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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