## 535 Reputation

11 years, 201 days

## Social Networks and Content at Maplesoft.com

Seldom to ask question after retired math hobby Just waiting for beauty who born in 1994 And waited for her email to mavio@protonmail.com What is the difference in ownership among different universe?

## @acer  how to colour these lines w...

how to colour these lines with specified colour?

## @Carl Love  how to colour these li...

how to colour these lines with specified colour?

## @nm  is there division ring that h...

is there division ring that has differential groebner based on division ring can solve this?

## @Kitonum  this not correct n = 1,...

this not correct

n = 1, result should be 01 , number of ways Catalan number 1

n = 2, result should be 0011, 0101, number of ways Catalan number 2

n = 3, result should be 000111, 001011, 001101, 010011, 010101, number of ways Catalan number 5

n = 4, result.... , number of ways 14

n = 5, result .... , number of ways 42

n = 6, result ...., number of ways  132

n = 7, number of ways 429

how to generate these binary sequence?

## @nm  i notice that the 2x2 in 3x3 ...

i notice that the 2x2 in 3x3 change position every time

sometimes 2x2 at top left Corner , sometimes 2x2 at top right corner

sometimes at bottom left , sometimes at bottom right ,

sometimes four number at four corner separately

but sorting will make the 2x2 matrix changed

is there any better method ?

## @tomleslie actually i would like to...

actually i would like to apply in opencv to use the matrix is numpy

i use hash(str(frame))

but i expect the hash reversible back to 2d array frame

i am writing an application to predict the hash or frame, that the hash after predicted can be reversed to a correct 2d array format just elements in matrix are different.

## @Carl Love  but delete “for ...

but delete “for n from 1 “ before do

it is wrong when there is “od”

how to edit this function to make work in maple 12?

and why not know the terminating value but it know this dynamic value in maple 2015

does it mean n had value ? Which variable of this value refer to?

i still do not understand this new feature in maple language.

## @Kitonum  i don't know your mi...

can you post the procdeure P for maple 12?

i use print count of for loop in maple 2015, but can not print to see this clues.

any maple help file explain when to use this for loop without terminating value and how it work?

i tested with code below

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:

sourcesamples := [evalf(-1-sqrt(7)), -2, 1, evalf(-1 + sqrt(7)), 2];
templatesamples := [A, evalf(-1-sqrt(7)), A, -2, A, 1, A, evalf(-1 + sqrt(7)), A, 2, A];
samples := [-4, evalf(-1-sqrt(7)), -3, -2, 0, 1, evalf(3/2), evalf(-1 + sqrt(7)), evalf(9/5), 2, 3]
FindSamples(sourcesamples);

sourcesamples :=[2,4,6,8,10];
n:=nops(sourcesamples);
samples:=sort(convert({ceil(sourcesamples[1])-1, seq(op([sourcesamples[i],(sourcesamples[i]+sourcesamples[i+1])/2,sourcesamples[i+1]]), i=1..n-1),floor(sourcesamples[n])+1},list),(x,y)->evalf(x)<evalf(y));

sourcesamples :=[-1,1,3,5,7,9];
n:=nops(sourcesamples);
samples:=sort(convert({ceil(sourcesamples[1])-1, seq(op([sourcesamples[i],(sourcesamples[i]+sourcesamples[i+1])/2,sourcesamples[i+1]]), i=1..n-1),floor(sourcesamples[n])+1},list),(x,y)->evalf(x)<evalf(y));

sourcesamples :=[-1,0,3,5,7,9];
n:=nops(sourcesamples);
samples:=sort(convert({ceil(sourcesamples[1])-1, seq(op([sourcesamples[i],(sourcesamples[i]+sourcesamples[i+1])/2,sourcesamples[i+1]]), i=1..n-1),floor(sourcesamples[n])+1},list),(x,y)->evalf(x)<evalf(y));

sourcesamples := [evalf(-1-sqrt(7)), -2, 1, evalf(-1 + sqrt(7)), 2];
n:=nops(sourcesamples);
samples := [-4, evalf(-1-sqrt(7)), -3, -2, 0, 1, evalf(3/2), evalf(-1 + sqrt(7)), evalf(9/5), 2, 3]
FindSamples(sourcesamples);
samples:=sort(convert({ceil(sourcesamples[1])-1, seq(op([sourcesamples[i],(sourcesamples[i]+sourcesamples[i+1])/2,sourcesamples[i+1]]), i=1..n-1),floor(sourcesamples[n])+1},list),(x,y)->evalf(x)<evalf(y));

## @Kitonum  can not run in maple 12 ...

can not run in maple 12

there is no ending value of n for loop

for n from 1 to  where ?

## @Kitonum  I just find example from...

I just find example from book

the example show neighbor values are beautiful integers or round values , not sure which decimal it round

this question is part of random values samples for cylindrical decompose algorithm use.

## @Kitonum  your code is hard coded ...

your code is hard coded position 1 and -1

I mean input list such as sourcesample

[evalf(-1-sqrt(7)), -2, 1, evalf(-1 + sqrt(7)), 2];

any number can be float or integer

then insert position follow the template

how to write this in general function ?

## @tomleslie  yes correct, then I u...

yes correct,

then I use projection to calculate , it return [c,0] which display c <> 0 and 0

is this projection correct?

i do not understand how one sample point from it that can go to b^2 -4*a*c using CAD

## @Kitonum  is there any projection ...

is there any projection function for algebra and differential case which is Collins’s projection function or improved or final version of projection function?

## @Kitonum  how to extract the right...

how to extract the right hand side solution?

does it mean that regular chain library is wrong and only solve function can do this CAD method?

any starting point method from quantifier expression?

## @vv  i follow help file to fill in...

i follow help file to fill in N,P,H,R, but i am not sure whether H is correct.

so far it is slow and no result due to running long time. i find a book in the book photo i posted it use a number of seconds then calculated result. Aurthor are different from the author stated in help file. it seems different algorithms.

the algorithm is not easy. is it myparameters wrong , so that it is slow?

with(RegularChains):
with(ChainTools):
with(MatrixTools):
with(ConstructibleSetTools):
with(ParametricSystemTools):
with(SemiAlgebraicSetTools):
with(FastArithmeticTools):
R := PolynomialRing([x,y,z,a,b]):
#sys := [x^2 + y^2 - x*y - 1 = 0, y^2 + z^2 - y*z - a^2 = 0, z^2 + x^2 - x*z - b^2 = 0,x > 0, y > 0, z > 0, a - 1 >= 0, b-a >= 0, a+1-b > 0]:

sys := [x^2 + y^2 - x*y - 1 , y^2 + z^2 - y*z - a^2 , z^2 + x^2 - x*z - b^2]:
N := [a-1,b-a]:
P := [x, y, z, a+1-b]:
H := [x,y,z]:
dec := RealTriangularize(sys,N,P,H,R):
Display(dec, R);

dec := LazyRealTriangularize(sys,N,P,H,R):
dec2 := value(dec):
value(dec2);

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