρₒ)) // store ρ
// x(Ρ) are the bound vars in Ax≡b
// columns Ρ of M are a basis for its range
for kcₒ,range(1,nₒ) // swap rows ρ & r
tmpₒ:el(Aₒ,ρₒ,kcₒ)
el(Aₒ,ρₒ,kcₒ):el(Aₒ,rₒ,kcₒ)
el(Aₒ,rₒ,kcₒ):tmpₒ
kₒ:range(cₒ,nₒ) // divide & substract
pₒ:el(Aₒ,rₒ,cₒ) // pivot value
el(Aₒ,rₒ,kₒ):el(Aₒ,rₒ,kₒ)/pₒ
el(Bₒ,krₒ,kₒ):el(Aₒ,krₒ,kₒ)- ...
if(krₒ≠rₒ,el(Aₒ,krₒ,cₒ)*el(Aₒ,rₒ,kₒ),0)
el(Aₒ,krₒ,kₒ):el(Bₒ,krₒ,kₒ) // update
do rₒ:rₒ+1 , cₒ:cₒ+1
Aₒ

Code >> nRank(Mₒ,Tₒ)
Aₒ:nRREF(Mₒ,Tₒ,Rₒ) ¦ length(Rₒ)

Code >> nIsZ(xₒ) ¦ nIsZ(xₒ,'ZTOL)
Code >> nRREF(Mₒ) ¦ nRREF(Mₒ,'ZTOL,0)
Code >> nRank(Mₒ) ¦ nRank(Mₒ,'ZTOL)

nRREF.Code nRREF.Code : 7 1 0 0 3 x * 28 / 3 14 / - 1 7 / 0 1 0 1 2 / 0 0 0 0 1 x 12 / - 1 6 / 0 3 6 mat 3 1 0 0 0 0 5 1 mat 0 1 0 1 2 / 0 1 5 mat 1 1 1 0 1 - 0 1 2 0 0 0 3 3 mat 2 0 1 0 0 0 0 0 1 1 - 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 5 5 mat 4 3

Code >> nBisection(fsₒ,αₒ,βₒ,εₒ)
// Bisection method
str2num(strrep( ...
"fₒ(xₒ):@ₒ(xₒ)","@ₒ",num2str(fsₒ)))
do aₒ:αₒ , bₒ:βₒ , εoₒ:UoM(bₒ-aₒ)*εₒ
if (saₒ:sign(fₒ(aₒ)))≡0
aₒ
elif (sbₒ:sign(fₒ(bₒ)))≡0
bₒ
elif saₒ*sbₒ>0
error("nBisection_Wrong_interval.")
else
for iterₒ , range(1, ...
1+trunc(log(abs((bₒ-aₒ)/εoₒ),2)))
do cₒ:{aₒ+bₒ}/2 , scₒ:sign(fₒ(cₒ))
if scₒ≡0
break
elif saₒ*scₒ>0
do aₒ:cₒ , saₒ:scₒ
else
do bₒ:cₒ , sbₒ:scₒ
cₒ

Code >> nNR.1(fsₒ,xₒ,εoxₒ,εoyₒ,hoₒ,MIₒ)
str2num(strrep( ...
"fₒ(xₒ):@ₒ(xₒ)","@ₒ",num2str(fsₒ)))
do aₒ:xₒ , εxₒ:εoxₒ*UoM(aₒ)
do hₒ:hoₒ*UoM(aₒ) , εyₒ:εoyₒ*UoM(fₒ(aₒ))
for iterₒ,range(1,MIₒ)
yₒ:fₒ(aₒ)
if abs(yₒ)>εyₒ
bₒ:eval(aₒ-(hₒ*yₒ)/(fₒ(aₒ+hₒ)-yₒ))
if abs(aₒ-bₒ)>εxₒ
aₒ:bₒ
else
break
else
break
if(MIₒ≥iterₒ,aₒ,error("nNR.1_MaxIt_Rached"))

nBisection.Code nBisection.Code : 2 1.4142 1.4142 MPa 5.1974 x MPa * h kg kJ / * ho kg kJ / * po MPa / ho kg kJ / * o augment eval 3 1 sys MPa 5.1974

nRKA(Dsₒ,xoₒ,toₒ,teₒ,Nₒ,εₒ) // Runge–Kutta method
// with adaptive step
str2num(strrep( ...
"Dₒ(tₒ,xₒ):@ₒ(tₒ,xₒ)","@ₒ",num2str(Dsₒ)))
Xₒ:el(xoₒ,range(1,length(xoₒ)))
hₒ:(teₒ-toₒ)/Nₒ
do ktₒ:range(1,Nₒ+1) , Toₒ:eval(toₒ+hₒ*(ktₒ-1))
for tₒ:toₒ+hₒ,tₒ≤teₒ,tₒ:tₒ+hₒ
xₒ:col(Xₒ,cols(Xₒ))
k1ₒ:hₒ/3*Dₒ(tₒ,xₒ)
k2ₒ:hₒ/3*Dₒ(tₒ+hₒ/3,xₒ+k1ₒ)
k3ₒ:hₒ/3*Dₒ(tₒ+hₒ/3,xₒ+{k1ₒ+k2ₒ}/2)
k4ₒ:hₒ/3*Dₒ(tₒ+hₒ/2,xₒ+{3*k1ₒ+9*k3ₒ}/8)
k5ₒ:hₒ/3*Dₒ(tₒ+hₒ,xₒ+{3*k1ₒ-9*k3ₒ}/2+6*k4ₒ)
δₒ:k1ₒ-9/2*k3ₒ+4*k4ₒ-1/2*k5ₒ
if normi(δₒ)≤5*εₒ
Xₒ:augment(Xₒ,xₒ+1/2*(k1ₒ+4*k4ₒ+k5ₒ))
el(Tₒ,cols(Xₒ)):tₒ
hₒ:2*hₒ
else
tₒ:tₒ-hₒ
hₒ:hₒ/2
Xₒ:eval(transpose(Xₒ))
for kₒ,range(1,cols(Xₒ))
el(RKₒ,ktₒ,kₒ):cinterp(Tₒ,col(Xₒ,kₒ),el(Toₒ,ktₒ))
eval(augment(Toₒ,RKₒ))

nRKA.Code nRKA.Code : 1 1 RK 2 col RK 3 col augment RK' 2 col RK' 3 col augment 2 1 sys <content> <p>new if</p> </content>

if2(x)

if x>0
ln(x)

if2 if2 :

if3(x)

if x>0
ln(x)
else
ln(-x)

if3 if3 :

if4(x)

if x>0
ln(x)
elif x<0
ln(-x)
else
-∞

if4 if4 : 1 1 1 1.0986 1.0986 1.0986 # 1.0986 1.0986 # # ∞ - x if2 x if3 x if4 <content> <p>fnc</p> </content>

Compound functions inside the main body. Also shows it using ; as argument separator in the script, and using mathcad block.

 Fun.Code

Fun(x;a)
let f(u): // declare f
if u≥0
a+x*atan(a;2*x)
elif u>-2
a*if(u>-1;u^2;-u)
else
-a-x*atan(a;x/2)
f(x) // call it

 1

SMath code for the script:

 x 3 Fun Fun.Code

Fun(x;a)
do s:0 ; p:1
if a≥0
let f(u):
for k;range(1;a)
s:s+k*u
s
else
let f(u):
for k;range(1;-a)
p:p*u/k
p
f(x)

 1 x 3 Fun x 3 - Fun 2 1 sys 1.1.8763.0