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{{Short description|Solution in radicals of a polynomial equation}} {{DEFAULTSORT:Algebraic Solution}}

...ion|last=Zelikin|first=Mikhail I.|title=Homogeneous Spaces and the Riccati Equation in the Calculus of Variations|year=2000|publisher=Springer-Verlag|location= * {{springer|title=Riccati equation|id=p/r081770}}

{{Short description|Polynomial equation, generally univariate}} * {{springer|title=Algebraic equation|id=p/a011480}}

! [[Implicit equation|निहित समीकरण]] ! [[Parametric equation|पैरामीट्रिक समीकरण]]

That algebraic analysis' requires keen intelligence and sagacity has been observed by him [[File:Algebraic equation notation.svg|alt=Algebraic Equation|thumb|Algebraic Equation]]

| image = [[File:Algebraic equation notation.svg|150px]] We need to form the equation ( ''samī-karaṇa, samī-kāra'' or ''samī-kriyā; from sama, equal and k

.../archive.org/details/academicpressdic00morr|url-access=registration |quote=algebraic expression over a field. }}</ref> इस प्रकार उदाहर [[File:algebraic equation notation.svg|256px]]<br>

...ort description|Algebraic equation on which the solution of a differential equation depends}}

{{short description|Analytic function that does not satisfy a polynomial equation}}

...adius formula]], it implies that the C*-norm is uniquely determined by the algebraic structure: ** [[Fredholm theory]] of [[integral equation]]s

{{Short description|Equation that is satisfied for all values of the variables}} ...612171441/https://encyclopedia-of-equation.webnode.jp/ The Encyclopedia of Equation] Online encyclopedia of mathematical identities(archived)

...ion and ''b'' is said to be integrally dependent on ''A'' (as opposed to [[algebraic dependent]].)</ref> B के तत्वों का समूह जो ...l=https://wstein.org/books/ant/ant.pdf|title=Computational Introduction to Algebraic Number Theory|pages=101}}</ref> अर्थात यदि

...ा उपसमुच्चय है। विशेष रूप से, यह तर्कसंगत 4 गुना है।<ref>Dolgachev (2012), equation (9.57).</ref> ![[Singular point of an algebraic variety|विलक्षणता]]

{{Equation|1=A_0\;\xrightarrow{\ f_1\ }\; A_1 \;\xrightarrow{\ f_2\ }\; A_2 \;\xrighta {{Equation|1=\begin{align}

...from the equation <math>x^2 + y^2 = 1</math> for the [[unit circle]]. This equation can be solved for either the sine or the cosine: ...eedings of the ACM-[[SIGSAM]] 1989 International Symposium on Symbolic and Algebraic Computation |editor-first= G. H. |editor-last=Gonnet |conference=ISSAC '89

| title = Beyond the Quartic Equation | title = Sur la résolution de l'equation du cinquième degré, extrait d'une lettre adressée à M. Hermite

...tatistical mechanics and Riemann surfaces of genus greater than one", in ''Algebraic Analysis'', Vol. 1, M. Kashiwara and T. Kawai, eds., Academic Press, pp. 29 ...name="AP89Tani">Au-Yang H and Perk J H H (1989). "Onsager's star-triangle equation: Master key to integrability", ''Proc. Taniguchi Symposium, Kyoto, October

{{Short description|Polynomial equation of degree two}} {{About|algebraic equations of degree two and their solutions|the formula used to find soluti

...ty (1).) This problem (namely, ax - by = 1) is a special case of Bézout's equation and was used by Bachet to solve the problems appearing on pages 199 ff.</re

{{Short description|Polynomial equation whose integer solutions are sought}} .../20190403144351/https://core.ac.uk/download/pdf/81109310.pdf Arithmetic of Algebraic Curves from Diophantus to Poincaré"] ''Historia Mathematica'' 8(1981), 393

...ynthesis and Dimensional Optimization of Planar Parallel Manipulator Using Algebraic Fitting of a Family of Quadrics], ASME 2013 International Design Engineerin

...घी द्वारा पूर्ण रूप से विकसित किया गया था।<ref name=AQCA>Pablo Arrighi, An algebraic study of unitary one dimensional quantum cellular automata, Proceedings of ...nd W. Taylor, "Quantum lattice-gas model for the many-particle Schrödinger equation in d dimensions", Physical Review E 57, 1998: pp. 54–66.</ref> क्व

|algebraic=<math>\sqrt{5}</math> ...करें<ref name=conrad>{{cite web |last1=Conrad |first1=Keith |title=Pell's Equation II |url=https://kconrad.math.uconn.edu/blurbs/ugradnumthy/pelleqn2.pdf |web

...का समतल [[बीजगणितीय वक्र]] होता है।<ref>For a derivation of the algebraic equation in the case where ''n'' = 2/3, see p. 3 of http://xahlee.info/SpecialPlaneC

...e state vector <math>|\psi(t)\rangle</math> is governed by the Schrödinger equation, where <math>H(t)</math> is the observable associated with the total energy {{Equation box 1

...aption=The [[quadratic formula]], which is the solution to the [[quadratic equation]] <math>ax^2+bx+c=0</math> where <math>a\neq0</math>. Here the symbols {{mv [[File:algebraic equation notation.svg|256px|thumb|center|{{ordered list

{{Short description|Formula that provides the solutions to a quadratic equation}} ...ary School Algebra Teachers' Mathematical Knowledge for Teaching Algebraic Equation Solving'', p. 56 (ProQuest, 2007): "The quadratic formula is the most gener

{{Main|Algebraic equation}} ...मीकरण है<ref>{{Cite book |last=Proskuryakov |first=I.V. |chapter=Algebraic equation |editor=Hazewinkel, Michiel |editor-link=Michiel Hazewinkel |title=Encyclop

...ds and affine algebraic groups are group objects in the category of affine algebraic varieties.</ref> ...ेत्रों को जन्म देती हैं।<ref>Such as [[group cohomology]] or [[Equivariant algebraic K-theory|equivariant K-theory]].</ref> एक ओर, यह समूह G

...of Mechanics|publisher=[[University of Toronto Press]]|pages=304–312}} See equation 94.16, page 305. The following algebra compares to Lanczos, except he uses ...3=Le Bihan|year=2010|arxiv=1001.0240|title=Fundamental representations and algebraic properties of biquaternions or complexified quaternions|journal=[[Advances

[[File:Clay tablet, mathematical, geometric-algebraic, similar to the Pythagorean theorem. From Tell al-Dhabba'i, Iraq. 2003-1595 [[File:Clay tablet, mathematical, geometric-algebraic, similar to the Euclidean geometry. From Tell Harmal, Iraq. 2003-1595 BCE.

...र एक से अधिक अवसरों पर उनके द्वारा विचक्षणता देखी गई है। [[File:Algebraic equation notation.svg|thumb|बीजीय समीकरण]]

{{Short description|Differential equation containing derivatives with respect to only one variable}} ...le = Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations | year = 1998 | publisher = SIAM | isbn = 978-1-61197-139-2}}

...>f:X\to Y</math> है जहाँ फिर क्रमविनिमेय आरेख होता है<ref>{{Cite web|title=algebraic topology - How to understand the Todd class?|url=https://math.stackexchange ...3= Patodi|first3= V. K.|author3-link=Vijay Kumar Patodi|title= On the heat equation and the index theorem|journal= Invent. Math.|volume= 19 |year=1973|pages= 2

...>f</math> है.<ref>{{harvnb|Atkinson|1989|p=346}}; {{harvnb|Lakoba|2012|loc=equation (1.16)}}</ref> ...itle=Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations |publisher=[[Society for Industrial and Applied Mathematics]] |lo

...s?id=ETPYC74OlNMC&pg=PA289|title=Chapter 26, Spear, in: Solving Polynomial Equation Systems II: Macaulay's Paradigm and Gröbner Technology|first=Teo|last=Mora

| image = [[File:Algebraic equation notation.svg|150px]] [[File:Equation illustration colour.svg|thumb|बीजीय व्यंजक और ब

which is the functional equation. which is the functional equation.

...ticle, and see p.160 in {{cite book | last=Holcombe | first=W.M.L. | title=Algebraic automata theory | zbl=0489.68046 | series=Cambridge Studies in Advanced Mat ...+\dotsb+p_k(n)\lambda_k^n</math>.<ref>Flajolet & Sedgweick, section V.3.1, equation (13).</ref><ref>{{cite web|url=https://cs.stackexchange.com/q/1048 |title=N

{{short description|Algebraic expansion of powers of a binomial}} ...को में उपयोगी होता है।<ref>Artin, ''Algebra'', 2nd edition, Pearson, 2018, equation (4.7.11).</ref>

{{Equation box 1 |equation = <math> \widehat{S}(\theta , \hat{\mathbf{a}}) = \exp\left( - \frac{i}{\hb

...menez J.C, Shoji I.,Ozaki T. (1999) "Simulación of stochastic differential equation through the local linearization method. A comparative study". J. Statist. P ...ल योजना प्रस्तुत करता है। <ref name=":23">Jimenez, J. C. (2002). "A simple algebraic expression to evaluate the local linearization schemes for stochastic diffe

...f>{{harvnb|Granville|2008|loc=section 1}}: "The main difference is that in algebraic number theory [...] one typically considers questions with answers that are ...iste Galois]]; in modern language, the main outcome of his work is that an equation ''f''(''x'')&nbsp;=&nbsp;0 can be solved by radicals

...definite integral inputs a function and outputs a number, which gives the algebraic sum of areas between the graph of the input and the [[x-axis]]. The technic ...r [[antiderivative]]s. It is also a prototype solution of a [[differential equation]]. Differential equations relate an unknown function to its derivatives, an

...रम|journal=Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation |year=1997 |pages=197–204 |doi=10.1145/258726.258783| isbn=97 ...ोन्मुख श्रृंखला|journal=SIGSAM (ACM Special Interest Group in Symbolic and Algebraic Manipulation) |volume=47 |issue=185 |pages=75–83|doi=10.1145/2576802.2576

...rezin | first1=F. A. | last2=Shubin | first2=M. A. | title=The Schrödinger Equation | publisher=Kluwer | year=1991 }} ...atical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation | publisher=Springer-Verlag | year=2018 | isbn=978-3-319-70706-

...= David |last1 = Colton |first2 = Rainer |last2 = Kress |title = Integral Equation Methods in Scattering Theory |publisher = Society for Industrial and Appli ...atical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation |edition = 2nd |publisher=Springer |year=2018 |isbn=978-3-319-7

|journal = SIAM Journal on Algebraic and Discrete Methods ...र्ण था)।{{efn|Alternatively <math>\mathbf {y}</math> can be defined by the equation <math>\mathbf{y} := M\mathbf {x}</math>, where multiplication is [[logical

...'Principia Mathematica'' actually used a finite difference version of this equation based upon ''impulse''. See ''[[Newton's laws of motion#Impulse|Impulse]]'' ...f>{{cite book|last=Howland|first=R.A.|title=Intermediate dynamics a linear algebraic approach|date=2006|publisher=Springer|location=New York|isbn=9780387280592|

...imaginary numbers have necessarily to appear in the cubic formula when the equation has three real, different roots by Pierre Laurent Wantzel in 1843, Vincenzo ...us resolvi posse."''] [New proof of the theorem that any rational integral algebraic function of a single variable can be resolved into real factors of the firs

...itle=A particle approximation of the solution of the Kushner–Stratonovitch equation |journal=Probability Theory and Related Fields |date=1999 |volume=115 |issu ...oceeding ISSAC '92 Papers from the International Symposium on Symbolic and Algebraic Computation |pages=123–129 |doi = 10.1145/143242.143290 |isbn = 978-0-897