Integration of Algebraic Functions - Trager - 1984 () Citation Context ...deration, the pioneer work is due to Risch. In [17], Risch gave an algorithm to find the elementary integration of ∫ udx where u is a rational function or a monomial over Q(x). In Trage’s Ph.D thesis =-...
A characterization of functions with vanishing averages over products of disjoin 01:57:28 A Heegaard Floer analog of algebraic torsion - Cagatay Kutluhan 01:04:32 A Mathematical Theory of Solids-from Atomic to Macroscopic Scales - Weinan E 01:12:46 A new potential theory for the Maxwell...
For any algebraic expression containing integral powers of \(x\) along with fractional powers of an expression of the form, \(a + bx\) is immediately reduced to rational functions by the substitution \(a + bx = {t^m}\), where \(m\) is the LCM of the denominators of the several f...
Integrating algebraic functions (only for RootOf notation) > (22) > > (23) > (24) Define a Maple operator using the unapply command. > (25) > (26) Specify the 'AllSolutions' option. > Warning, unable to determine if 0 is between a and 2; try to use assumptions or ...
These methods have applications in the solution of implicit equations and the Taylor Model based integration of Differential Algebraic Equations (DAE) as well as other tasks where obtaining verified high-order models of inverse functions is... MARTIN BERZ,JENS HOEFKENS - 《Reliable Computing》 被引...
Two methods for computing theintegrals of rational functions over are considered. Thefirst is applicable to differentials with rational antiderivatives and uses theinterpretation of as achain of integration in some toric compactification. Thesecond method is based on thetheory of multidimensional residues ...
Here C is the constant of integration. Therefore, the general solution of the integral by applying the constant of integration is ex+x33+Cex+x33+C. Example 2: Find the integration of the algebraic expression x−1x2x−1x2, using the constant of integration. Solution: The given expressio...
Thus, we have TE at the end of our mnemonic. (We could just as easily have used ET at the end, since when these types of functions appear together it usually doesn’t really matter which one is uu and which one is dvdv.) Algebraic functions are generally easy both to integrate and ...
We introduce an algebraic theory of integration on quantum planes and other braided spaces. In the one dimensional case we obtain a novel picture of the Jackson q-integral as indefinite integration on the braided group of functions in on... SM Achim Kempf 被引量: 127发表: 1994年 Integration...
It culminates in a purely algebraic proof, due to M. Rosenlicht [Ros 2 ], of an 1835 theorem of Liouville on the existence of "elementary" integrals of "elementary" functions. The precise meaning of elementary will be specified. As an application of that theorem we prove that the ...