@Kitonum 

thank you

da := [[1,m],[2,m2],[3,1],[4,2]]

i replace it with less number of points

by the way, is random number such as decimal number that can not roots ?

if not, what conditions are needed to be roots?

@tomleslie 

i had tried to search in manual, nothing is found.

sys := DiffEquation([g[1]=1, g[2]=1, D(a)(-1)=0, D(b)(-1)=0], inputvariable = [b(t)], outputvariable = [a(t)]):
ts := 0.1:
t_sim := 10.0:
in_t := Sine(1, 1, 0, 0);
in_z := Sine(1, 1, 0, 0, samplecount = round(t_sim/ts), sampletime = ts, discrete);
#in_z := t;
sysz := ToDiscrete(sys, ts):
ret := Simulate(sysz, [in_z]):
in_t := t:
sol := Simulate(sys, [in_t]);

Error, (in ToDiscrete:-ToDiscrete) improper independent variable of diff(b(t1), t1)
Error, (in DynamicSystems:-Simulate) equations must be linear with time-independent coefficients
Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, t1}

i got above error , 

there is no t1 variable, i do not know where it coming from

and 

searched can not convert to explicit system error due to no initial condition, then i added initial condition

and use coordinate (0, -1) this point's gradient is 0 as initial condition

however still have error

still hope to draw a x^2-1 this graph, how to draw?

this post is moving back in the list of active conversation

@acer 

this method succeed, however, if number of dependent variables increase

such as diff(y(a,b,c),a)*diff(y(a,b,c),b)*diff(y(a,b,c),c)

diff(y(a,b,c),a)*diff(y(a,b,c),b), diff(y(a,b,c),a)*diff(y(a,b,c),c)

it will be a very long command and need large manual typing

@tomleslie 

could you tell me in the final command in the your maple file

which row is correspond to which variable x, x^2 , x^3 etc?

there are two column, 

does it mean that it has two polynomials in result?

@vv 

composition of two ideals result in one ideal , not only one equation

isomorphoric ideal is for inverse of ideal

goal is to find kernel of ideal  = ideal o ideal ^(-1) = ideal o Syz(ideal) 

what are the goals of SGA mentioning about ideals?

actually i just do some experiment with this defintion, 

i do not know the goal of SGA.

out of topic is that i would like to know what SGA would like to find.

@tomleslie 

beside previous question, 

if not for a o b = identity

just simply a o b , not require to be identity

how do they composite?

@tomleslie 

how to convert this final command into a polynomial?

if doing for system of polynomials, does it mean to zip with your command 

for ideal [poly1a, poly2a, poly3a] and ideal [poly1b, poly2b, poly3b]

[poly1a o poly1b, poly2a o poly2b, poly3a o poly3b] ?

@vv 

i discover your method's result implied that no matter how we rotate permutation group, it is also comnig from the same polynomial !!!!!!!

@vv 

i use your method to calculate and factor, it is so beautiful,

your method's result is equal to that elements of group are the root of system!!!!

but my method's result can not be factorized, it seems my method is wrong.

f2 := x^4-c1sol2*x^3+c2sol2*x^2-c3sol2*x+c4sol2;
f2 := -(x1+x2+x3+x4)*x^3+x^4+(x1*x2+x1*x3+x1*x4+x2*x3+x2*x4+x3*x4)*x^2-(x1*x2*x3+x1*x2*x4+x1*x3*x4+x2*x3*x4)*x+x1*x2*x3*x4
factor(f2);
(x-x4)*(x-x3)*(x-x2)*(x-x1);

After tried your method, it seems that the group should be unchanged.

have ever someone found some other group that can be reverse calculated and can be factorized into separable form?

@vv 

this is the only way i think that can do.

can you tell me a reason to falsify this method?

@vv 

my intention is simple that is to find c1,c2,c3,c4 in terms of x1,x2,x3,x4

what is _Z ?

how to solve without these _Z ?

@vv 

my idea is to the differentiate them and find

any two of c1,c3,c4 relations and then subs into them and make

it become 2 equations for 2 variables

but after i choose 

diff(lhs(sys2),c4) = diff(rhs(sys2),c4);

 the final result has _Z this unknown term, is my method correct?

how to solve this?

ferrai := -x1^3*x2*x3*x4-x1^2*x2^2*x3^2-x1^2*x2^2*x4^2-x1^2*x3^2*x4^2-x1*x2^3*x3*x4-x1*x2*x3^3*x4-x1*x2*x3*x4^3-x2^2*x3^2*x4^2+x1^2*x2*x3*y+x1^2*x2*x4*y+x1^2*x3*x4*y+x1*x2^2*x3*y+x1*x2^2*x4*y+x1*x2*x3^2*y+x1*x2*x4^2*y+x1*x3^2*x4*y+x1*x3*x4^2*y+x2^2*x3*x4*y+x2*x3^2*x4*y+x2*x3*x4^2*y-x1*x2*y^2-x1*x3*y^2-x1*x4*y^2-x2*x3*y^2-x2*x4*y^2-x3*x4*y^2+y^3;
coeff(ferrai, y^3);
coeff(ferrai, y^2);
coeff(ferrai, y);
res := simplify(ferrai - coeff(ferrai, y^3)*y^3 - coeff(ferrai, y^2)*y^2 - coeff(ferrai, y)*y);

c2 := -coeff(ferrai, y^2)/coeff(ferrai, y^3);
sys1 := c1*c3 - 4*c4 = coeff(ferrai, y)/coeff(ferrai, y^3);
sys2 := -c3^2-(c1^2)*c4+4*c2*c4 = res/coeff(ferrai, y^3);

diff(lhs(sys1),c1) = diff(rhs(sys1),c1);
diff(lhs(sys1),c3) = diff(rhs(sys1),c3);
diff(lhs(sys1),c4) = diff(rhs(sys1),c4);

diff(lhs(sys2),c1) = diff(rhs(sys2),c1);
diff(lhs(sys2),c3) = diff(rhs(sys2),c3);
diff(lhs(sys2),c4) = diff(rhs(sys2),c4);

c1sol := solve(diff(lhs(sys2),c4) = diff(rhs(sys2),c4), c1)[1];
indets(subs(c1=c1sol,sys1));
indets(subs(c1=c1sol,sys2));
indets([subs(c1 = c1sol, sys1), subs(c1 = c1sol, sys2)]);
result := solve({subs(c1 = c1sol, sys1), subs(c1 = c1sol, sys2)},{c3,c4});

@Markiyan Hirnyk 

why 1^n can not be a power of prime?

should i use 2^n , such 2,4,6,8?

2^n, 3^n, 5^n

or

you mean n^2, n^3, n^5, n^7, n^11 etc?

i follow help file, n = 3, q <= 10.

and i use 

G := SpecialUnitaryGroup(3, 2);

the results are not permutation group