ComputerUser

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@vv 

can these triangularize function that can be used to find the condition when anomalies happen ? And act as performance metric in optimisation function?

how the anomalies can be described into a equation  for this to use? Any example?

 

@Kitonum 

answer should be like this 

I follow N, P, H, R in example to fill in the equation like help file, still very slow

premcustom := proc(Fparam,Gparam, MainVar)
local R, G, F, lcg, lcr, dr, dg:
R := Fparam:
G := Gparam:
F := Fparam:
#p1 := x^2+5-2*x*z;
#p2 := z^3*y+x*y^2;
#p3 := -8*z^3+3*y^2;
#R := p2:
#G := p1:
#F := p2:
#MainVar := z:
if degree(G,MainVar) = 0 then
 print("return 0"):
 return 0:
elif degree(F, MainVar) < degree(G, MainVar) then 
 print("return R"):
 return R:
end if:
lcg := coeff(G, MainVar, degree(G, MainVar)):
print("lcg",lcg):
dg := degree(G, MainVar):
print("dg",dg):
while degree(R, MainVar) >= degree(G, MainVar) do
  lcr := coeff(R, MainVar, degree(R, MainVar)):
  print("lcr",lcr):
  dr := degree(R, MainVar):
  print("dr",dr):
  R := simplify(lcg * R - lcr * G * (x^(dr - dg))):
  print("R",R):
od:
return R:
end proc:
p1 := x^2+5-2*x*z;
p2 := z^3*y+x*y^2;
p3 := -8*z^3+3*y^2;
prem(p1,p2,x);
prem(p2,p1,z);
prem(p3, p2, y);

premcustom(p1,p2,x);
premcustom(p2,p1,z); #why this looping
premcustom(p3,p2,y);
 

i use expand or simplify to solve looping but case 2 , premcustom(p2,p1, z) still looping

@Kitonum 

I still have not define m(x) and s(x)

but it had already made it 0

why maple think it is 0?

is maple 's lambda calculus can predict it is 0?

 

 

@Kitonum 

g := x;
r1 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));
g := x^2;
r2 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));
g := x^n;
rn := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));

g := exp(x);
r1 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));
g := cos(x);
r2 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));
g := sin(x);
rn := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));

g := diff(m(x), x);
r1 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));
g := diff(m(x), x$2);
r2 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));
g := diff(m(x), x$k);
rn := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-x)*(-x+diff(s(x), x)), x))*exp(x)),h(x) =-(1/2)*x^2+s(x));

same 0

g := x;
r1 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
g := x^2;
r2 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
g := x^3;
r3 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
g := x^4;
r4 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
g := x^5;
r5 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));

r1 + r2 + r3 + r4 + r5;

g := diff(m(x),x);
r1 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
g := diff(m(x),x$2);
r2 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
g := diff(m(x),x$3);
r3 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
g := diff(m(x),x$4);
r4 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
g := diff(m(x),x$5);
r5 := eval((eval(g,x=x + diff(h(x),x)) - eval(g,x=diff(s(x),x)))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)),h(x) = -(1/2)*x^2+s(x));
guess := sum(subs(g=x^k, rk), k=1..infinity);

@Kitonum 

this is my work, but return 0

 

g := x^n;
r1 := subs(h(x) = -(1/2)*x^2+s(x), (subs(x=x + diff(h(x),x), g) - subs(x=diff(s(x),x), g))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)));
 

g := diff(m(x),x);
r1 := subs(h(x) = -(1/2)*x^2+s(x), (subs(x=x + diff(h(x),x), g) - subs(x=diff(s(x),x), g))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)));
g := diff(m(x),x$2);
r2 := subs(h(x) = -(1/2)*x^2+s(x), (subs(x=x + diff(h(x),x), g) - subs(x=diff(s(x),x), g))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)));
g := diff(m(x),x$3);
r3 := subs(h(x) = -(1/2)*x^2+s(x), (subs(x=x + diff(h(x),x), g) - subs(x=diff(s(x),x), g))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)));
g := diff(m(x),x$4);
r4 := subs(h(x) = -(1/2)*x^2+s(x), (subs(x=x + diff(h(x),x), g) - subs(x=diff(s(x),x), g))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)));
g := diff(m(x),x$5);
r5 := subs(h(x) = -(1/2)*x^2+s(x), (subs(x=x + diff(h(x),x), g) - subs(x=diff(s(x),x), g))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)));
guess := sum(subs(g=x^k, rk), k=1..infinity);

restart:
g := diff(m(x),x$k);
rk := subs(h(x) = -(1/2)*x^2+s(x), (subs(x=x + diff(h(x),x), g) - subs(x=diff(s(x),x), g))/((Int(exp(-(1/2)*x^2)*(-x+diff(s(x), x)), x))*exp((1/2)*x^2)));
guess := sum(rk, k=1..n);


g := Diff(m(x),x$k);
rk := subs(h(x) = -(1/2)*x^2+s(x), (subs(x=x + Diff(h(x),x), g) - subs(x=Diff(s(x),x), g))/((Int(exp(-(1/2)*x^2)*(-x+Diff(s(x), x)), x))*exp((1/2)*x^2)));
guess := sum(value(rk), k=1..n);
 

@Kitonum 

before I reply the full code

i would like to know

if custom function on X^n = 0

does it mean custom function on m(x) = 0

then does it mean that diff(m(x), x) = 0 too?

@Carl Love 

I have invented a new calculus above existing calculus

would like to implement a new solver

so I need Diff and diff kind of symbol and have function

how to make this symbol to have function to run?

for example diff is doing limit

Diff is doing two part of things accept a function f(t) and  variable t. And when eval , can really act as function

@Carl Love 

if not using this example,

when 2 valued logic had 16 logic, 

if i got a list of permutation, how to find something equivalent to implication logic this kind of important logic after extension to 3 valued logic which a logic of 0,1,2 ?

and i imagined to use common subset to search assumed that new unknown logic can be expressed in terms of 2 valued logic, but seems not success

 

@Carl Love 

i had a permutation

but input to table[1] = 1

table [2] = 1

table [3] = 3

there is missing 2 -> 3

how to express into disjoint cycle ?

[[1] [2 1] [3]] it seems wrong, because 1 will not return 2, meaning no 1--> 2

and this result can not recover to my above permutation example because 2 -> 3 missing

 

@mmcdara 

i just hide my function

important point i want to show is that i had used Complex(a,b) and input to Vector

but FourierTransform return error and assign to Vector had error too

how to do when decimal number is very small?

@Carl Love 

I know this

but permgroup input a list and b list in example in help of maple

I convert to permutation but only one list

what are a and b list ?

sometimes permutation

[[1,2],[3]]
 How to input to permgroup function?

what is degree ? is there any degree function?

and how to do multiple two permgroup?

 

 

@mmcdara 

I had time series data and want get the signal such as increasing spike or starting have noise 

but data are 10^(-89)

in dual graph it show correctly have signal 

but how to programmatically to get this signal for automation?

I remember that my university course teach Fourier transform is to extract wireless signal communication

and want to apply in data. But I remember that is accumulated to sum up things by passing a window through the data. Can not remember or imagine how to extract.

 

@Carl Love 

i discover

New state = state * state

after adding a new key note of piano

and then generate frequency matrix

and then convert to transition matrix again 

The new state and steady state are different from the state if count frequency again

if count frequency again each time, there seems not convergent

Though it is suitable to generate music

, new music is not expected as the original song.

where is wrong?

if I use the new state by multiply state with state 

how to increase or decrease the steady rate ? If it can be done, will the new generated music different again?

@acer 

how to control the time it play the note like piano player do?

 

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