Maple 12 Questions and Posts

These are Posts and Questions associated with the product, Maple 12

I have the polynomial :P=X⁴+X³+aX²+√2X+b

Determine a and b so that (1 + i) is zero of P; then calculate all the zeros of P

i would like to to test and do hash on a 2d array and then predict this hash and then reverse back to another hash which can convert back to 2d array , how to do?

i want to know the sign of all the coefficient of CharacteristicPolynomial of such matrix, can anyone help me to do this ?

calcul_determinant.mw

 

 

Is there lifting function for polynomials or algebra use?

expect input a list univariate polynomial , then output a list of polynomials of two variables.

it should be the reverse operation of projection.

Which library has this function in maple 12 or maple 2015?

sourcesamples := [evalf(-1-sqrt(7)), -2, 1, evalf(-1 + sqrt(7)), 2];
templatesamples := [A, evalf(-1-sqrt(7)), A, -2, A, 1, A, evalf(-1 + sqrt(7)), A, 2, A];
samples := [-4, evalf(-1-sqrt(7)), -3, -2, 0, 1, evalf(3/2), evalf(-1 + sqrt(7)), evalf(9/5), 2, 3]

want to insert value alternatively according to the template and neighbor values

 

Some inserted values come from

floor(evalf(-1-sqrt(7)))
ceil(evalf(-1-sqrt(7)))

(round(evalf(-1+sqrt(7)),0) + 1)/2;
(2 + 1)/2
=evalf(3/2)

(round(evalf(-1+sqrt(7)),1) + 2)/2;
(1.6 + 2)/2
=evalf(9/5);

how to generalize this method into general case function instead of manual inesrt?

LeadingTerm(y^2-x^2/y, plex(x, y));
 

(in Groebner:-LeadingTerm) the input is not polynomial in, {x, y}

how to do when fraction in it ?

it return error

pointset := [A, [0,0], B, [0,v_B], C, [u_C, v_C], D, [x_D, y_D], O, [x_O, y_O]];
for i from 1 to nops(pointset)/2 do
print(i, i+1);
pointset[i] := pointset[i+1];
od:
how to Make A := [0,0] instead of pointset[1] 


 

eqs := [II-(phi+mu)*DD+tau*D__g, phi*DD+lambda__2*D__a+lambda__3*D__H-(lambda__4+lambda__1*D__a/(S+D__g)+mu)*D__g, lambda__1*D__g*D__a/(S+D__g)-(lambda__2+beta+mu)*D__a, beta*D__a-(lambda__3+mu+gamma__t)*D__H+lambda__4*D__g, gamma__t*D__H-(delta+mu)*D__c];

[II-(phi+mu)*DD+tau*D__g, phi*DD+lambda__2*D__a+lambda__3*D__H-(lambda__4+lambda__1*D__a/(S+D__g)+mu)*D__g, lambda__1*D__g*D__a/(S+D__g)-(lambda__2+beta+mu)*D__a, beta*D__a-(lambda__3+mu+gamma__t)*D__H+lambda__4*D__g, gamma__t*D__H-(delta+mu)*D__c]

(1)

Sol := {DD = (II+B*tau)/(phi+mu), D__H = E/P, D__a = ((lambda__3+mu+gamma__t)*E/P-lambda__4*B)/beta, D__c = gamma__t*E/((delta+mu)*P), D__g = B};

{DD = (II+B*tau)/(phi+mu), D__H = E/P, D__a = ((lambda__3+mu+gamma__t)*E/P-lambda__4*B)/beta, D__c = gamma__t*E/((delta+mu)*P), D__g = B}

(2)

Inter := [B = S*(lambda[2]+beta+mu)/(lambda[1]-lambda[2]-beta-mu), C = 1/(S+B), E = lambda[2]*lambda[4]*B/beta+B*lambda[4]+mu*B-(lambda[4]*B/beta*B)*C-(phi*II+B*tau*phi)*P/(phi+mu) and lambda[2]*lambda[4]*B/beta+B*lambda[4]+mu*B-(lambda[4]*B/beta*B)*C-(phi*II+B*tau*phi)*P/(phi+mu) = lambda[2]*(lambda[3]+mu+gamma[t])/beta+lambda[3]-lambda[1]*(lambda[3]+mu+gamma[t])*C*B/beta];

[B = S*(lambda[2]+beta+mu)/(lambda[1]-lambda[2]-beta-mu), C = 1/(S+B), false]

(3)

simplify(eval(eqs, eval[recurse](Sol, Inter)))

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received Inter

 

``


 

Download tes.mwtes.mw

Dear All,

How do I use the piecewise function z[k]:=piecewise(k<>0,0,k=0,1) in the loop 

for k from 0 to 10 do

(sum((m^2-1)/z(z[k]+1),m,0..k))

end:

i want the value of z[k] to be automatically used in the loop for the corresponding value of k

I rename text file as mws when I click it , it show a few button and then need to extra click maple input and then need to click enter in order to run.

 

how to run directly when I open it with maple?

I find eval(Diff(x,x)) still is Diff(x,x)

how to make become 1

or how to evaluate Capital Diff ?

 

and I find sum(diff(x^k,x)/k! , k=1..n)

return exp(x) *gamma(n,x)/gamma(n)

why not exp(x)?

 

and diff( m(x+ diff(...) ...) / diff without m(x) , why return 0

i still have not define m(x)

 

if there is a equation subs(...)

how to make a similar symbol like Diff(f(t),t) and diff(f(t),t) use for a new solver procedure use?

restart;
Digits:=4:
n:=11:
M := 2:
Le := 5:
Lb := 2:
L:= 1:
l := 0.5:
Pr := 1:
Pe := 2:
Nt := 0.5:
Nb := 0.8:
F[0]:=0:
F[1]:=l*F[2]:
F[2]:=a:
T[0]:=1:
T[1]:=b:
d:=k->piecewise(k<>0,0,k=0,1):
for k from 0 to n do F[k+3]:=-1/(d(k)+(k+1)*(k+2)*F(k+2))*((sum(F[k-m]*(m+1)*(m+2)*F[m+2],m=0..k))-(sum((k-m+1)*(m+1)*F[k-m+1]*F[m+1],m=0..k))-M*(k+1)*F[k+1])*(factorial(k)/factorial(k+3));
T[k+2]:=-1*(Pr/(k+1)*(k+2))*((sum(F[k-m]*(m+1)*T[m+1],m=0..k))+Nt*(sum((k-m+1)*(m+1)*T[k-m+1]*T[m+1],m=0..k))+Nb*(sum((k-m+1)*(m+1)*T[k+1]*F[k-m+1],m=0..k))) end do: 
f:=sum(F[k]*y^k,k=0..n); 
t:=sum(T[k]*y^k,k=0..n); 
with(numapprox):
pade(diff(f,y),y,[4,4]):
pade(t,y,[4,4]):
solve({limit(pade(diff(f,y),y,[4,4]),y=infinity)=0.,limit(pade(t,y,[4,4]),y=infinity)=0.,[a,b]);

   1 1 1 2 2 3 3  

(  1 3 3 2 2 1 2 )

how to input this permutation into permgroup ?

 

with(DiscreteTransforms);
Digits := 600;
ss := 1:
windowlength := 50:
ma := []:
me := []:
counter1 := 1:
Z := Vector(windowlength, datatype = complex[8]);
Z5 := []:
for i from windowlength+ss to 1+ss by -1 do
eq2 := x:
eq2a := x*2:
god := solve(eq2a=y, t);
ma := [op(ma), evalf(subs(t=100, eq2a))]:
me := [op(me), 100]:
Z[counter1] := [Complex(evalf(subs(t=100, eq2a)),0)];
counter1 := counter1 + 1:
od:
Z2 := FourierTransform(Z);
Z5 := []:
for i from 1 to counter1 do
Z5 := [op(Z5),Re(Z2[i])]:
od:
p := dualaxisplot(listplot(Z, color = red), listplot(me, color = blue), style = line, gridlines = false):
p3 := dualaxisplot(listplot(ma, color = red), listplot(me, color = blue), style = line, gridlines = false):
> Z[counter1] := [Complex(evalf(subs(t = 100, eq2a)), 0)];
Error, unable to evaluate expression to hardware floats: [0.1395407376854069872222364799062994087470140319577366200576294159849633469734297167456440703192248821030980068084453175485138428545865904609881858312543669285411895851509107873579430804484462212873775830538595858575740816705029437533106045686220745333574567547827085763824574616984653193169818770743931611305635956093618789559193701301264280264321394773730076308141252308187470580964653518965117431518571850910086488220847415724949651796448259541027929735646487459091205173804995401770417274097230705447077344465381061736283732438996738107330437055827420813951050981604075837450139995544638...
> Complex(evalf(subs(t=100, eq2a));
Error, unable to match delimiters
Typesetting:-mambiguous(Complexlparevalf(subs(tequals100comma eq2a)),
  Typesetting:-merror("unable to match delimiters"))
> Complex(evalf(subs(t = 100, eq2a)), 0);
1.395407376854069872222364799062994087470140319577366200576294159849633469734\
  297167456440703192248821030980068084453175485138428545865904609881858312543\
  669285411895851509107873579430804484462212873775830538595858575740816705029\
  437533106045686220745333574567547827085763824574616984653193169818770743931\
  611305635956093618789559193701301264280264321394773730076308141252308187470\
  580964653518965117431518571850910086488220847415724949651796448259541027929\
  735646487459091205173804995401770417274097230705447077344465381061736283732\
                                                                               -571
  43899673810733043705582742081395105098160407583745013999554463814123790354 10   
   + 0. I
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