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# Edit detail for SandBoxMIWHall revision 14 of 14

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Editor: Bill Page Time: 2015/07/31 18:16:42 GMT+0 Note: From Poirier to Hall

added:

From BillPage Fri Jul 31 18:16:42 +0000 2015
From: Bill Page
Date: Fri, 31 Jul 2015 18:16:42 +0000
Subject: From Poirier to Hall
Message-ID: <20150731181642+0000@axiom-wiki.newsynthesis.org>

SandBoxPoirier


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))

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))),...)

From Poirier to Hall --Bill Page, Fri, 31 Jul 2015 18:16:42 +0000 reply
SandBoxPoirier