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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?

## how to do reversible hash on 2d array ?...

Maple 12

i would like to to test and do hash on a 2d array and then predict this hash and then reverse back to another hash which can convert back to 2d array , how to do?

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

Maple 12

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 generalize this inserting values ...

Maple 12

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]

want to insert value alternatively according to the template and neighbor values

Some inserted values come from

floor(evalf(-1-sqrt(7)))
ceil(evalf(-1-sqrt(7)))

(round(evalf(-1+sqrt(7)),0) + 1)/2;
(2 + 1)/2
=evalf(3/2)

(round(evalf(-1+sqrt(7)),1) + 2)/2;
(1.6 + 2)/2
=evalf(9/5);

how to generalize this method into general case function instead of manual inesrt?

## how to write : a <> 0 and (some x)(a*x^2...

Maple

with(RegularChains):
with(ChainTools):
with(MatrixTools):
with(ConstructibleSetTools):
with(ParametricSystemTools):
with(SemiAlgebraicSetTools):
with(FastArithmeticTools):
R := PolynomialRing([x,y,z,a,b]):
sys := [a*x^2+b*x+c]:
N := []:
P := [a]:
H := [x,y,z]:
dec := RealTriangularize(sys,N,P,H,R):
Display(dec, R);

how to write : a <> 0 and (some x)(a*x^2+b*x+c) for quantifier elimination in maple?

is RealTriangularize parameters are after quantifier elimination or it accept quantifer expression?

if not, how to input above statement into real or lazy triangularize and expect return b^2 + 4*a*c;

## how to find necessary condition for real...

Maple 2015

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]:

dec := RealTriangularize(sys,R): # very slow
Display(dec, R);

dec := LazyRealTriangularize(sys,R): # it is faster
dec2 := value(dec): # very slow
value(dec2);

find a , b to satisfy sys have real solution

expect  one of solution is below, but above function are very slow, load a very time still no result, where is wrong?

R1 = a^2+a+1-b^2;
R1 = a^2-1+b-b^2;

[R1 > 0, R2 > 0]

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