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Why is $k[S_{r+1},\ldots,S_n]\to k[X_1,\ldots,X_n]/I$ injective?

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#abstract-algebra #algebraic-geometry #polynomials #commutative-algebra #ring-homomorphism
122
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Factorisation and roots of infinite polynomial

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#polynomials #generating-functions
152
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How can I use software to check the accuracy of my equations and which software?

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#polynomials #math-software
5.8k
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how to memorize the sum and product of roots for an $n^{th}$ degree equation

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#polynomials #quadratics
70
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Express the sum of three roots as combination of quotients

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#algebra-precalculus #polynomials #symmetric-polynomials
39
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How to find the splitting field for $x^3-x^2-x-2$ over $\Bbb Q$?

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#polynomials #field-theory #splitting-field
66
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How to find polynomials satisfying a given ideal of relations

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#polynomials #commutative-algebra #ideals #groebner-basis
354
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Prime ideals in multi-variable polynomial rings over $\mathbb{Z}$

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#abstract-algebra #polynomials #ring-theory #maximal-and-prime-ideals #polynomial-rings
707
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FFT: Multiplying multiple poynomials in O(KSlogS) time

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#polynomials #algorithms #computational-complexity #trees #fast-fourier-transform
22
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Proving an equality on the derivative of given polynomials

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#polynomials #linear-transformations
136
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Solve the equation $\sqrt{x + 2} - \sqrt{3 - x} = x^2 - 6x + 9$.

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#algebra-precalculus #polynomials #roots
224
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How can you determine if a root of a polynomial is a repeated one?

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#polynomials #roots
61
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Find all the monic polynomials P(x) ∈ C [X] satisfying the below condition

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#abstract-algebra #polynomials #roots
70
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Is $a^4 + b^4 + c^4$ a spherical harmonic?

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#multivariable-calculus #polynomials #hilbert-spaces #spherical-harmonics
64
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Polynomial ring over an arbitrary set

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#abstract-algebra #polynomials #field-theory

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