## Maple 12 Questions and Posts

##### These are Posts and Questions associated with the product, Maple 12

solve((&PartialD;(-    &nabla;(f) ))/(&PartialD; t)+((DotProduct(v[0],&nabla;f))*(1-e(DotProduct(B,Omega)))+(c[s0]^(2)*rho[1])/(rho[0])(1-e(DotProduct(B,Omega)))+e(CrossProduct(&nabla; f,B))*Omega-e((DotProduct(-&nabla;f,Omega))*(DotProduct(B,&nabla;)))*(-&nabla;f)+e(E)*(1-(DotProduct(B,Omega)))+e^(2)(DotProduct(E,B))*Omega-e*((CrossProduct(E,Omega))*(&nabla;(-&nabla;f)),rho[1]);

## How to plot piecewise function?...

eval.mw This is the maple worksheet The regions are u<=-1, -1<=u<=1,u>=1

## how to dsolve to a solution in terms of a number o...

A system of differential equations

But solution I want to express in terms of other specified function

How to dsolve to get a solution that in terms of a list of specified function? For example in terms of sin , cos , Bessel etc ?

Sol := [a(t) = sin(t) + cos(t) , b(t)= sin(t) ....]

## How can maple be trusted app when window 10 device...

How can maple be trusted app when window 10 device guard enabled?

## How to export a list of thousands numbers elements...

Would like to export a list into a text file

when I tried , it show ... 1234 items... , can not export a whole list into text file.

[[[0,0,0,0]], [[0,0,0,0]], .....]
thousands of [[...]] elements

## How to sort and group by list of lists...

[[1,1,["ab","xy"]], [0,1,["xy"]]]

how to sort by first number , second number , and list of string ?

how to count and group by third list of strings having first two number 0,0 or 0,1 or 1,0 or 1,1

for example

["xy"] at most count 4  , at least count 1

would like to find which is [1,1,... ] and only count 1

## how to guess 1 or 2 when rsolve is wrong at some n...

second has rsolve solution

compare original sequence

accsum(ListTools[Reverse]([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])),

with rsolve solution , it start from third number wrong, some number are wrong but correct at next number,

but i just want to guess next number is 1 or 2

[seq(subs(k=kk, sol), kk=0..(lengthofsequence+1))],

with(SumTools):
with(gfun):
accsum := proc(xx)
local result,mm:
result := []:
for mm from 1 to nops(xx) do
temp := Summation(xx[k], k = 1 .. mm):
result := [op(result), temp]:
od:
return result:
end proc:

patterngroup := [2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1]: # left is latest, 2,1,1..
lengthofsequence := 5:
for mm from 1 to 12 do
if guessgf(accsum(Reverse([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])), x) = FAIL then
print(patterngroup[mm]):
else
sol := rsolve(listtorec(accsum(ListTools[Reverse]([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])), u(n))[1], u(k)):
acxxc := accsum(ListTools[Reverse]([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])):
olist := [seq(patterngroup[k], k=(mm)..(mm+5))]:
#start from 0
print(patterngroup[mm], olist, accsum(ListTools[Reverse]([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])), [seq(subs(k=kk, sol), kk=0..(lengthofsequence+1))], sol, subs(k=(lengthofsequence+1), sol), subs(k=(lengthofsequence+1), sol)-acxxc[nops(acxxc)]):
end if:
od:

## how to remove newline for csv format?...

interface(prettyprint=2):
with(ListTools):
with(StringTools):
for xx from 1 to 2 do
xx := 1:
openindex := [SearchAll("[",Source)]:
endindex := [SearchAll("]",Source)]:
beforefiltered := []:
for mm from 1 to nops(openindex) do
if mm > 27 then
beforefiltered := [op(beforefiltered), Chop(substring(Source, openindex[mm]..endindex[mm]))]:
end if:
od:
afterfiltered := []:
for mm in beforefiltered do
if Has(mm,"--") or Has(mm,"|") or Has(mm,"{") or Has(mm,"}") then
dummy := 0:
elif Has(mm,"Root") then
dummy := 0:
else
afterfiltered := [op(afterfiltered),mm]:
end if:
od:
afterfiltered[1];

however after chop still has new line, can not make a beautiful csv format,

"[b(t,k)+ a
(t,k)*
x(t,k)]"

# I try to export to text first and then use Excel to use "|" as delimiter instead comma as delimiter,
#because b(t,k) has comma "," will separate to open a new column

appendto("C:\\Users\\Student\\Documents\\IQ1-200csv.txt"):
for mm in afterfiltered do
AA := parse(mm):
lprint(xx,"|","hello := [","|",AA[1],"|",AA[2],"|","]:");
od:
od:

Expect csv in format
1,b(t,k)+a(t,k)*x(t,k)
2,a(t,k)+s(t,k)*z(t,k)

## which sample points are correct and how to general...

P1 := x^2+y^2-4:
P2 := y^2-2*x+2:

Original question is find CAD of (some y)[P1 <0 and P2 <0]

how to use maple 12 and maple 2015 to find Q1,Q2,Q3 which are projection of P1 and P2

my book show sample points are [-4,-1-sqrt(7),-3,-2,0,1,3/2,-1+sqrt(7),9/5,2,3]
but FindSamples result is not the same with my book, is it my book wrong or FindSamples function wrong?
I find result of my script is the same as book's quantifier position at 7,8,9 though sample points has little different

how to generalize my following script to multiple variables x, y, z, and more ?

and

I compare with maple 2015 result are different from my book solution, is maple 2015 more advanced version CAD?

with(ListTools):

P1 := x^2+y^2-4:
P2 := y^2-2*x+2:

Q1 := x^2 + 2*x - 6;
Q2 := x^2 - 4;
Q3 := x - 1;

sourcesamples := sort(evalf([solve(Q1), solve(Q2), solve(Q3)]),`<`);

FindSamples:=proc(sourcesamples)
local N, P;
N:=nops(sourcesamples);
P:=proc(a,b)
local a1, b1, m1, n, m;
if a=b then error "Should be a<>b" fi;
a1,b1:=op(convert(sort([a,b],(x,y)->evalf(x)<evalf(y)),rational));
count := 0:
for n from 1 do
m1:=a1*n;
m:=`if`(type(m1,integer),m1+1,ceil(m1));
count := count + 1:
if is(m/n>a1) and is(m/n<b1) then return m/n fi;
od;
print("count=",count);
end proc:
[ceil(sourcesamples[1])-1, seq(op([sourcesamples[i],P(sourcesamples[i],sourcesamples[i+1])]), i=1..N-1),sourcesamples[N],floor(sourcesamples[N])+1];
end proc:

RemoveComplex := proc(yy)
local result, k:
result := []:
for k in yy do
if Im(k) = 0 then
result := [op(result), k]:
end if:
od:
if result = [] then
result := []:
end if:
return result:
end proc:

Joinsolution := proc(param1, param2group)
local result, k:
result := []:
for k in param2group do
result := [op(result), [param1, k]]:
od:
return result:
end proc:

#print(mm):
if MakeUnique(RemoveComplex([solve(subs(x=mm, P1)), solve(subs(x=mm, P2))])) = [] then
else
end if:
od:

if subs(x=mm[1],subs(y=mm[2], P1)) < 0 and subs(x=mm[1],subs(y=mm[2], P2)) < 0 then
end if:
od:

Compare with

with(RegularChains):
with(ChainTools):
with(MatrixTools):
with(ConstructibleSetTools):
with(ParametricSystemTools):
with(SemiAlgebraicSetTools):
with(FastArithmeticTools):
R := PolynomialRing([x,y]):
sys := [x^2+y^2-4,y^2-2*x+2]:
N := []:
P := []:
H := [x]:
dec := RealTriangularize(sys,N,P,H,R):
proj := Projection(sys, N, P, H, 1, R);
Display(dec, R);

P := SamplePoints(sys, R);
Display(P, R);

## How to make eigenvectors result the same every tim...

Eigenvector result is changing every time it run.

How to make eigenvectors result the same every time it run?

## How to get rules after doing clustering?...

If A then B After clustering B , how to find a set of A in machine learning topic and fuzzy topic？

## Is there lifting function for a algebra use?...

Is there lifting function for polynomials or algebra use?

expect input a list univariate polynomial , then output a list of polynomials of two variables.

it should be the reverse operation of projection.

Which library has this function in maple 12 or maple 2015?

## how to use permgroup ?...

1 1 1 2 2 3 3

(  1 3 3 2 2 1 2 )

how to input this permutation into permgroup ?

## How to guess which physics data suit to theorem eq...

If maple can auto discover derived equations,

then most variable are unknown name which may or may not be physics variable.

so, how to guess which physics data suitable for these look like meaningless variable?

or these tools only visualize the relationship of existing known equations?