## randpoly problem...

Asked by:

Hi all I am attempting to use the randpoly feature to generate a random polynomial of 1st degree with non-zero coeffs between -2 and 2.

I have tried the following:

factor1 := randpoly(x, dense, degree = 1, coeffs = rand(-2 .. 2))

unfortunately as you will find quite often this produces the polynomial "0".  Which it is very clear this is not wanted.

Any ideas would be appreciated.

Thanks,

Mark

## Arithmetic operations on finite field...

Asked by:

Hello!, Is there any package to do arithmetic operations on finite field?

Example: Z(5) - over field 5: calculate with remainders:

(x^8 + 2x^4 + 1) / (x^5 + 4x^3 + x^2 + 3x +3).

thanks.

## AFactor doesn't factor a (supposedly) reducible po...

Asked by:

I have the following Polynomial F. Computing the genus shows that this curve has negative genus and thus is reducible. But using AFactor doesn't produce a factorization. Any ideas?

```with(algcurves):
F := z^9+(-3/2+(3/2*I)*sqrt(3))*y^3*z^6+(-3/2-(3/2*I)*sqrt(3))*x^3*z^6+(-3/2-(3/2*I)*sqrt(3))*y^6*z^3+(-3/2+(3/2*I)*sqrt(3))*x^6*z^3+y^9+(-3/2-(3/2*I)*sqrt(3))*x^3*y^6+(-3/2+(3/2*I)*sqrt(3))*x^6*y^3+x^9-3*(x*y*z)^3:
z:=1:
genus(F, x, y);
evala(AFactors(F));
```

## "expand" command does not act as it should...

Asked by:

Hello!

I am working with the Maple 18.02 version. I just want want to perform a basic polynomial expansion using the command "expand" and it does not respond as it should according to what Maple Programming Help says it would. For example:

Maple Programming Help says:

I get:

.

Also, one sees that this isn't even true, as x(x+2) + 1 = x^2 +2x +1, which is not equal to x^2 + 3x +2.

Moreover, maple tells me it is equal..:

What is going on here? I woul like to get the full expanded form (without factors). Also, this is obviously not true, or maybe Maple means something else by x(x+2) +1...

Thank you!

## Apply igcd to a list...

Asked by:

I have a list of univariate polynomials

P:=[x^2-7*x+10, x^2, x^2+2*x+1]

How do I get the gcd of all of these?

It doesn't like it when I do the following:

igcd(P)

Thanks

## Question: How to i convert a complicated equations...

Asked by:

Hi everyone, i am using Maple 18 and i have a problem in converting a equation to a nice polynomial form (a cubic equation with a form of A*x^3+B*x^2+C*x+D), can anyone please help me on the command? Thanks in advance.

My equation is "  d := s*x*(E*K*q-K*r+K*sigma[1]+r*x)*(1-x*(E*K*q-K*r+K*sigma[1]+r*x)/(K*sigma[2]*L))/(K*sigma[2])+sigma[1]*x-x*(E*K*q-K*r+K*sigma[1]+r*x)/K  " or for simplicity is

Can someone please teach me on the command? Really appreciate the help!

## Get homogenous expressions from symmetric polynomi...

Asked by:

How to get homogenous expressions from symmetric polynomial.

Example. Let P = (a^2 + 2)(b^2 + 2)(c^2 + 2), we have deg(P) = 6. I want to get polynomials of degree n on A[n] with n = 0, 1, ..., 6. Specific

P = a^2b^2c^2 + 2(a^2b^2 + b^2c^2 + c^2a^2) + 4(a^2 + b^2 + c^2) + 8.

And

A[0] = 8

A[1] = 0

A[2] = 4(a^2 + b^2 + c^2)

A[3] = 0

A[4] = 2(a^2b^2 + b^2c^2 + c^2a^2)

A[5] = 0

A[6] = a^2b^2c^2

Thank you very much.

## What procedure parameter coding will accept any po...

Asked by:

Dragilev:=proc(Polynomials::depends(list(ratpoly(integer,Variables))),Variables::list(symbol),DEvar::symbol,DEsuffix::string)

The above procedure parameter Polynomials accepts a list of polynomials containing indeterminates contained in parameter Variables, but also accepts simple arithmetic expressions such as 34.

Is there any parameter qualifying coding which will only accept polynomials containing one or more of the indeterminates passed in parameter Variables?

## Factoring polynomials in real radicals...

Asked by:

Hi!

I a have a question about factorizing real polynomials.

Suppose I have a real polynomial p(x) with integer coefficients. If the degree of p(x) is less than or equal to 4, we can factorize it into linear radical factors. On the other hand, if we require the factorization to be real, theoretically we can factorize it into linear and irreducible quadratic factors.

My question is, if the input p(x) is real polynomial with integer coefficients, is there any Maple function that can give me factorization output with real linear and irreducible quadratic factors, with radical coeffs?

For example, I tried q := 20*x^3+10*x^2+4*x+1, it has one real root and 2 complex roots. I want a factorization like q(x) = 20*(x-r1)*(a*x^2 + b*x + c), with r1, a, b, c, all real radicals.

I compared functions: factors(), solve(), sqrfree(), Splits(), and none of them give what I want.

factors(q) gives:
[20, [[x^3+(1/2)*x^2+(1/5)*x+1/20, 1]]]

factors(q, real)  gives:
[20., [[x+.3423840948583691316993036540027816871936619136844427977504078911, 1], [x^2+.1576159051416308683006963459972183128063380863155572022495921089*x+.1460348209828001458360112632660894203743660942160039146818509889, 1]]]

solve(q)   gives:
-(1/30)*(350+105*sqrt(15))^(1/3)+7/(6*(350+105*sqrt(15))^(1/3))-1/6, (1/60)*(350+105*sqrt(15))^(1/3)-7/(12*(350+105*sqrt(15))^(1/3))-1/6+(1/2*I)*sqrt(3)*(-(1/30)*(350+105*sqrt(15))^(1/3)-7/(6*(350+105*sqrt(15))^(1/3))), (1/60)*(350+105*sqrt(15))^(1/3)-7/(12*(350+105*sqrt(15))^(1/3))-1/6-(1/2*I)*sqrt(3)*(-(1/30)*(350+105*sqrt(15))^(1/3)-7/(6*(350+105*sqrt(15))^(1/3)))

simplify(convert(Splits(q,x),radical))    gives:
[20, [[(1/30)*(350+105*sqrt(5)*sqrt(3))^(1/3)+1/6-7/(6*(350+105*sqrt(5)*sqrt(3))^(1/3))+x, 1], [-(1/60)*(I*sqrt(3)*(350+105*sqrt(5)*sqrt(3))^(2/3)+(35*I)*sqrt(3)+(350+105*sqrt(5)*sqrt(3))^(2/3)-60*x*(350+105*sqrt(5)*sqrt(3))^(1/3)-10*(350+105*sqrt(5)*sqrt(3))^(1/3)-35)/(350+105*sqrt(5)*sqrt(3))^(1/3), 1], [(1/60*I)*sqrt(3)*(350+105*sqrt(5)*sqrt(3))^(1/3)+(7/12*I)*sqrt(3)/(350+105*sqrt(5)*sqrt(3))^(1/3)-(1/60)*(350+105*sqrt(5)*sqrt(3))^(1/3)+1/6+7/(12*(350+105*sqrt(5)*sqrt(3))^(1/3))+x, 1]]]

None of them give me what I want. Is there any build-in function that can help me do that?

Thanks!

William

## is it possible to find the missing part?...

Asked by:

after solve a set of equations, i got a set of solutions, [A,B,C], if i remove one of solution [C]

is it possible to find this removed solution from solutions set [A,B]

## how to convert a equation into functions...

Asked by:

how to convert a^2*b+c to func2(func1(func1(abc[1],abc[1]),abc[2]),abc[3])

when i use custom function func2 to represent plus, func1 to represent multiply

input 3 parameters,

one is a^2*b + c one is [func1, func2] and second is [abc[1],abc[2],abc[3]] corresponding to a, b, c
a^2*b + c = func2(func1(func1(abc[1],abc[1]),abc[2]),abc[3]);

## Symbolic cut-off of high-order terms...

Asked by:

Hi! I have a variable polynomial expression and I want to cut off all the terms of order 3 and more, for every product of variables.

For example consider the polynomial `P = x + y + a*x^2 + b*x^3 + c*x*y + d*x^2*y + e*x*y^2 + y^2`, I want an operation who returns me `a*x^2 + c*x*y + y^2`

(terms for which the sum of exponents in `x` and `y` exceeds or less two are being deleted)

Is it possible?

## Slick technique to select positive root of polynom...

Asked by:

I want to solve for the roots of a polynomial, such as a x^2+b x + c = 0, for which the output is only the positive root. All coefficients/variables in the polynomial are positive.

Recently, someone posted an answer to a question where at some point they performed this task and their solution was really slick. But I can't find it. The answer used either solve, or eval or something like that. (Yes, I did perform a search via the MaplePrimes search before asking this question.)

## move 1 under sqrt...

Asked by:

Silly, but what command will move the one first under the sqrt here...

a:=sqrt(1+x^2)  # maple moves the x^2 in front
sqrt(x^2+1)

What maple command will move the 1 in front of the x^2 under the square root?

## Quotient of multi-polynomial division...

Asked by:

For remainder of division of a (multivariable) polynomial to several polynomials at a same time one can use NormalForm in Maple. It is easy to write a procedure to also show the division but I wonder if there is any determined command such as NormalForm for this aim?

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