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Christian Wolinski

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20 years, 214 days
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These are answers submitted by Christian Wolinski

Radnormal....

Christian Wolinski 1650
January 06 2019
2 1


Simply:

 

expand(applyop(radnormal, 1, f));
evalc(applyop(radnormal, 1, f));

#for the larger samples:
F := f -> evalc(applyop(radnormal, 1, f));
G := ((x, s) -> map(collect, x, s, distributed)), (x, s) -> collect(x, s, distributed);
t := ln(anything);

factor(evalindets(f, t, F));
G[1]('%', indets('%', t));


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Delete....

Christian Wolinski 1650
January 03 2019
3 0


Before "GCD3:=" you have the "proc". Delete it.

Tests....

Christian Wolinski 1650
December 26 2018
0 1

A very low order test is implemented in `combine/polylog`.

You can see it with:
stopat(`combine/polylog`, 17);
showstat(`combine/polylog`);

Line 17 in "type(x,'complex(numeric)') and 1 <= abs(x) or is(1 <= x) or is(x <= -1)" replace with
with say "1<=abs(x)^2" or "signum(1-abs(x))=-1" or "is(1<=abs(x))", whichever is preferred.

You missed it....

Christian Wolinski 1650
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 1650
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 1650
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 1650
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 1650
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 1650
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 1650
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 1650
October 26 2018
1 4

This is a basic rule of valuations:

'log[2]'(3);

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Simply:...

Christian Wolinski 1650
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 1650
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 1650
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 1650
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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