DuncanA

693 Reputation

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13 years, 146 days

MaplePrimes Activity


These are answers submitted by DuncanA

nops and op

f := 2*x+3*y+2;
2 x + 3 y + 2
nops(f);
3
op(1, f);
2 x
op(2, f);
3 y
op(3, f);
2
op(f);
2 x, 3 y, 2

---

Duncan

evalf can be used to obtain a numerical solution

r := RootOf(189*_Z^6-756*_Z^5+567*_Z^4+819*_Z^3-1386*_Z^2+672*_Z-104):
evalf(r);
0.3260605103
s := allvalues(r);
/ 6 5 4 3 2
RootOf\189 _Z - 756 _Z + 567 _Z + 819 _Z - 1386 _Z + 672 _Z - 104,

\ /
index = 1/, RootOf\

6 5 4 3 2 \
189 _Z - 756 _Z + 567 _Z + 819 _Z - 1386 _Z + 672 _Z - 104, index = 2/,

/ 6 5 4 3 2
RootOf\189 _Z - 756 _Z + 567 _Z + 819 _Z - 1386 _Z + 672 _Z - 104,

\ /
index = 3/, RootOf\

6 5 4 3 2 \
189 _Z - 756 _Z + 567 _Z + 819 _Z - 1386 _Z + 672 _Z - 104, index = 4/,

/ 6 5 4 3 2
RootOf\189 _Z - 756 _Z + 567 _Z + 819 _Z - 1386 _Z + 672 _Z - 104,

\ /
index = 5/, RootOf\

6 5 4 3 2 \
189 _Z - 756 _Z + 567 _Z + 819 _Z - 1386 _Z + 672 _Z - 104, index = 6/
t := evalf(s);
0.3260605103, 0.6407586587, 0.8042832092, 1.033180831, 2.475877226,

-1.280160435

---

Duncan

The problem appears to be that the unknowns are assumed to be complex quantities.  ?evalc assumes that the unknown variables are real-valued. Applying evalc gives the desired solution

G := s -> 1 / (1 + 2*zeta*s / Omega + (1/(Omega)^2)*s^2):
abs( G(I*omega) ):
evalc(%):
diff(%, omega):
sols := solve(%, omega);
(1/2) (1/2)
/ 2\ / 2\
0, \1 - 2 zeta / Omega, -\1 - 2 zeta / Omega
omega_peak := sols[2];
(1/2)
/ 2\
\1 - 2 zeta / Omega

the same result can be achieved using assume:

assume(omega::real, Omega::real, zeta::real);
G := s -> 1 / (1 + 2*zeta*s / Omega + (1/(Omega)^2)*s^2):
abs( G(I*omega) ):
diff(%, omega):
sols := solve(%, omega);
(1/2) (1/2)
/ 2\ / 2\
0, \1 - 2 zeta~ / Omega~, -\1 - 2 zeta~ / Omega~

---

Duncan

You don't give an example of the result set, but assuming the results have the form given below, then they can be programmatically converted into functions.

resultset := {f=x^2+1, g=x^2*y+2};
/ 2 2 \
{ f = x + 1, g = x y + 2 }
\ /
for p in resultset do expr := rhs(p); funcname := lhs(p); varnames := op( indets(expr, name) ); assign( funcname=unapply(expr, varnames) ); od:
print(f);
2
x -> x + 1
print(g);
2
(x, y) -> x y + 2
f(5);
26
g(3,2);
20

---

Duncan

(1) Maple uses upper case I as sqrt(-1) not lower case i. (2) Maple interprets omega[n] as an indexed version of plain omega instead of an atomic identifier. In the following I have replaced i with I and omega[n] with Omega.

G(s) := 1/(1+2*zeta*s/Omega+(1/(Omega)^2)*s^2):
'abs(G(j*omega))'=subs(s=I*omega,abs(G(s))):
Abs := simplify(normal(rhs(%))):
diff(Abs,omega):
solve(%,omega);
I zeta Omega

If you must have omega with subscript n, one way to achieve this is to use 2D Math and convert omega_n to an atomic identifier

---

Duncan

?applyrule is one option

applyrule(a::integer^(-n)*b::integer^(n)=(b/a)^(n), t);
(2/5)^n

---

Duncan

plot([sin(x), sin(x + 120/180 * Pi), sin(x + 240/180 * Pi)]);

---

Duncan

Have you tried Ctrl+Alt+0?

---

Duncan

The correct shortcut is Ctrl+= not Ctrl+Shift+=. On my keyboard, the = sign is below the + sign so I don't need to hold down Shift to enter =. Do you need to hold down Shift to enter =? If not, what happens when you enter Ctrl+= instead of Ctrl+Shift+=? There is also Ctrl+Alt+0 (Cmd+Alt+0, on Macintosh) for international keyboards.

---

Duncan

The GenAdd procedure, as you have defined it, writes to Array a that is in the global namespace. The solution is to create a new Array inside the procedure

 

GenAdd := proc(at, bt)
local tempvec;
tempvec := Array(Dimensions(at)[1]);
tempvec[bt] := 1;
at+tempvec
end proc:
a;
[1, 2, 3, 1, 1, 2]

GenAdd(a, 3);
[1, 2, 4, 1, 1, 2]

a;
[1, 2, 3, 1, 1, 2]

 

---

Duncan

zip is one option

u:=<1,1,1>:
v:=<2,3,4>:
f:=(x,y)->ln(x-y):
zip(f, u, v);
[ I Pi ]
[ ]
[ln(2) + I Pi]
[ ]
[ln(3) + I Pi]

 

although map can also be used for the example given

u-v;
[-1]
[ ]
[-2]
[ ]
[-3]

map(ln, %);
[ I Pi ]
[ ]
[ln(2) + I Pi]
[ ]
[ln(3) + I Pi]

 

---

Duncan

If beta is an element of a finite field, the corresponding minimal polynomial can be found by calculating the powers of beta, beta^2, beta^(2^2) until we find the least positive integer d for which beta^(2^d) = beta. This d is the degree of minimal polynomial g and g is given by g(x) = (x-beta)*(x-beta^2) ... (x-beta^(2^(d-1)))

 

restart;
f := x -> x^4+x+1; # Field polynomial
4
x -> x + x + 1
m := degree(f(x));
4
alias(alpha=RootOf(f(x))):

 

beta := alpha^3;
3
alpha
beta := Rem(beta, f(x), x) mod 2;
3
alpha
L := NULL: for d from 1 to 2^m do d; t := Powmod(beta, 2^d, f(x), x) mod 2; L := L, t: if t = beta then break end if; end do:
mul(x - L[i], i = 1 .. nops([L]));
/ 3 2\ / 3 2 \ / 3 \ /
\x - alpha - alpha / \x - alpha - alpha - alpha - 1/ \x - alpha - alpha/ \x

3\
- alpha /
Expand(%) mod 2;
4 3 2
x + x + x + x + 1
g := unapply(%, x);
4 3 2
x -> x + x + x + x + 1
g(beta);
12 9 3 6
alpha + alpha + alpha + alpha + 1
Expand(%) mod 2;
0

---

Duncan

Quote sum's first argument to prevent premature evaluation

y:=n->sum('y(k)',k=0..n-1):
y(0):=a:
y(4);
8 a

This is a common problem when using sum.

---

Duncan

There are various options some of which are operating system dependent,

?worksheet/managing/export 

My preferred solution would be to export or print to PDF:

http://www.maplesoft.com/support/help/Maple/view.aspx?path=worksheet%2fmanaging%2fexportPDF

 

---

Duncan

Another option is to use the  ?curry procedure. In the examples below, the procedure with three arguments, g, is transformed into procedures taking two arguments, g's first argument having been supplied in the call to curry.

http://en.wikipedia.org/wiki/Currying

g := proc(w, x, y)
  x + y^w
end proc:
h := curry( g, 2 ):
h(x, y);
2
x + y
for j to 3 do f[j] := curry(g, j); end do:
f[1](x, y);
x + y
for j to 3 do f[j](x, y) end do;
x + y
2
x + y
3
x + y

 

---

Duncan

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