# Tag Info

Accepted

### What is Mathematica's equivalent to Maple's collect with distributed option?

CoefficientRules[eq, {x, y}] /. ({a_, b_} -> c_) :> c x^a y^b // Total Generalize it to a function: ...
• 66.8k

### What is Mathematica's equivalent to Maple's collect with distributed option?

Update 2: An alternative way to define a function that works like Maple's collect using CoefficientRules + FromCoefficientRules: ...
• 396k

Another way: ...
• 236k
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### What is the smallest degree of polynomial so that its graph includes four extreme points

Use the form InterpolatingPolynomial[{{x1,f[x1],f'[x1]},{x2,f[x2],f'[x2]},...}] We use f[x]==y,f'[x]==0,f''[x]!=0 to verify the ...
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### What is Mathematica's equivalent to Maple's collect with distributed option?

Another idea is to use a wrapper around the coefficients, and then expanding: ...
• 131k
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• 145k

### Eliminating one variable from two simple polynomial equations

Since you want an implicit equation in x and u... get rid of the denominators ...
• 12.1k

### How to get the analytical form of a solution to an algebraic equation?

The simplest approach relies on observation that our polynomial $x^5 + 10 x^3 + 20 x -4$ is of the fifth order with integer coefficients divisible by $2$ (beside one with the highest order power). ...
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### How do I extract terms from a complicated polynomial?

Try this: Let us introduce the following function: f[expr_, factor1_, factor2_] := Select[Select[expr, MemberQ[#, factor1] &], MemberQ[#, factor2] &]; ...
• 39.5k
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### Calculating the basis set of quotient spaces

Here is code for producing a monomial basis set for a polynomial algebra with a finite dimensional vector space. It is taken from the resource function CountPolynomialSolutions with very minor ...
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### Calculating the basis set of quotient spaces

I do't think @Domen's answer is quite correct. Take, for example, basisSet[(x + y)^3] (* {1, y, x, x y} *) which I don't think is a correct answer: the ...
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### How to verify a solution of an ordinary differential equation?

You can't plugin in the implicit solution as is, need to first solve for a[u] from it. This gives 3 solutions. Then verify each one, one by one. Maple can verify ...
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### How to convert a polynomial into a list?

A variant of E. Chan-López answer pol = p[1, 2, 5] p[3, 6, 9] p[4, 7, 8] - 3 p[1, 2, 4] p[3, 6, 9] p[5, 7, 8]; ...
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### How to implement the Vieta's formula in Mathematica in the general case?

I wrote a snippet of Mathematica code for demonstration of Vieta's formula. $$\sum_{1 \leq i_1<i_2<\cdots<i_k \leq n}\left(\prod_{j=1}^k r_{i_j}\right)=(-1)^k \frac{a_{n-k}}{a_n}$$ ...
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### Check if polynomial is subtraction free

Perhaps something like: ...
• 396k
Accepted

### Check if polynomial is subtraction free

The expressions: t1 = x1x2 (1 + x1x3 - x2); t2 = -x1 (1 + x2 + x2x3); should be bad/good. For this look at the FullForm of t1/t2: ...
• 52.6k

### Relation between coefficients of polynomial to get real roots

Try: Solve[a*x^3 + b*x^2 - x + 2 == 0 && x >= 0, x, Reals] You should get the roots (3) with the conditional domains for the coefficients. The ...

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### How to rearrange both sides of a polynomial equation?

Since V 12.3 we have SubtractSides and other related functions. f = a x == b y; SubtractSides[f, b y] a x - b y == 0
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### How to extract coefficients of polynomial formatted like this?

Subscript[x, 1, 2] + Subscript[a, 2] Subscript[x, 4, 2] // Apply[List] // # /.a_. * Subscript[x, m_?NumericQ, n_?NumericQ ] :> {{m,n},a} & {{{1, 2}, 1}, {{...
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### How to factorize high-order polynomials that have only complex roots?

As you have the roots, you can get a factorization up to a overall factor of 455 (the coefficient of x^12) by: ...
• 52.6k

### How to convert a polynomial into a list?

pol = p[1, 2, 5] p[3, 6, 9] p[4, 7, 8] - 3 p[1, 2, 4] p[3, 6, 9] p[5, 7, 8]; Using FactorList and the following rules: <...
• 25.2k

### How to get the analytical form of a solution to an algebraic equation?

Here is a way to do the manipulations in Mathematica/Wolfram Language: ...
• 61.6k
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### How to divide a known root out of a polynomial?

PolynomialQuotient is enough. I just used PolynomialQuotientRemainder to see that remainder is indeed ...
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### How to divide a known root out of a polynomial?

FindInstance returns a rule, not a number. Therefore you need: root = x /. FindInstance[pol == 0, x][[1]] 1/2 (-1 - I Sqrt[3]) To divide the polynomial by the ...
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### How to get the multiplicity of a certain root in a system of polynomial equation

I would expect the multiplicity of (0,0) to be 12. sol = SolveValues[{x^3 == 0, y^4 == 0}, {x, y}] Tally[sol] Regarding comment, this is what I get for the new ...
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