Wikipedia:WikiProject Mathematics/PlanetMath Exchange/12-XX Field theory and polynomials
This page provides a list of all articles available at PlanetMath in the following topic:
- 12-XX Field theory and polynomials.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status | means PM article |
N | not needed |
A | adequately covered |
C | copied |
M | merged |
NC | needs copying |
NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
edit- PM: order and degree of polynomial, id=4289 -- WP guess: order and degree of polynomial -- Status:
- PM: homogeneous polynomial, id=3872 -- WP guess: homogeneous polynomial -- Status:
- PM: weighted homogeneous polynomial, id=7177 -- WP guess: weighted homogeneous polynomial -- Status:
- PM: cardinality of monomials, id=8769new! -- WP guess: cardinality of monomials -- Status:
12D05 Polynomials: factorization
edit- PM: factor theorem, id=1810 -- WP: factor theorem -- Status: NM
- PM: polynomial long division, id=5803 -- WP guess: polynomial long division -- Status:
- PM: proof of factor theorem, id=2937 -- WP: factor theorem -- Status: NM
- PM: proof of rational root theorem, id=3472 -- WP guess: proof of rational root theorem -- Status:
- PM: rational root theorem, id=228 -- WP guess: rational root theorem -- Status:
- PM: sextic equation, id=4682 -- WP guess: sextic equation -- Status: NC
- PM: synthetic division, id=5531 -- WP: synthetic division -- Status: A
- PM: proof of factor theorem due to Fermat, id=7610 -- WP guess: proof of factor theorem due to Fermat -- Status:
- PM: proof of factor theorem using division, id=6896 -- WP guess: proof of factor theorem using division -- Status:
12D10 Polynomials: location of zeros (algebraic theorems)
edit- PM: Cardano's derivation of the cubic formula, id=1408 -- WP: cubic equation -- Status: A
- PM: cubic formula, id=1407 -- WP: cubic equation -- Status: N
- As the talk page suggests that the formula shouldn't be put in the article, I've put in an external link - AdamSmithee 21:58, 29 December 2005 (UTC)
- PM: derivation of quadratic formula, id=700 -- WP: quadratic equation -- Status: A
- PM: Ferrari-Cardano derivation of the quartic formula, id=2883 -- WP: quartic equation -- Status: A
- PM: Galois-theoretic derivation of the cubic formula, id=1438 -- WP: cubic equation -- Status: NM
- PM: Galois-theoretic derivation of the quartic formula, id=2825 -- WP: quartic equation -- Status: A
- PM: irreducible polynomial, id=5907 -- WP: irreducible polynomial -- Status: A
- PM: multiplicity, id=5905 -- WP: multiplicity -- Status: NM
- PM: properties of quadratic equation, id=6115 -- WP: quadratic equation -- Status: NM
- PM: quadratic formula, id=227 -- WP: quadratic equation -- Status: A
- PM: quartic formula, id=1525 -- WP: quartic equation -- Status: N
- There is already an external link - AdamSmithee 21:58, 29 December 2005 (UTC)
- PM: reciprocal polynomial, id=4239 -- WP: reciprocal polynomial -- Status: NM
- PM: root, id=1307 -- WP: root (mathematics) -- Status: NM
- PM: variant of Cardano's derivation, id=4296 -- WP guess: variant of Cardano's derivation -- Status:
- PM: Cardano's formulae, id=7172 -- WP guess: Cardano's formulae -- Status:
- PM: irreducibility of binomials with unity coefficients, id=6982 -- WP guess: irreducibility of binomials with unity coefficients -- Status:
- PM: polynomial equation of odd degree, id=7588 -- WP guess: polynomial equation of odd degree -- Status:
- PM: trigonometric cubic formula, id=6746 -- WP guess: trigonometric cubic formula -- Status:
12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
edit- PM: Euclidean field, id=5869 -- WP guess: Euclidean field -- Status:
- PM: formally real field, id=5863 -- WP guess: formally real field -- Status:
- PM: positive cone, id=6430 -- WP guess: positive cone -- Status:
- PM: Pythagorean field, id=5868 -- WP guess: Pythagorean field -- Status:
- PM: stufe of a field, id=6829 -- WP guess: stufe of a field -- Status:
- PM: theorems on sums of squares, id=6830 -- WP guess: theorems on sums of squares -- Status:
- PM: constructible numbers, id=9583new! -- WP guess: constructible numbers -- Status:
- PM: criterion for constructibility of regular polygon, id=9660new! -- WP guess: criterion for constructibility of regular polygon -- Status:
- PM: motivation of definition of constructible numbers, id=9607new! -- WP guess: motivation of definition of constructible numbers -- Status:
- PM: theorem on constructible angles, id=9605new! -- WP guess: theorem on constructible angles -- Status:
- PM: theorem on constructible numbers, id=9614new! -- WP guess: theorem on constructible numbers -- Status:
12D99 Miscellaneous
edit- PM: Archimedean property, id=3396 -- WP: Archimedean property -- Status: NM
- The WP article is rather advanced. The PM article can be used to improve on WP - AdamSmithee 21:58, 29 December 2005 (UTC)
- PM: calculating the nth roots of a complex number, id=5667 -- WP guess: calculating the nth roots of a complex number -- Status:
- PM: complex, id=720 -- WP: complex number -- Status: A
- PM: complex conjugate, id=1508 -- WP: complex conjugate -- Status: A
- PM: complex number, id=471 -- WP: complex number -- Status: A
- PM: proof that every ordered field with the least upper bound property is isomorphic to \mathbb{R}, id=5607 -- WP guess: proof that every ordered field with the least upper bound property is isomorphic to \mathbbR -- Status:
- PM: every ordered field with the least upper bound property is isomorphic to the real numbers, id=5602 -- WP guess: every ordered field with the least upper bound property is isomorphic to the real numbers -- Status:
- PM: examples of totally real fields, id=4675 -- WP guess: examples of totally real fields -- Status:
- PM: extended real numbers, id=4441 -- WP guess: extended real numbers -- Status:
- PM: fundamental theorem of algebra, id=1927 -- WP: fundamental theorem of algebra -- Status: A
- PM: fundamental theorem of algebra result, id=5851 -- WP: fundamental theorem of algebra -- Status: A
- PM: imaginary unit, id=2018 -- WP: imaginary unit -- Status: A
- PM: indeterminate form, id=2658 -- WP guess: indeterminate form -- Status:
- PM: inequalities for real numbers, id=4742 -- WP guess: inequalities for real numbers -- Status:
- PM: Lindemann-Weierstrass theorem, id=5791 -- WP guess: Lindemann-Weierstrass theorem -- Status:
- PM: modulus of complex number, id=4242 -- WP: complex number -- Status: NM
- Can be used for a better wording of section 1.3 - AdamSmithee 21:58, 29 December 2005 (UTC)
- PM: proof of fundamental theorem of algebra, id=3603 -- WP guess: proof of fundamental theorem of algebra -- Status:
- PM: proof of fundamental theorem of algebra (argument principle), id=6174 -- WP guess: proof of fundamental theorem of algebra (argument principle) -- Status:
- PM: proof of fundamental theorem of algebra (due to D'Alembert), id=6171 -- WP guess: proof of fundamental theorem of algebra (due to D'Alembert) -- Status:
- PM: proof of fundamental theorem of algebra (Rouché's theorem), id=6177 -- WP guess: proof of fundamental theorem of algebra (Rouché's theorem) -- Status:
- PM: proof of the fundamental theorem of algebra (Liouville's theorem), id=1928 -- WP guess: proof of the fundamental theorem of algebra (Liouville's theorem) -- Status:
- PM: proof of the fundamental theorem of algebra (using Brouwer's fixed point theorem), id=6187 -- WP guess: proof of the fundamental theorem of algebra (using Brouwer's fixed point theorem) -- Status:
- PM: proportion equation, id=6585 -- WP guess: proportion equation -- Status:
- PM: real and complex embeddings, id=4666 -- WP guess: real and complex embeddings -- Status:
- PM: real number, id=454 -- WP guess: real number -- Status:
- PM: totally real and imaginary fields, id=4673 -- WP guess: totally real and imaginary fields -- Status:
- PM: 0\ne 1 as real numbers, id=7218 -- WP guess: 0\ne 1 as real numbers -- Status:
- PM: axiomatic definition of the real numbers, id=7591 -- WP guess: axiomatic definition of the real numbers -- Status:
- PM: Hermite polynomials, id=7061 -- WP guess: Hermite polynomials -- Status:
- PM: index of inequalities, id=7629 -- WP guess: index of inequalities -- Status:
- PM: opposite number, id=6775 -- WP guess: opposite number -- Status:
- PM: quadratic inequality, id=7233 -- WP guess: quadratic inequality -- Status:
- PM: taking square root algebraically, id=7175 -- WP guess: taking square root algebraically -- Status:
- PM: topic entry on real numbers, id=7618 -- WP guess: topic entry on real numbers -- Status:
- PM: Archimedean ordered fields are real, id=9819new! -- WP guess: Archimedean ordered fields are real -- Status:
- PM: continuous functions on the extended real numbers, id=9272new! -- WP guess: continuous functions on the extended real numbers -- Status:
- PM: examples of continuous functions on the extended real numbers, id=9273new! -- WP guess: examples of continuous functions on the extended real numbers -- Status:
- PM: existence of nth root, id=7867new! -- WP guess: existence of nth root -- Status:
- PM: existence of nth root, id=8222new! -- WP guess: existence of nth root -- Status:
- PM: infimum and supremum for real numbers, id=7638new! -- WP guess: infimum and supremum for real numbers -- Status:
- PM: rational numbers are real numbers, id=7719new! -- WP guess: rational numbers are real numbers -- Status:
- PM: solving certain polynomial inequalities, id=9226new! -- WP guess: solving certain polynomial inequalities -- Status:
- PM: the groups of real numbers, id=8226new! -- WP guess: the groups of real numbers -- Status:
12Dxx Real and complex fields
edit12E05 Polynomials (irreducibility, etc.)
edit- PM: discriminant, id=2759 -- WP guess: discriminant -- Status:
- PM: Gauss's Lemma I, id=3566 -- WP guess: Gauss's Lemma I -- Status:
- PM: Gauss's Lemma II, id=3567 -- WP guess: Gauss's Lemma II -- Status:
- Planetmath link points on resultant. Wiki link is a disambiguation page.
- Article on resolvent in Galois theory is lacking everywhere.
- Resultant is lacking in this list. D.Lazard (talk) 11:49, 29 October 2011 (UTC)
- PM: Tchirnhaus transformations, id=4572 -- WP guess: Tchirnhaus transformations -- Status:
- PM: calculation of square root of polynomial, id=7430 -- WP guess: calculation of square root of polynomial -- Status:
- PM: partial fractions for polynomials, id=7613 -- WP guess: partial fractions for polynomials -- Status:
- PM: square root of polynomial, id=7428 -- WP guess: square root of polynomial -- Status:
- PM: examples of minimal polynomials, id=9184new! -- WP guess: examples of minimal polynomials -- Status:
12E10 Special polynomials
edit- PM: de Moivre identity, id=1994 -- WP: De Moivre's formula -- Status: A
- PM: proof of de Moivre identity, id=6126 -- WP: De Moivre's formula -- Status:A
- PM: all one polynomial, id=6712 -- WP guess: all one polynomial -- Status:
12E15 Skew fields, division rings
edit- PM: proof of Wedderburn's theorem, id=3627 -- WP: proof of Wedderburn's theorem -- Status: N
- PM: second proof of Wedderburn's theorem, id=4198 -- WP guess: second proof of Wedderburn's theorem -- Status: N
- PM: Wedderburn's Theorem, id=3473 -- WP guess: Division ring -- Status: A
- PM: subfield criterion, id=8598new! -- WP guess: subfield criterion -- Status:
12E20 Finite fields (field-theoretic aspects)
edit- PM: proof that Q is the prime subfield of any field of characteristic 0, id=7600 -- WP guess: proof that Q is the prime subfield of any field of characteristic 0 -- Status:
12E25 Hilbertian fields; Hilbert's irreducibility theorem
edit- PM: Hilbert's irreducibility theorem, id=7010 -- WP guess: Hilbert's irreducibility theorem -- Status:
- PM: thin algebraic set, id=7009 -- WP guess: thin algebraic set -- Status:
12E99 Miscellaneous
edit- PM: characteristic, id=1160 -- WP: characteristic (mathematics) -- Status:
- PM: characterization of field, id=4715 -- WP guess: characterization of field -- Status:
- PM: characterizations of integral, id=6642 -- WP guess: characterizations of integral -- Status:
- PM: example of an infinite field of finite characteristic, id=3635 -- WP guess: example of an infinite field of finite characteristic -- Status:
- PM: examples of fields, id=3162 -- WP: Field (mathematics) -- Status: A
- PM: field, id=355 -- WP: Field (mathematics) -- Status: A
- PM: field homomorphism, id=4670 -- WP: Ring homomorphism -- Status: NM
- The WP article may use a separate section on fields; also, a redirect AdamSmithee 14:08, 30 December 2005 (UTC)
- PM: Frobenius homomorphism, id=2157 -- WP guess: Frobenius homomorphism -- Status:
- PM: groups in field, id=6311 -- WP guess: groups in field -- Status:
- PM: homomorphisms from fields are either injective or trivial, id=6243 -- WP: Ring homomorphism -- Status: NM
- PM: integral element, id=5715 -- WP guess: integral element -- Status:
- PM: integrity characterized by places, id=6643 -- WP guess: integrity characterized by places -- Status:
- PM: place as extension of homomorphism, id=6651 -- WP guess: place as extension of homomorphism -- Status:
- PM: place of field, id=6640 -- WP guess: place of field -- Status:
- PM: prime subfield, id=2892 -- WP: prime subfield -- Status: NM
- PM: field homomorphisms fix prime subfields, id=8461new! -- WP guess: field homomorphisms fix prime subfields -- Status:
12Exx General field theory
edit12F05 Algebraic extensions
edit- PM: a finite extension of fields is an algebraic extension, id=4725 -- WP guess: a finite extension of fields is an algebraic extension -- Status:
- PM: algebraic closure, id=1510 -- WP guess: algebraic closure -- Status:
- PM: algebraic extension, id=4724 -- WP guess: algebraic extension -- Status:
- PM: algebraically closed, id=1509 -- WP guess: algebraically closed -- Status:
- PM: algebraically dependent, id=4741 -- WP guess: algebraically dependent -- Status:
- PM: existence of the minimal polynomial, id=4723 -- WP guess: existence of the minimal polynomial -- Status:
- PM: finite extension, id=708 -- WP guess: finite extension -- Status:
- PM: minimal polynomial, id=3850 -- WP guess: minimal polynomial -- Status:
- PM: primitive element theorem, id=214 -- WP guess: primitive element theorem -- Status:
- PM: proof of primitive element theorem, id=3912 -- WP guess: proof of primitive element theorem -- Status:
- PM: proof of primitive element theorem, id=5725 -- WP guess: proof of primitive element theorem -- Status:
- PM: splitting field, id=1303 -- WP guess: splitting field -- Status:
- PM: Steinitz theorem, id=5985 -- WP guess: Steinitz theorem -- Status:
- PM: the field extension \mathbb{R}/\mathbb{Q} is not finite, id=4726 -- WP guess: the field extension \mathbbR/\mathbbQ is not finite -- Status:
- PM: p-extension, id=6764 -- WP guess: p-extension -- Status:
- PM: Kummer theory, id=6793 -- WP guess: Kummer theory -- Status:
- PM: algebraic closure of a finite field, id=8889new! -- WP guess: algebraic closure of a finite field -- Status:
- PM: alternative definition of algebraically closed, id=9145new! -- WP guess: alternative definition of algebraically closed -- Status:
- PM: cardinality of algebraic closure, id=8649new! -- WP guess: cardinality of algebraic closure -- Status:
- PM: every algebraically closed field is perfect, id=9139new! -- WP guess: every algebraically closed field is perfect -- Status:
- PM: examples of trace and norm, id=7937new! -- WP guess: examples of trace and norm -- Status:
- PM: expressible, id=9192new! -- WP guess: expressible -- Status:
- PM: finite field cannot be algebraically closed, id=8654new! -- WP guess: finite field cannot be algebraically closed -- Status:
- PM: integral closures in separable extensions are finitely generated, id=9323new! -- WP guess: integral closures in separable extensions are finitely generated -- Status:
- PM: quadratic closure, id=7659new! -- WP guess: quadratic closure -- Status:
- PM: quadratic extension, id=7656new! -- WP guess: quadratic extension -- Status:
- PM: relative algebraic closure, id=7939new! -- WP guess: relative algebraic closure -- Status:
- PM: separability is required for integral closures to be finitely generated, id=9324new! -- WP guess: separability is required for integral closures to be finitely generated -- Status:
- PM: separably algebraically closed field, id=7991new! -- WP guess: separably algebraically closed field -- Status:
- PM: splitting field of a finite set of polynomials, id=9140new! -- WP guess: splitting field of a finite set of polynomials -- Status:
12F10 Separable extensions, Galois theory
edit- PM: Abelian extension, id=3599 -- WP guess: Abelian extension -- Status:
- PM: absolute Galois group, id=1515 -- WP guess: absolute Galois group -- Status:
- PM: cyclic extension, id=3600 -- WP guess: cyclic extension -- Status:
- PM: example of nonperfect field, id=3580 -- WP guess: example of nonperfect field -- Status:
- PM: example of normal extension, id=6051 -- WP guess: example of normal extension -- Status:
- PM: fixed field, id=1325 -- WP guess: fixed field -- Status:
- PM: Galois closure, id=3601 -- WP guess: Galois closure -- Status:
- PM: Galois conjugate, id=1519 -- WP guess: Galois conjugate -- Status:
- PM: Galois extension, id=1326 -- WP guess: Galois extension -- Status:
- PM: Galois group, id=1317 -- WP guess: Galois group -- Status:
- PM: infinite Galois theory, id=2918 -- WP guess: infinite Galois theory -- Status:
- PM: normal closure, id=3602 -- WP guess: normal closure -- Status:
- PM: normal extension, id=1310 -- WP guess: normal extension -- Status:
- PM: perfect field, id=3577 -- WP guess: perfect field -- Status:
- PM: proof of characterization of perfect fields, id=6448 -- WP guess: proof of characterization of perfect fields -- Status:
- PM: radical extension, id=1329 -- WP guess: radical extension -- Status:
- PM: separable closure, id=1514 -- WP guess: separable closure -- Status:
- PM: symmetric polynomial, id=1337 -- WP guess: symmetric polynomial -- Status:
- PM: casus irreducibilis, id=7171 -- WP guess: casus irreducibilis -- Status:
- PM: example of an extension that is not normal, id=8038new! -- WP guess: example of an extension that is not normal -- Status:
- PM: Galois is not transitive, id=8041new! -- WP guess: Galois is not transitive -- Status:
- PM: normal is not transitive, id=8043new! -- WP guess: normal is not transitive -- Status:
- PM: solvable by radicals, id=9191new! -- WP guess: solvable by radicals -- Status:
12F15 Inseparable extensions
edit- PM: purely inseparable, id=6480 -- WP guess: purely inseparable -- Status:
12F20 Transcendental extensions
edit- PM: linearly disjoint, id=5793 -- WP guess: linearly disjoint -- Status:
- PM: transcendence degree, id=4740 -- WP guess: transcendence degree -- Status:
12F99 Miscellaneous
edit- PM: composite field, id=1511 -- WP guess: composite field -- Status:
- PM: extension field, id=703 -- WP guess: extension field -- Status:
- PM: field adjunction, id=5875 -- WP guess: field adjunction -- Status:
- PM: p-adic canonical form, id=5665 -- WP guess: p-adic canonical form -- Status:
- PM: simple field extension, id=5878 -- WP guess: simple field extension -- Status:
- PM: non-constant element of rational function field, id=6762 -- WP guess: non-constant element of rational function field -- Status:
- PM: simple transcendental field extension, id=6751 -- WP guess: simple transcendental field extension -- Status:
- PM: lattice of fields, id=9550new! -- WP guess: lattice of fields -- Status:
12Fxx Field extensions
edit12H05 Differential algebra
edit- PM: differential field, id=5778 -- WP guess: differential field -- Status:
12Hxx Differential and difference algebra
edit12J05 Normed fields
edit- PM: Gelfand-Tornheim theorem, id=5628 -- WP guess: Gelfand-Tornheim theorem -- Status:
12J10 Valued fields
edit- PM: complete ultrametric field, id=6615 -- WP guess: complete ultrametric field -- Status:
12J12 Formally $p$-adic fields
edit12J15 Ordered fields
edit- PM: some properties of uncountable subsets of the real numbers, id=8886new! -- WP guess: some properties of uncountable subsets of the real numbers -- Status:
12J20 General valuation theory
edit- PM: discrete valuation, id=4761 -- WP guess: discrete valuation -- Status:
- PM: non-isomorphic completions of \mathbb{Q}, id=6671 -- WP guess: non-isomorphic completions of \mathbbQ -- Status:
- PM: value group of completion, id=6670 -- WP guess: value group of completion -- Status:
12J99 Miscellaneous
edit- PM: topological ring, id=3076 -- WP guess: topological ring -- Status:
12Jxx Topological fields
edit12K10 Semifields
edit12Kxx Generalizations of fields
edit12Y05 Computational aspects of field theory and polynomials
edit- PM: proof of Vieta's formula, id=7297 -- WP guess: proof of Vieta's formula -- Status:
- PM: Vieta's formula, id=7190 -- WP guess: Vieta's formula -- Status: