## Maple 12 Questions and Posts

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

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]

## can anyone help me to find the error...

 >
 (1)
 >
 (2)
 >
 (3)
 >
 Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received Inter
 >

## piecewise function in a loop...

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

## How to open text file and run without choose maple...

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?

## How to eval Diff(x,x)?...

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)

## How to set a equation like Diff or diff as symbol?...

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?

## I do not understand the error in this code....

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):

## how to use permgroup ?...

1 1 1 2 2 3 3

(  1 3 3 2 2 1 2 )

how to input this permutation into permgroup ?

## Error when using FourierTransform...

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

## How to guess which physics data suit to theorem eq...

If maple can auto discover derived equations,

then most variable are unknown name which may or may not be physics variable.

so, how to guess which physics data suitable for these look like meaningless variable?

or these tools only visualize the relationship of existing known equations?

## No matter of scale, How to use Fourier transform t...

How to use Fourier transform to extract the part of data which higher than near flat data no matter of scale such as very small decimal value?

would like to extract part when very small decimal small start to increasing or a noise start to appear in time series data.

and then highlight with rectangle in plot for that part of data.

if Fourier transform can not detect this noise or an increasing data or spike then return 0, if detected then return 1

## matrix eigenvalues...

can anyone help me to calculate the exact  value of the eigenvalues of this matrix:

## how to remove 10^(-k) ?...

2.22 *10^(-87)

2.55 *10^(-90)

would like to get 2.22 and 2.55 only by ignoring any power

how to do this?

## Why does my procedure not work?...

with(RegularChains);
R := PolynomialRing([x, y, z]);
p1 := x^2+5-2*x*z;
p2 := z^3*y+x*y^2;
p3 := -8*z^3+3*y^2;
F := [p1, p2, p3];
MainVariable(p1, PolynomialRing([x, y, z]));
MainVariable(p1, PolynomialRing([z, y, x]));
prem(p1, p2, x);
prem(p2, p1, z);
prem(p3, p2, y);
premcustom := proc(Fparam,Gparam, xparam)
local R, G, F, lcg, lcr, dr, dg:
R := Fparam:
G := Gparam:
F := Fparam:
if degree(G,xparam) = 0 then
print("return 0"):
return 0:
elif degree(F, xparam) < degree(G, xparam) then
print("return R"):
return R:
else
lcg := coeff(G, xparam, degree(G, xparam)):
dg := degree(G, xparam):
while degree(R, xparam) > degree(G, xparam) do
lcr := coeff(R, xparam, degree(R, xparam)):
dr := degree(R, xparam):
R := lcg * R - lcr * G * (x^(dr - dg)):
od:
end if:
return R:
end proc:
coeff(p1, x, degree(p1, x));
coeff(p2, x, degree(p2, x));
prem(p1,p2,x);
prem(p2,p1,z);

premcustom(p1,p2,x);
premcustom(p2,p1,z);

why premcustom looping?

is this coeff(p1, x, degree(p1, x)); wrong ?

should this to get real coefficient in number instead of variable and how?

is there equivalent function as dprem?

with(diffalg):with(diffalg):
FlessThanG := proc(Fparam, Gparam, PRing)
F := Fparam:
G := Gparam:
return True:
else
return False:
end if:
end proc:
dprem := proc(Fparam, Gparam, x, PRing)
local R, theta, thetax, thetaG, F, G;
F := Fparam:
G := Gparam:
R := F:
while FlessThanG(R, G, PRing) or FlessThanG(G, R, PRing) do
R := prem(R, thetaG, theta)
od:
return R:
end proc:
R := differential_ring(ranking = [[x,y,r]], derivations = [t], field_of_constants=[m,l], notation = diff):
p1 := m*x[2] + r*x;
p2 := m*y[2] + r*y - g;
p3 := x^2 + y^2 - l^2;
dprem(p1, p3, x, R);

is x[2] = diff(x,t\$2) in diffalg ?

if not how to write in this way?

but got error

Error, (in DifferentialAlgebra:-Tools:-LeadingDerivative) unknown symbol (approx. error location: [m*x[2 --> ] <-- +r*x])