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Christian Wolinski

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20 years, 13 days
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These are answers submitted by Christian Wolinski

You missed it....

Christian Wolinski 1625
December 26 2018
1 0

Look at the line:

 

x[2] := unapply(invlaplace(laplace(t^(alpha-1), t, s)*laplace(y[2](t)-20*y[13](t)+(19/2)*y[14]-60*y[16](t)+21*y[17](t)-y[13](t)*(6*(3*y[2](t)-y[5](t)))+y[15](t)*(12*(3*y[1](t)-y[4](t))-2*(2*y[1](t)-y[4](t)))-y[16](t)*(12*(3*y[2](t)-y[5](t)))+y[18](t)*(24*(3*y[1](t)-y[4](t))-6*(2*y[1](t)-y[4](t))), t, s), s, t), t);


Instead of (19/2)*y[14] it should be (19/2)*y[14](t). This is my best bet. Replace with:

 

x[2] := unapply((subs(y[14] = y[14](t), eval(x[2])))(t), t);
#or simply
x[2] := unapply(invlaplace(laplace(t^(alpha-1), t, s)*laplace(y[2](t)-20*y[13](t)+(19/2)*y[14](t)-60*y[16](t)+21*y[17](t)-y[13](t)*(6*(3*y[2](t)-y[5](t)))+y[15](t)*(12*(3*y[1](t)-y[4](t))-2*(2*y[1](t)-y[4](t)))-y[16](t)*(12*(3*y[2](t)-y[5](t)))+y[18](t)*(24*(3*y[1](t)-y[4](t))-6*(2*y[1](t)-y[4](t))), t, s), s, t), t);


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Solve then plot...

Christian Wolinski 1625
November 17 2018
1 1

gives this:
 

 

R := z = RootOf(-8649 + 270100*_Z + 9000*_Z^2 + 100*_Z^3, .3198736765e-1) .. .1;
A := [[3/2 + 1/10*(-8649+270100*z + 9000*z^2 + 100*z^3)^(1/2), z, 'R'], [3/2 - 1/10*(-8649 + 270100*z + 9000*z^2 + 100*z^3)^(1/2), z, 'R']];
plot(A);


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Just rename....

Christian Wolinski 1625
November 14 2018
1 2

If you dont want something expanded, then name it:
 

 

CG:=proc(E) map(q -> collect(q, G, proc(E) if type(E, `*`) then map(collect, E, [F], factor) else collect(E, [F], factor) end if end@factor), E); end:

eqn := 5*(x*y)^2 + x/G = 2*F^3 + x^2, F = 3*x^3 + y^2, G^2 = y, G = sqrt(y);
#implicitdiff({eqn[1..-2]}, {y, F, G}(x), {y}, x):
implicitdiff({eqn[1..-2]}, {x, F, G}(y), {x}, y):
simplify(%, [eqn[-2]]);

applyop(CG, [1,2], convert(%, parfrac, G));
subs([eqn[2..-1]], %);  

 

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Domains package....

Christian Wolinski 1625
November 12 2018
1 4

Maybe this is what you need:

 

with(Domains):
GI := Gaussian(Z):
F:=proc(a,b)
   local i, s, t, g;
   g := op('procname');
   i := g[Input](a), g[Input](b);
   i, PrincipalIdeal(g, i, 's, t'), s, t;
end proc;
F[GI](-87+47*I, -90+43*I); 

 

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Not algsubs....

Christian Wolinski 1625
November 09 2018
1 0

What you are trying to do is specifically intended for the command simplify:

 

simplify(expr, [expression = V1]); 

 

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Two ways:...

Christian Wolinski 1625
October 30 2018
0 0


Two ways:

 

GST := AE + AI - ANB - AR - CP;


GSTf := evalindets(GST, name, unapply('unapply(a[i], i), a'));
GSTf ~ ([$1..3]);

GSTg := evalindets(GST, name, unapply('G[a], a'));
G := () -> op(procname)['args'];
GSTg ~ ([$1..3]); ;


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Algebra....

Christian Wolinski 1625
October 27 2018
2 1

Replace the capital I in your formulas with lower case i and the problem will disappear. Capital I means (-1)^(1/2) which in algebraic formulas will be transformed by simplifications.

 

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Like this....

Christian Wolinski 1625
October 26 2018
1 4

This is a basic rule of valuations:

'log[2]'(3);

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Simply:...

Christian Wolinski 1625
October 16 2018
2 5


 

 

A := Y = (-2*k^3+6*k^2+sqrt(k^8-12*k^7+64*k^6-198*k^5+448*k^4-636*k^3+369*k^2)-7*k-15)/((k^3-3*k^2+5*k-15)*(1+k));
collect((evala@Norm)((lhs-rhs)(A)), Y, proc(E) convert(E, parfrac, k, {I, sqrt(5)}); map(radnormal, %); end);
collect((evala@Norm)((lhs-rhs)(A)), Y, proc(E) convert(E, parfrac, k); map(normal, %); end); 


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Two versions....

Christian Wolinski 1625
October 12 2018
0 2

Edit:

Try these two. If you need the derivation I can post it too.

 

(abs(psi)^2*abs(rho)^2+abs(chi)^2*abs(phi)^2)*abs(lambda1-lambda2)^2+(abs(phi)^2*abs(rho)^2+abs(chi)^2*abs(psi)^2)*abs(-conjugate(lambda1)+lambda2)^2-8*Re(conjugate(phi)*conjugate(rho)*chi*psi)*Im(lambda1)*Im(lambda2);

(abs(chi)^2*abs(phi)^2+abs(psi)^2*abs(rho)^2+2*Re(conjugate(phi)*conjugate(rho)*chi*psi))*abs(lambda1-lambda2)^2+(abs(psi)^2*abs(chi)^2+abs(phi)^2*abs(rho)^2-2*Re(conjugate(phi)*conjugate(rho)*chi*psi))*abs(-conjugate(lambda1)+lambda2)^2; 


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A simplier example....

Christian Wolinski 1625
October 04 2018
0 4


How long does this example take on your computer?

 

T := w^3 + w*z + x^2 + 1, w*z + x*y + x*z + 1, w*x + w*z + y*z + z;
P := Expand(`*`(T)) mod 2;
print(degree(P));
Factor(P) mod 2;

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Simplify....

Christian Wolinski 1625
August 25 2018
2 1


This code will suffice:

 

map(factor @ simplify, evecA1[2], [rho*c^2/(gamma-1)*(1/rho)+(1/2)*u^2 = H], [c, u, H]);


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Much simplier....

Christian Wolinski 1625
August 19 2018
1 4

Assuming your expression is contained in f, use the following code:

 

T[0]  := f:
T[10] := sqrt(omega) * 12^(1/4);
T[20] := evalindets(T[0], specfunc(anything, exp), exp @ proc(P) global T; radnormal(op(1, P) / T[10]) * T[10] end):
T[30] := [sqrt(omega) = Omega / (12^(1/4)), (omega) = (Omega / (12^(1/4)))^2];
T[40] := factor(expand(subs(T[30], T[20])));
T[50] := [exp(Omega) = beta[1], exp(I * Omega) = beta[2]];
T[60] := factor(radnormal(subs(T[50], T[40]))):
op(map(rhs = lhs, T[50])), Omega = solve(T[30][1], Omega), T[60];
subs(%);

 

omega = RootOf(cos(2*12^(1/4)*sqrt(_Z))*(exp(2*12^(1/4)*sqrt(_Z)))^2+cos(2*12^(1/4)*sqrt(_Z))-2*exp(2*12^(1/4)*sqrt(_Z)), 4.450852611);
or
omega = (1/24)*RootOf(cos(_Z)*exp(2*_Z)+cos(_Z)-2*exp(_Z),7.853204624)^2*sqrt(3);

Not a problem....

Christian Wolinski 1625
March 28 2018
1 0

Try this instead:

 

_interface(showassumed = 0):
assume(x > 0, t > 0, k > 0):
pde := diff(u(x, t), t) = k * diff(u(x, t), x$2):
ic := u(x, 0) = 0:
bc := u(0, t) = t:
sol:= pdsolve({pde, ic, bc}, u(x, t)):


Your problem arises from assume/additionally as it generates a chain of assignments every time you make an assumption on a variable. The is/assume facility responds to every variable in the chain the same way, but we can expect pdsolve does not, hence your error. Simply put the assumption (assignment) at the beginning of everything. Alleviating this difficulty was the one of the reasons why "assuming" was created.

Use map(Testzero, A-~B);...

Christian Wolinski 1625
February 11 2018
0 0

Evalb is too literal and not intended for the test case you included. For floats you'd always use fnormal.

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