Elisha

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0 years, 56 days

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These are replies submitted by Elisha

@tomleslie Thanks alot! It really worked.

 

@Carl Love Pls see what I did but seems am not yet home.How can I get numeric solution for values of t=0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5 in this system of ODE?


 

``

odesys := {diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t), diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t), diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t), diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t), diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)};

{diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t), diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t), diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t), diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t), diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)}

(1)

v(0) := .4;

.4

(2)

NULL

s(0) := 0.6e-1;

0.6e-1

(3)

e[0] := .24;

.24

(4)

i[0] := .17;

.17

(5)

r[0] := .13;

.13

(6)

c := 0.4e-1;

0.4e-1

(7)

f := .4;

.4

(8)

beta := .2;

.2

(9)

epsilon := .8;

.8

(10)

theta[1] := .1;

.1

(11)

theta[2] := .3;

.3

(12)

alpha := .9;

.9

(13)

rho := .7;

.7

(14)

eta := .99;

.99

(15)

delta := .3;

.3

(16)

a := 0.4e-1;

0.4e-1

(17)

phi := 1;

1

(18)

lambda := 0.96e-1;

0.96e-1

(19)

('`union`')(`~`[indets](odesys)[]);

`union`({t, s(t), v(t), diff(s(t), t)}, {t, s(t), v(t), diff(v(t), t)}, {t, s(t), diff((table( [( 0 ) = .24 ] ))(t), t), (table( [( 0 ) = .24 ] ))(t)}, {t, diff((table( [( 0 ) = .17 ] ))(t), t), (table( [( 0 ) = .17 ] ))(t), (table( [( 0 ) = .24 ] ))(t)}, {t, v(t), diff((table( [( 0 ) = .13 ] ))(t), t), (table( [( 0 ) = .13 ] ))(t), (table( [( 0 ) = .17 ] ))(t)})

(20)

dsolve(odesys)

Error, (in dsolve) invalid input: D expects its 1st argument, f, to be of type {set, array, list, algebraic, equation, procedure}, but received table( [( 0 ) = .13 ] )

 

``

``


 

Download odesys.mw

@tomleslie 
How can I get the exact solution for the system below?

``

diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t):

diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t):

diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t):

diff(r(t), t) = eta*i(t)+v(t)*f*theta[2]-(a+epsilon)*r(t)


 

Download SYSTEM_OF_EQUATIONS.mw

@Carl Love 
Kindly assist check if what I did is correct. I doubt this figures because it quite high above 1 which is not what I was expecting.

``

f := proc (t, s) options operator, arrow; (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v-(lambda+theta[1]+a+epsilon)*s end proc;

proc (t, s) options operator, arrow; (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v-(lambda+theta[1]+a+epsilon)*s end proc

(1)

f := proc (t, v) options operator, arrow; phi*epsilon+rho*a+theta[1]*s-((1-f)*alpha+f*theta[2]+a+epsilon)*v end proc;

proc (t, v) options operator, arrow; phi*epsilon+rho*a+theta[1]*s-((1-f)*alpha+f*theta[2]+a+epsilon)*v end proc

(2)

f := proc (t, e) options operator, arrow; `λs`-(delta+a+epsilon)*e end proc;

proc (t, e) options operator, arrow; `λs`-(delta+a+epsilon)*e end proc

(3)

f := proc (t, i) options operator, arrow; delta*e-(eta+a+epsilon)*i end proc;

proc (t, i) options operator, arrow; delta*e-(eta+a+epsilon)*i end proc

(4)

f := proc (t, r) options operator, arrow; `ηi`+f*theta[2]*v-(a+epsilon)*r end proc;

proc (t, r) options operator, arrow; `ηi`+f*theta[2]*v-(a+epsilon)*r end proc

(5)

t[0] := 0:

s[0] := 0.6e-1:

v[0] := .4:

e[0] := .24:

i[0] := .17:

r[0] := .13:

h := .1:

c := 0.4e-1;

0.4e-1

(6)

f := .4;

.4

(7)

beta := .2;

.2

(8)

epsilon := .8;

.8

(9)

theta[1] := .1;

.1

(10)

theta[2] := .3;

.3

(11)

alpha := .9;

.9

(12)

rho := .7;

.7

(13)

eta := .99;

.99

(14)

delta := .3;

.3

(15)

a := 0.4e-1;

0.4e-1

(16)

phi := 1;

1

(17)

lambda := 0.96e-1;

0.96e-1

(18)

NULL

for n to 10 do t[n] := n*h; k1 := f(t[n-1], s[n-1]); k2 := f(t[n-1]+(1/2)*h, s[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, s[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+s[n-1]); s[n] := s[n-1]+1/6*(k1+2*k2+2*k3+k4) end do;

.1

 

.4

 

.4

 

.4

 

.4

 

.4600000000

 

.2

 

.4

 

.4

 

.4

 

.4

 

.8600000000

 

.3

 

.4

 

.4

 

.4

 

.4

 

1.260000000

 

.4

 

.4

 

.4

 

.4

 

.4

 

1.660000000

 

.5

 

.4

 

.4

 

.4

 

.4

 

2.060000000

 

.6

 

.4

 

.4

 

.4

 

.4

 

2.460000000

 

.7

 

.4

 

.4

 

.4

 

.4

 

2.860000000

 

.8

 

.4

 

.4

 

.4

 

.4

 

3.260000000

 

.9

 

.4

 

.4

 

.4

 

.4

 

3.660000000

 

1.0

 

.4

 

.4

 

.4

 

.4

 

4.060000000

(19)

NULL

for n to 8 do t[n] := n*h; k1 := f(t[n-1], v[n-1]); k2 := f(t[n-1]+(1/2)*h, v[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, v[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+v[n-1]); v[n] := v[n-1]+1/6*(k1+2*k2+2*k3+k4) end do

.1

 

.4

 

.4

 

.4

 

.4

 

.8000000000

 

.2

 

.4

 

.4

 

.4

 

.4

 

1.200000000

 

.3

 

.4

 

.4

 

.4

 

.4

 

1.600000000

 

.4

 

.4

 

.4

 

.4

 

.4

 

2.000000000

 

.5

 

.4

 

.4

 

.4

 

.4

 

2.400000000

 

.6

 

.4

 

.4

 

.4

 

.4

 

2.800000000

 

.7

 

.4

 

.4

 

.4

 

.4

 

3.200000000

 

.8

 

.4

 

.4

 

.4

 

.4

 

3.600000000

(20)

NULL

NULL

NULL

``

for n to 8 do t[n] := n*h; k1 := f(t[n-1], e[n-1]); k2 := f(t[n-1]+(1/2)*h, e[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, e[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+e[n-1]); e[n] := e[n-1]+1/6*(k1+2*k2+2*k3+k4) end do
NULL

.1

 

.4

 

.4

 

.4

 

.4

 

.6400000000

 

.2

 

.4

 

.4

 

.4

 

.4

 

1.040000000

 

.3

 

.4

 

.4

 

.4

 

.4

 

1.440000000

 

.4

 

.4

 

.4

 

.4

 

.4

 

1.840000000

 

.5

 

.4

 

.4

 

.4

 

.4

 

2.240000000

 

.6

 

.4

 

.4

 

.4

 

.4

 

2.640000000

 

.7

 

.4

 

.4

 

.4

 

.4

 

3.040000000

 

.8

 

.4

 

.4

 

.4

 

.4

 

3.440000000

(21)

``

``

for n to 8 do t[n] := n*h; k1 := f(t[n-1], i[n-1]); k2 := f(t[n-1]+(1/2)*h, i[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, i[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+i[n-1]); i[n] := i[n-1]+1/6*(k1+2*k2+2*k3+k4) end do
NULL

.1

 

.4

 

.4

 

.4

 

.4

 

.5700000000

 

.2

 

.4

 

.4

 

.4

 

.4

 

.9700000000

 

.3

 

.4

 

.4

 

.4

 

.4

 

1.370000000

 

.4

 

.4

 

.4

 

.4

 

.4

 

1.770000000

 

.5

 

.4

 

.4

 

.4

 

.4

 

2.170000000

 

.6

 

.4

 

.4

 

.4

 

.4

 

2.570000000

 

.7

 

.4

 

.4

 

.4

 

.4

 

2.970000000

 

.8

 

.4

 

.4

 

.4

 

.4

 

3.370000000

(22)

``

NULL

NULL

for n to 8 do t[n] := n*h; k1 := f(t[n-1], r[n-1]); k2 := f(t[n-1]+(1/2)*h, r[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, r[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+r[n-1]); r[n] := r[n-1]+1/6*(k1+2*k2+2*k3+k4) end do
NULL

.1

 

.4

 

.4

 

.4

 

.4

 

.5300000000

 

.2

 

.4

 

.4

 

.4

 

.4

 

.9300000000

 

.3

 

.4

 

.4

 

.4

 

.4

 

1.330000000

 

.4

 

.4

 

.4

 

.4

 

.4

 

1.730000000

 

.5

 

.4

 

.4

 

.4

 

.4

 

2.130000000

 

.6

 

.4

 

.4

 

.4

 

.4

 

2.530000000

 

.7

 

.4

 

.4

 

.4

 

.4

 

2.930000000

 

.8

 

.4

 

.4

 

.4

 

.4

 

3.330000000

(23)

NULL

NULL

NULL

NULL

NULL

``


 

Download runge_and_maple.mw

@Carl Love Thank you for that update. I really will appreciate this recent method if I know how to go about it. Can you pls give me an example using my system of equation above to enable me follow? 

@Carl Love
Thank you for your response to my question on Rk4. I am actually doing a comparison between Adomian Decomposition method and Rk4. this error "Error, unable to parse"

is still there.
 

``

f := proc (t, s) options operator, arrow; (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v-(lambda+theta[1]+a+epsilon)*s end proc;

proc (t, s) options operator, arrow; (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v-(lambda+theta[1]+a+epsilon)*s end proc

(1)

f := proc (t, v) options operator, arrow; phi*epsilon+rho*a+theta[1]*s-((1-f)*alpha+f*theta[2]+a+epsilon)*v end proc;

proc (t, v) options operator, arrow; phi*epsilon+rho*a+theta[1]*s-((1-f)*alpha+f*theta[2]+a+epsilon)*v end proc

(2)

f := proc (t, e) options operator, arrow; `λs`-(delta+a+epsilon)*e end proc;

proc (t, e) options operator, arrow; `λs`-(delta+a+epsilon)*e end proc

(3)

f := proc (t, i) options operator, arrow; delta*e-(eta+a+epsilon)*i end proc;

proc (t, i) options operator, arrow; delta*e-(eta+a+epsilon)*i end proc

(4)

f := proc (t, r) options operator, arrow; `ηi`+f*theta[2]*v-(a+epsilon)*r end proc;

proc (t, r) options operator, arrow; `ηi`+f*theta[2]*v-(a+epsilon)*r end proc

(5)

t[0] := 0:

s[0] := 0.6e-1:

v[0] := .4:

e[0] := .24:

i[0] := .17:

r[0] := .13:

h := .1:

c := 0.4e-1;

0.4e-1

(6)

f := .4;

.4

(7)

beta := .2;

.2

(8)

epsilon := .8;

.8

(9)

theta[1] := .1;

.1

(10)

theta[2] := .3;

.3

(11)

alpha := .9;

.9

(12)

rho := .7;

.7

(13)

eta := .99;

.99

(14)

delta := .3;

.3

(15)

a := 0.4e-1;

0.4e-1

(16)

phi := 0;

0

(17)

lambda := 0.96e-1;

0.96e-1

(18)

NULL

"for n from 1 to 2 do   t[n]:=n*h:  k1:=f(t[n-1],v[n-1]):  k2:=f(t[n-1]+(h/(2)),v[n-1]+(h/(2))*k1):  k3:=f(t[n-1]+(h/(2)),s[n-1]+(h/(2))*k2):  k4:=f(t[n-1]+h,s[n-1]+h*k3):  s[n]:=s[n-1]+(1/(6))*(k1+2 k2+2 k3+k4):"

"od;"

Error, unable to parse

"od;"

 

``

Error, unable to parse

"od;"

 

"for n from 1 to 2 do"

t[n] := n*h

k1 := f(t[n-1], v[n-1])

k2 := f(t[n-1]+(1/2)*h, v[n-1]+(1/2)*h*k1)

k3 := f(t[n-1]+(1/2)*h, v[n-1]+(1/2)*h*k2)

k4 := f(t[n-1]+h, h*k3+v[n-1])

v[n] := v[n-1]+1/6*(k1+2*k2+2*k3+k4)

"od;"

NULL

``

"for n from 1 to 8 do"

t[n] := n*h

k1 := f(t[n-1], e[n-1])

k2 := f(t[n-1]+(1/2)*h, e[n-1]+(1/2)*h*k1)

k3 := f(t[n-1]+(1/2)*h, e[n-1]+(1/2)*h*k2)

k4 := f(t[n-1]+h, h*k3+e[n-1])

e[n] := e[n-1]+1/6*(k1+2*k2+2*k3+k4)

"od;"

``

``

"for n from 1 to 8 do"

t[n] := n*h

k1 := f(t[n-1], i[n-1])

k2 := f(t[n-1]+(1/2)*h, i[n-1]+(1/2)*h*k1)

k3 := f(t[n-1]+(1/2)*h, i[n-1]+(1/2)*h*k2)

k4 := f(t[n-1]+h, h*k3+i[n-1])

i[n] := i[n-1]+1/6*(k1+2*k2+2*k3+k4)

"od;"

``

NULL

NULL

"for n from 1 to 8 do"

t[n] := n*h

k1 := f(t[n-1], r[n-1])

k2 := f(t[n-1]+(1/2)*h, r[n-1]+(1/2)*h*k1)

k3 := f(t[n-1]+(1/2)*h, r[n-1]+(1/2)*h*k2)

k4 := f(t[n-1]+h, h*k3+r[n-1])

r[n] := r[n-1]+1/6*(k1+2*k2+2*k3+k4)

"od;"

NULL

NULL

NULL

NULL

NULL

``


 

Download runge_and_maple.mw

thank you
Elisha

@ThU 

Thanks Sir,

Your response is quite helpful

Regards.

@AmusingYeti 

Thanks for you quick and timely response.

Regards

@John May 

Dear John, Thanks for your effort. Find detail of what am trying to do below
 

restart

with(student)

``

G := S(t)*L(t)

S(t)*L(t)

(1)

m := 10

S[lambda] := sum(S[b]*lambda^b, b = 0 .. m); L[lambda] := sum(L[b]*lambda^b, b = 0 .. m); G[lambda] := subs(S(t) = S[lambda], G); G[lambda] := subs(L(t) = L[lambda], G[lambda]); G := G[lambda]; s := expand(G, lambda); ft := unapply(s, lambda); for i from 0 while i <= m do A1[i] := ((D@@i)(ft))(0)/factorial(i); print(A[i] = A1[i]) end do

A[0] = S[0]*L[0]

 

A[1] = L[0]*S[1]+L[1]*S[0]

 

A[2] = L[0]*S[2]+L[1]*S[1]+L[2]*S[0]

 

A[3] = L[0]*S[3]+L[1]*S[2]+L[2]*S[1]+L[3]*S[0]

 

A[4] = L[0]*S[4]+L[1]*S[3]+L[2]*S[2]+L[3]*S[1]+L[4]*S[0]

 

A[5] = L[0]*S[5]+L[1]*S[4]+L[2]*S[3]+L[3]*S[2]+L[4]*S[1]+L[5]*S[0]

 

A[6] = L[0]*S[6]+L[1]*S[5]+L[2]*S[4]+L[3]*S[3]+L[4]*S[2]+L[5]*S[1]+L[6]*S[0]

 

A[7] = S[5]*L[2]+S[2]*L[5]+S[1]*L[6]+S[0]*L[7]+S[4]*L[3]+S[3]*L[4]+S[6]*L[1]+S[7]*L[0]

 

A[8] = S[2]*L[6]+S[0]*L[8]+S[8]*L[0]+S[4]*L[4]+S[1]*L[7]+S[3]*L[5]+S[6]*L[2]+S[5]*L[3]+S[7]*L[1]

 

A[9] = S[6]*L[3]+S[9]*L[0]+S[4]*L[5]+S[2]*L[7]+S[3]*L[6]+S[8]*L[1]+S[0]*L[9]+S[1]*L[8]+S[7]*L[2]+S[5]*L[4]

 

A[10] = S[0]*L[10]+S[10]*L[0]+S[1]*L[9]+S[6]*L[4]+S[7]*L[3]+S[3]*L[7]+S[2]*L[8]+S[4]*L[6]+S[9]*L[1]+S[5]*L[5]+S[8]*L[2]

(2)

s[n+1] := (1-f)*alpha*(int(v__n, t = 0 .. t))-beta*c*(int(A__n, t = 0 .. t))-(`&theta;__1`+a+Pi)*(int(s__n, t = 0 .. t))

v[n+1] := `&theta;__1`*(int(s__n, t = 0 .. t))-((1-f)*alpha+f*`&theta;__2`+a+Pi)*(int(v__n, t = 0 .. t))

e[n+1] := `&beta;c`*(int(A__n, t = 0 .. t))-(delta+a+Pi)*(int(e__n, t = 0 .. t))

i[n+1] := delta*(int(e__n, t = 0 .. t))-(eta+a+Pi)*(int(i__n, t = 0 .. t))

r[n+1] := eta*(int(i__n, t = 0 .. t))+`f&theta;__2`*(int(v__n, t = 0 .. t))-(a+Pi)*(int(r__n, t = 0 .. t))

for n from 0 to 4 do  end do

``

(1-f)*alpha*v__n*t-beta*c*s__0*i__0*t-(`&theta;__1`+a+Pi)*s__n*t

(3)

"for n:=0, n=1, n=2, n=3, n=4:  `s__1, ``s__2__`, `s__3, ``s__4`,  `i__1`, `i__2, ``i__3`, `i__4`,   `r__1`, `r__2`, `r__3, ``r__4`:"

Error, unterminated for loop

"for n:=0, n=1, n=2, n=3, n=4:  `s__1, ` `s__2__`, `s__3, __3__, s__4`, `i__1__`, `i__2, ` `i__3`, `i__4`, `r__1`, `r__2`, `r__3, ` `r__4`:"

 

and s(t)= s1+s2+s3+s4

i(t) = i__1+`i__2, `+i__3+i__4, r(t) = r__1+r__2+r__3_+r__4

"but A[n]:=(1)/(n!) [((&DifferentialD;)^(n))/(&DifferentialD; lambda^(n)) ((&sum;)`s__k`lambda^(k))((&sum;)`i__k`lambda^(k)) ]() ? ()|() ? (lambda=0)"

Error, missing numerator

Typesetting:-mambiguous(Typesetting:-mrow(Typesetting:-mi("but", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msub(Typesetting:-mi("A", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mi("n", fontstyle = "italic", mathcolor = "#c800c8", mathvariant = "italic", placeholder = "true"), subscriptshift = "0"), Typesetting:-mo("&Assign;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfrac(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&excl;", accent = "false", fence = "false", largeop = "false", lspace = "0.1111111em", mathvariant = "normal", movablelimits = "false", rspace = "0.1111111em", separator = "false", stretchy = "false", symmetric = "false")), bevelled = "false", denomalign = "center", linethickness = "1", numalign = "center"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-msup(Typesetting:-mo("&DifferentialD;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.0em", mathvariant = "normal", movablelimits = "unset", rspace = "0.0em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-mrow(Typesetting:-mo("&DifferentialD;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.0em", mathvariant = "normal", movablelimits = "unset", rspace = "0.0em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), bevelled = "false", denomalign = "center", linethickness = "1", numalign = "center"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-munderover(Typesetting:-mo("&sum;", accent = "unset", fence = "unset", largeop = "true", lspace = "0.0em", mathvariant = "normal", movablelimits = "true", rspace = "0.1666667em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mrow(Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mn("4", mathvariant = "normal"), accent = "false", accentunder = "false"), Typesetting:-mi("`s__k`"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-munderover(Typesetting:-mo("&sum;", accent = "unset", fence = "unset", largeop = "true", lspace = "0.0em", mathvariant = "normal", movablelimits = "true", rspace = "0.1666667em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mrow(Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mn("4", mathvariant = "normal"), accent = "false", accentunder = "false"), Typesetting:-mi("`i__k`"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), mathvariant = "normal"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false")), open = "&lsqb;", close = "&rsqb;", mathvariant = "normal"), Typesetting:-mfrac(Typesetting:-mambiguous(Typesetting:-merror("?"), Typesetting:-merror("missing numerator")), Typesetting:-mphantom(Typesetting:-mrow(Typesetting:-mi("x", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "unset", rspace = "0.2777778em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mi("a", fontstyle = "italic", mathvariant = "italic")), constraints = "height-only"), bevelled = "false", denomalign = "center", linethickness = "0", numalign = "center"), Typesetting:-mo("&verbar;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.1111111em", mathvariant = "normal", movablelimits = "unset", rspace = "0.1111111em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mfrac(Typesetting:-mphantom(Typesetting:-mi("f(x)", fontstyle = "italic", mathvariant = "italic"), constraints = "height-only"), Typesetting:-mrow(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), bevelled = "false", denomalign = "center", linethickness = "0", numalign = "center")))

 

NULL

> The one highlighted in red is the error that was generated wthen i tried generating the values of s1,s2,s3,s4 ; i1,i2,i3,i4 and r1,r2,r3,r4

NULL

``

``


 

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