Edit detail for SandBoxMIWHall revision 13 of 14

removed:
-Poirier
-
-  1-D
-\begin{axiom}
-x := operator('x)
-C:List Symbol := [subscript('x,[0])]
-d := #C
-J := matrix [[D(x(C(1),t),C(1))]]
-K := inverse J
-Req18a:=[reduce(+,[reduce(+,[reduce(+,[reduce(+,[ (1/4)*D( K(k,i)*K(m,j)*D( D( K(l,j),C(k) ),C(l) ),C(m) ) for m in 1..d]) for k in 1..d]) for j in 1..d]) for l in 1..d]) for i in 1..d]
-diff1(n)==subscript('x,[n])-subscript('x,[n-1])
-Req18b:=eval(Req18a,D(x(C(1),t),C(1))=diff1(n))
-diff2(n)==diff1(n+1)-diff1(n)
-diff2(n)
-Req18c:=eval(Req18b,D(x(C(1),t),[C(1),C(1)])=diff2(n));
-numer Req18c.1
-diff3(n)==diff2(n)-diff2(n-1)
-diff3(n)
-Req18d:=eval(Req18c,D(x(C(1),t),[C(1),C(1),C(1)])=diff3(n));
-numer Req18d.1
-diff4(n)==diff3(n+1)-diff3(n)
-diff4(n)
-Req18e:=eval(Req18d,D(x(C(1),t),[C(1),C(1),C(1),C(1)])=diff4(n));
-numer Req18e.1
-\end{axiom}
-2-D
-\begin{axiom}
-x := operator('x)
-y := operator('y)
-C:List Symbol := [subscript('x,[0]),subscript('y,[0])]
-d := #C
-J := matrix [[D(x(C(1),C(2),t),C(1)), D(x(C(1),C(2),t),C(2))], 
-             [D(y(C(1),C(2),t),C(1)), D(y(C(1),C(2),t),C(2))]]
-K := inverse J
-Req18:=[reduce(+,[reduce(+,[reduce(+,[reduce(+,[
- (1/4)*D( K(k,i)*K(m,j)*D( D( K(l,j),C(k) ),C(l) ),C(m) )
-   for m in 1..d]) for k in 1..d]) for j in 1..d]) for l in 1..d]) for i in 1..d];
-#Req18
-kernels Req18.1
-\end{axiom}

Many Interacting Worlds - Hall, et al.

fricas

P:=operator('P);

Type: BasicOperator?

fricas

Q:=operator('Q);

Type: BasicOperator?

fricas

g:=operator('g);

Type: BasicOperator?

fricas

U:=operator('U);

Type: BasicOperator?

fricas

r:=operator('r);

Type: BasicOperator?

fricas

ℏ:=h;

Type: Variable(h)

Hall equations 15,19,20

fricas

eq15:= r(q) = -D(U(q),q)

(1)

Type: Equation(Expression(Integer))

fricas

eq19:= U(q) = 1/(2*m)*g(q)^2

(2)

Type: Equation(Expression(Integer))

fricas

eq20:= g(q) = ℏ/2 * 1/P(q)*D(P(q),q)

(3)

Type: Equation(Expression(Integer))

fricas

eval(eq19,eq20)

(4)

Type: Equation(Expression(Integer))

fricas

RHall:=eval(eq15,D(lhs %,q)=D(rhs %,q))

(5)

Type: Equation(Expression(Integer))

Hall equations 6, 7, A3

fricas

eq6:= r(q) = -D(Q(q),q)

(6)

Type: Equation(Expression(Integer))

fricas

eq7:= Q(q) = 1/sqrt(P(q))*-ℏ^2/2/m*D(sqrt(P(q)),[q,q])

(7)

Type: Equation(Expression(Integer))

fricas

Rforce:=eval(eq6,D(lhs eq7,q)=D(rhs eq7,q))

(8)

Type: Equation(Expression(Integer))

Gaussian

fricas

PdfNorm(x)==1/2*sqrt(2)*exp(-1/2*x^2)/sqrt(%pi)

Type: Void

fricas

eval(RHall,[P(q)=PdfNorm(q), _
            D(P(q),q)=D(PdfNorm(q),q), _
            D(P(q),[q,q])=D(PdfNorm(q),[q,q])])

fricas

Compiling function PdfNorm with type Variable(q) -> Expression(
      Integer)

(9)

Type: Equation(Expression(Integer))

fricas

eval(Rforce, [P(q)=PdfNorm(q), _
              D(P(q),q)=D(PdfNorm(q),q), _
              D(P(q),[q,q])=D(PdfNorm(q),[q,q]), _
              D(P(q),[q,q,q])=D(PdfNorm(q),[q,q,q])])

(10)

Type: Equation(Expression(Integer))

Cauchy

fricas

PdfCauchy(x)==1/%pi/(1+x^2)

Type: Void

fricas

eval(RHall,[P(q)=PdfCauchy(q), _
            D(P(q),q)=D(PdfCauchy(q),q), _
            D(P(q),[q,q])=D(PdfCauchy(q),[q,q])])

fricas

Compiling function PdfCauchy with type Variable(q) -> Expression(
      Integer)

(11)

Type: Equation(Expression(Integer))

fricas

eval(Rforce,[P(q)=PdfCauchy(q), _
             D(P(q),q)=D(PdfCauchy(q),q), _
             D(P(q),[q,q])=D(PdfCauchy(q),[q,q]), _
             D(P(q),[q,q,q])=D(PdfCauchy(q),[q,q,q])])

(12)

Type: Equation(Expression(Integer))

... --Bill Page, Tue, 21 Jul 2015 20:17:15 +0000 reply

fricas

J(i,j)==matrix([[x[i,j]-x[i-1,j],y[i,j]-y[i-1,j]],[x[i,j]-x[j,j-1],y[i,j]-y[j,j-1]]])

Type: Void

fricas

J(i,j)

fricas

Compiling function J with type (Variable(i),Variable(j)) -> Matrix(
      Polynomial(Integer))

(13)

Type: Matrix(Polynomial(Integer))

fricas

determinant(J(i,j))

(14)

Type: Polynomial(Integer)

fricas

K(i,j)==inverse(J(i,j))

Type: Void

fricas

K(i,j)

fricas

Compiling function K with type (Variable(i),Variable(j)) -> Union(
      Matrix(Fraction(Polynomial(Integer))),"failed")

(15)

Type: Union(Matrix(Fraction(Polynomial(Integer))),...)